LONG THROATED FLUMES AND BROAD CRESTED WEIRS. (debiet meetgoten met lange keel en lange overlaten) Cover photo: Portable RBC flume in a natural stream

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2 LONG THROATED FLUMES AND BROAD CRESTED WERS (debiet meetgoten met lange keel en lange overlaten) Cover photo: Portable RBC flume in a natural stream

3 M.G. Bos LONG - THROATED FLUMES AND BROAD - CRESTED WERS Proefshrift ter verkrijging van de graad van dotor in de landbouwwetenshappen, op gezag van de retor magnifius, dr. C.C. Oosterlee, in het openbaar te verdedigen op woensdag 19 deember 1984 des namiddags te vier uur in de aula van de Landbouwhogeshool te Wageningen

4 Keywords hannels; ~~~is~_~~!~e~; fluid flow;!l~~~; history; E~~!~~~~~; researh; sediments; ~~ie~ Abstrat Vital for water management are strutures that an measure the flow in a wide variety of hannels. Chapter 1 introdues the longthroated flume and the broad-rested weir; it explains why this family of strutures an meet the boundary onditions and hydrauli demands of most measuring sites. Chapter 2 reords the history of these strutures. t desribes how the hydrauli theory of flumes and weirs, and their design, developed separately. The hapter onludes by reporting reent attempts to develop a generally valid theory for any long-throated flume or broad-rested weir in any hannel. The remainder of the thesis explains the steps haken to develop a proedure that yields the hydrauli dimensions and rating table of the appropriate weir or flume. The major steps over the hydrauli theory of flow through ontrol setions of different shapes and dimensions, the theory and proedure of estimating the head loss required for modular flow, the boundary onditions of the hannel, and the demands plaed on the struture regarding the range and auray of its flow measurements. REFERENCE: BOS, M.G., Long-throated flumes and broad-rested weirs, Martinus Nijhoff/Dr W. Junk Publishers, Dordreht, The Netherlands, 1985 Promotor: ir. D.A. Kraijenhoff van de Leur, hoogleraar in de hydraulia, afvoerhydrologie en de grondmehania

5 Prefae n the ontext of water management, strutures that measure the flow rate in open hannels are used for a variety of purposes: (i) n hydrology, they measure the disharge from athments; (ii) n irrigation, they measure and ontrol the distribution of water at anal bifurations and at off-take strutures; (iii) n sanitary engineering, they measure the flow from urban areas and industries into the drainage system; (iv) n both irrigation and drainage, they an ontrol the upstream water at a desired level. This thesis represents an attempt to plae suh flow measurements on a solid foundation by explaining the theory of water flow through 'long-throated flumes' and their hydraulially related 'broad-rested weirs'. On the basis of this theory, and on pratial experiene, these strutures are reommended for use whenever the water surfae in the hannel at the measuring site an remain free. The thesis onludes with a design proedure that will failitate the appliation of these strutures. The idea to undertake researh on disharge measurement strutures was born upon my appointment as the first ivil engineer with the nternational nstitute for Land Relamation and mprovement (LR). Beause my reruiter, r. J.M. van Staveren, then Diretor of LR, had left the nstitute before my arrival, and beause was the 'first of Y kind' in an agriultural environment, looked for ontat and found

6 - viii - - ix - support from: the late Prof. r. J. Nugteren, Prof. r. D.A. Kraijenhoff van de Leur, and r. R.H. Pitlo of the University of Agriulture and from r. J. Wijdieks, r. A.H. de Vries, and ng. W. Boiten of the Delft Hydrauli Laboratory. We pooled our efforts on disharge measurement strutures in the informal 'Working Group on Small Hydrauli Strutures'. This thesis is founded on the pleasant and fruitful ooperation within that Working Group. The opportunity was given to ooperate with Dr. J.A. Replogle and A.J. Clemmens, M.S., of the U.S. Water Conservation Laboratory, Phoenix, on a book on long-throated flumes in open hannel systems greatly expanded my knowledge of this subjet. am indebted to Dr. r. H. Brouwer, Diretor of the U.S. Water Conservation Laboratory, and to r. F.E. Shulze and Dr. r. J.A.H. Hendriks, former and present Diretor of LR, for their interest in that researh program and for their efforts to ensure the required funding. express my gratitude first and foremost, to my promotor Prof. lr. D.A. Kraijenhoff van de Leur, for his gift of ompelling me to disuss with him every onept and detail of this thesis. f the thesis is without errors, it is beause of his influene on my writing. am grateful to LR for providing me with the opportunity to write the thesis. thank Prof.Dr. N.A. de Ridder for enouraging me to do so and for his positive omments when needed them. thank Mrs. M.F.L. Wiersma-Rohe for editing the manusript, Mr. J. van Dijk, who designed the over and drew the figures, Mrs. G.W.C. Pleijsant-Paes and Mrs. J.B.H. van Dillen, who typed all the drafts and arranged the lay-out, to Mr. J. Ariese and rr. M.C. van Son rcw) who reprodued all figures photographially, and to Mr. J. van Manen and Miss E.A. Rijksen for the final prodution of the book. am indebted to their great ollaboration in meeting the neessary time shedule. There are more debts to be paid. thank my mother and late father for sending me to 'study something to do with water' at Delft after r had deided not to join the merhant marine. Of ourse, am most grateful to my wife, Joke, for her resourefulness and independene in managing our household while was abroad. hope that our sons Steven, Mihiel, and Gijs will understand why their father was not around when he was playing with water. The thesis required the outside support and skills of various people. am very grateful to Prof. Dr. lng. G. Garbreht of the Leihtweiss nstitute for Water Researh, Braunshweig, for reading through Chapter 2, to Dr. Ph. Tb. Stol of the nstitute for Land and Water Management Researh CleW) for reading and disussing Setion 3.5.2, and to Dr. J.A. Replogle of the U.S. Water Conservation Laboratory for reading and disussing the entire thesis. Speial thanks are due to r. J.H.A. Wijbenga and ng. J. Driegen of the Delft Hydraulis Laboratory for performing the laboratory test on the passage of sediments through weirs and flumes, and for their throughgoing disussions of this subjet.

7 Table of ontents KEYWORDS, ABSTRACT v PREFACE vii THE ADVANTAGES OF USNG BROAD-CRESTED WERS AND LONG-THROATED FLUMES ntrodution Advantages HSTORY OF FLUMES ntrodution Flumes with piezometer tap in the onverging transition Strutures with head measurement upstream of the onverging transition Evolution of the struture until about 1940 Disharge rating based on boundary layer development Disharge rating based on HlL ratio Estimate of the modular limit THE HEAD-DSCHARGE RELATONSHP Basi equations Speifi energy Head-disharge equations General equation for ideal flow Retangular ontrol setion Triangular ontrol setion

8 - xii - - xiii - page Trunated triangular ontrol setion 25 Energy losses downstream of the ontrol Trapezoida1 ontrol setion Paraboli ontrol setion setion Experimental verifiation of modular limit Cirular ontrol setion 30 estimate with reent tests U-shaped ontrol setion Visual detetion of modular limit Trunated irular ontrol setion Summary of equations 38 5 DEMANDS PLACED ON A STRUCTURE N AN RRGATON Equivalent shapes of ontrol setions Disharge oeffiient, Cd AND DRANAGE SYSTEM ntrodution Physial meaning Cd values nfluene of transition shapes on Cd Approah veloity oeffiient, C v Physial meaning Cv values for various ontrol shapes Funtion of the struture Measurement of flow rate Controlled regulation of flow rate Upstream water level ontrol Head loss for modular flow Range of disharges to be measured Summary of Cv values Alternative rating by iteration Equations for ideal flow The rating proedure REQURED HEAD LOSS OVER THE STRUCTURE Error in the measurement of flow Restrition of bakwater effet Sediment transport apaity Design rule Laboratory experiments Design proedure for a struture ntrodution Theory 67 SUMMARY Energy losses upstream of the ontrol setion 68 SAMENVATTNG Frition losses downstream of the ontrol setion Losses due to turbulene in the zone of 70 BBLOGRAPHY deeleration Total energy loss requirement LST OF SYMBOLS Proedure to estimate the modular limit Hydrauli laboratory tests Desription of model tests Measuring the modular limit Head loss H 1 - H SUBJECT NDEX 138 CURRCULUM VTAE 142

9 1 The advantages of using broad -rested weirs and long-throated flumes 1.1 NTRODUCTON Strutures built for the purpose of measuring or regulating the rate of flow in open hannels usually onsist of a onverging transition where subritially flowing water is aelerating, a throat where it aelerates to super-ritial flow, and a downstream transition where the flow veloity is redued to an aeptable sub-ritial veloity. Figure 1.1. General layout of a long-throated flume Replogle, and Clemmens 19R4) (from Bos,

10 Upstream of the struture is an approah hannel, whih influenes the veloity distribution of the flow approahing the struture. Downstream of the struture is a tailwater hannel, whih is fundamentally important to the design of the struture beause the range of tailwater levels that will result from varying flow rates determines the elevation of the rest of the throat above the tailwater hannel WER bottom. f this tailwater is suffiiently low (Chapter 4), a diverging transition is not needed so that the struture may be trunated at the downstream end of the throat. The measuring or regulating struture an also be ombined with a drop struture. f so, an energy dissipator should be added between the throat and the tailwater hannel. The differene in elevation between the water level in the approah hannel, some distane upstream of the struture and the rest or invert of the horizontal throat, is known as the 'upstream sill-referened head'. That setion of the approah hannel where this water surfae elevation is measured is known as the 'head measurement setion' or 'gauging station'. ross setions are through ontrol at weir rest or flume throat Figure 1.2. Distintion between a weir and and Clemmens 1984). a flume (from Bos, Replogle The terms 'broad-rested weir' and 'long-throated flume' are used for two branhes of the same hydrauli family of strutures. Both are haraterized by a throat or rest that is horizontal in the diretion of flow. The differene between them is that a weir has a throat bottom whih is higher than the bottom of the approah hannel, whereas a flume is formed by a narrowing of the hannel only. f flow is ontrolled by a throat that both raises the hannel bottom and narrows the hannel, the struture is usually alled a flume (see Figure 1.2). There are, however, several strutures that may be named either weir or flume. Above the throat, the deviation from a hydrostati pressure distribution beause of entripetal aeleration may be negleted beause the streamlines are pratially straight and parallel. To obtain this situation, the length of the throat in the diretion of flow (L) should be related to the sill-referened energy head (H) as 0.10 < HlL < 0.50 (Chapter 3). 1.2 ADVANTAGES The use of broad-rested weirs or long-throated flumes is reommended for measuring flow in open hannels whenever the water surfae an remain free. This reommendation is made beause this family of strutures has the following major advantages over any other known weir or flume (Cone 1917; nglis 1928; Jameson 1930; Bos, Replogle and Clemmens 1984): a) Provided that ritial flow ours in the throat, a rating table an be alulated with an error of less than 5% in the listed disharge. This an be done for any ombination of a prismati throat and an arbitrarily-shaped approah hannel (Chapter 3); b) The throat, perpendiular to the diretion of flow, an be shaped in suh a way that the omplete range of disharges an be measured aurately, and without reating an exessive bakwater effet; ) The headloss over the weir or flume required to obtain modularity i.e. a unique relationship between the upstream sill-referened

11 - 4 - d) This head-loss requirement an be estimated with suffiient auray for any of these strutures plaed in any arbitrary hannel (Chapter 4); e) Beause of their gradually onverging transitions, these strutures have few problems with floating debris; f) Field and laboratory observations have shown that the strutures an be designed to pass sediment transported by hannels with 2 History of flumes subritial flow; g) Provided that their throat is horizontal in the diretion of flow, a rating table based upon post-onstrution dimensions an be produed, even if errors were made in onstruting to the designed dimensions. Suh post-onstrution rating also allows the throat to be reshaped, if required; h) Under similar hydrauli and other boundary onditions, these weirs/ flumes are usually the most eonomial of all strutures for the aurate measurement of flow. As these advantages are being inreasingly reognized, the use of long-throated flumes and broad-rested weirs is propagating. n the ontext of water management, they are serving a variety of purposes; (i) n hydrology, they measure the disharge from athments; (ii) n irrigation, they measure and ontrol the distribution of water at anal bifurations and at off-take strutures; (iii) n sanitary engineering, they measure the flow from urban areas and industries into the drainage system; (iv) n both irrigation and drainage, they an ontrol the upstream water at a desired level. 2.1 NTRODUCTON The world's irrigated area has inreased with its population. Around 1800, only some 10 million ha were irrigated, and some 16 million ha in 1900 (James, Hanks, and Jurinak 1982). The irrigated area inreased rapidly during the period , and remained about onstant during World War 11 and the subsequent period of deolonization. By 1955, the irrigated area was about 120 million ha (Gulhati 1955), and has now inreased to about 200 million ha (FAO 1979). Before 1900, a ommon method of drawing water from the onveyane system was to make an open ut in the banks of the irrigation anals. Gradually, these uts were replaed by some form of pipe or barrel outlet. Mahbub and Gulhati (1951) give a good summary of a survey made in 1893 by the Chief Engineer of rrigation in the Punjab. With the inrease of the irrigated area, numerous attempts were made to develop an outlet struture that provided a unique relationship between the upstream head and the disharge through the outlet. Sine about 1920, the various irrigated regions have yielded various strutures, amongst whih were several shapes of long-throated flumes and broad-rested weirs. Many of these strutures are still in use today. With the rapid inrease of the irrigated area sine 1960, the need to use irrigation water more effiiently beame apparent, giving new impulses to the hydrauli researh on disharge measuring and regulating strutures.

12 FLUMES WTH PEZOMETER TAP N THE CONVERGNG TRANSTON n the searh for an 'ideal' measuring devie, experiments made in 1915 in the hydrauli laboratory at Fort Collins, Colorado, led to the development of the 'Venturi flume' of Figure 2.1. Cone (1917) seleted this form and shape of devie beause it was 'most nearly ideal'. n his words: 'This devie was aurate in its PLAN ~B measurements, was free from sand, silt, or floating trash troubles, and required but little loss of head in the dith'. During the experiments at Fort Collins, the foundation was laid for what were to beome the two typial Amerian harateristis of a disharge measuring flume: (i) All flumes are alibrated against a piezometri head at a presribed loation within the onverging transition, the pressure tap being loated at a distane of two-thirds of the transition length upstream of the leading edge of the throat; (ii) Flumes of different apaity are obtained by hanging the throat width, its length remaining onstant; L = m (1 ft) in Figure 2.1. be ko b----~h-o.3o 7f' b----'-----~~ diretion of flow ~ ~A n his papers, Cone (1916, 1917) used the following empirial equation for modular flow through a retangular throated flume: (2.1) note: length of throat, one foot for all sizesof flumes ~B SECTON C-C i : : : : grade e grad of dith o 0 floor level throughout of dith g ' ~ J SECTON A-A ~~H ~~ ~~~<zz~ Q);: 0> 0 1;dl 0>.0 Figure 2.1. Plans for the setion (Cone 1917). SECTON B-B 1:'t<':-----3b ~ 'Venturi flume' with retangular ontrol where: = an empirial disharge oeffiient (dimensional); b = bottom width of the ontrol setion; ha = sill-referened head as measured in the upstream gauge well; u = empirial power (~ 1.6). f the head loss over the flume is limited to suh an extent that the water level in the tailwater hannel starts to influene the upstream head, flow is non-modular (Setion 4.1). For these non-modular flows, Cone measured heads in the two gauge wells shown in Figure 2.1 and presented graphs to find the flow rate for throat widths of b = 0.305, 0.457, and m. Although Cone reported that the flume had an ideal devie, he also stated: all the qualities to beome 't is not probable that the last word has been said on the design of the Venturi (long-throated) flume, although it has onsiderable promise, hanges in details may prove to be neessary'. for,

13 nstead of pursuing these hanges in details, Parshall (1926) further elaborated a design that had been tested and disarded by Cone (1915/16) in favour of the flume of Figure 2.1. Parshall's design had a downward hute in the throat and an upward sloping diverging transition. n 1931, this 'improved Venturi flume' was approved by the Committee on rrigation Hydraulis of the Amerian Soiety of Civil Engineers, and was named the 'Parshall measuring flume'. A omprehensive desription of this flume, with dimensions and rating tables in metri units, an be found in Bos (1976). The major disadvantages of the Parsha11 flume as ompared with Cone's design of 1917 are; (i) The number of plane surfaes to be onstruted aurately is greater, making the flume ostly to build; (ii) n the long-throated flume, the ontrol setion is in the throat at a (variable) distane of about L/3 from the end of the throat, whereas in the Parsha11 flume it is at the sharp leading edge of the throat. Although a sharp edge makes a good ontrol setion, any rounding of, or damage to this sharp edge results in a systemati error in the measured disharge; (iii) Water leaving the throat is guided towards the floor of the diverging transition, resulting in a 3 to 4 times higher head loss requirement for modular flow; (iv) Flow at the ontrol setion is three-dimensional, for whih no theoretial basis for a head-disharge equation is available. To save on the onstrution ost of measuring flumes, Skogerboe et al. (1967) proposed a different modifiation to Cone's original design. The throat of the flume, in whih the head-disharge relationship is based upon near two-dimensional flow (Chapter 3), was eliminated. The result was a flat bottomed 'Cut-throat Flume' having a onverging and diverging transition only, the side walls of whih interset at a truly sharp edge. Flumes with a similar geometry were tested by Harvey (1912) in the Punjab, and later by Blau (1960) in the Demorati Republi of Germany. Both soures, however, related the flow rate to a sill-referened head measured in the approah hannel. But, any rounding of, or damage to the sharp edges of the ontrol, any deviation in onstrution from the planned flume dimensions, and any hanges in the flow pattern in either the approah or tailwater hannel, influene the three-dimensional flow pattern in the flume. Beause of the unknown sensitivity of this struture to suh inidental influenes, the flow pattern in the struture must be heked regularly. f neessary, the flume must be alibrated in the field or in a laboratory sale model. This alibration more onstrution ost. 2.3 STRUCTURES WTH HEAD MEASUREMENT UPSTREAM OF THE Evolution of the struture until about 1940 The broad-rested weir, with the longitudinal setion of Figure 2.2, was tested by Bazin (1888). Experimental data for weirs with rest lengths between L = 0.20 and transition ranging from g m CONVERGNG TRANSTON Q where: ~ (2g)0.50 h 1.50 m 3 be 1 Q = rate of flow, m 3/s; = aeleration due to gravity, 9.81 m/s 2; = bottom width of ontrol setion, m; b h = upstream sill-referened head, m; :J;..o_m disharge oeffiient, dimensionless. L=0.20 to 0.40 m H 4 5 Figure 2.2. Longitudinal setion over weir tested by Bazin, 1888 (2.2) 6 ~,--.-:~_.:;;;;.._...:.::; :..;;;o.._;;,.;;;;;.-:--- flow than offsets the above-mentioned saving in the 0.40 m, and with slopes of the diverging l-to-l through 6-to-1, were published. Test results were ompared on the basis of the equation of Poleni (1717), whih is valid for a struture with retangular ontrol setion: k ~ > 2 >1 3 >1 6

14 Equation 2.2 was derived for a sharp-rested weir under the non-realisti assumption that suh a weir behaves like an orifie with a free water surfae at the entre line (Rouse and ne 1957; Bos 1976). For long-throated flumes and broad-rested weirs, this formula nowadays has been abandoned in favour of Eq. 2.3, whih is based on the sounder assumption of ritial flow in open hannels. between the upstream sill-referened head and the 'modular' rate of flow was established. A downstream 'standing wave' guaranteed the presene of ritial flow in the throat. nglis (1928) reported on Crump's experiments on these 'standing wave flumes'. The head-disharge equation of the long-throated (standing wave) flume, derived by B~langer (1848) and onfirmed by Crump, reads: The experiments of Bazin were widely disussed in German, English, and Amerian literature (Gravelius 1900; Rafter 1900; Horton 1907) and an be regarded as an important ontribution to the searh for the 'ideal' irrigation water measuring weir. = C ~ (~ )0.50 b h 1.50 Q 3 3 g 1 This equation is almost idential to Eq. aepted. (2.3) 3.18, whih today is generally Although B~langer (1849) and Bazin (1888) were fully aware of the existene of a unique relationship between the upstream sill-referened head and the disharge over a weir with ritial flow at the ontrol setion, their hydrauli theory was not used by irrigation engineers in their searh for a disharge measuring flume. A possible explanation for this is that hydrauli engineers regarded weirs and flumes as strutures with different hydrauli behaviour. n Colorado, Cone (1917) laid the foundation for the U.S. pratie of designing a style of flumes with a piezometer tap (Setion 2.2). The hydrauli theory of long-throated flumes and broad-rested weirs was further advaned by Jameson (1925, 1930), who derived the general equations for ideal flow (Eqs. 3.8 and 3.12). Parallel to this hydrauli development, field experiene (Lindley 1925) and laboratory experiments (Fane 1927) led to the lassi flume as desribed by nglis (1928). This long-throated flume, illustrated in Figure 2.3, beame very popular for irrigation water measurement. Mahbub and Gu1hati (1951) report that, in 1944, about 12,500 of these open flumes were being used in anals in the Punjab alone. A seond style of 'Venturi flume' was originated by the irrigation engineers, Harvey and Stoddard, both of the Punjab rrigation Department (1912). Lindley (1931) desribed their flume as follows: 'By introduing a smooth hump on the bed, or smooth ontrations of the sides of a regular hannel, a dip in the water surfae is produed equivalent to the head onverted into inreased veloity. Knowing the areas of the upstream and throat setions, and the amount of this dip, the disharge an be alulated' (Setion 3.1). The Venturi flume requires that both the upstream sill-referened head and the lowest head in the throat be measured. Beause the horizontal loation where the lowest head (water surfae dip) ours in the throat is variable with head and flow rate, a long-throated flume was developed in whih ritial flow ourred. Thus a unique relationship The first systemati researh on the minimum head loss required for ritial flow in 10ng-throated flumes with retangular ontrol setion and with diverging transitions of different flare angles and lengths was reported by Fane (1927). This minimum required head loss for flow to remain 'modular' was expressed in the maximum allowable submergene ratio H (Setion 4.1). Based on Fane's tests, and earlier 2/H1 experiments by Crump, nglis (1928) published the data of Table 2.1. Fane (1927) stated that, to obtain these modular limits, the energy loss due to turbulene in the zone of deeleration and to frition should be minimized. He noted that very gradual, but long, diverging transitions effetively suppress turbulene but have relatively high energy losses due to frition and thus may have a lower modular limit

15 than those listed in Table 2.1 (see also Bos and Reinink 1981 and This radius equals about 0.15 h (H denotes the maximum lmax lmax Chapter 4). To redue the onstrution ost of the upstream onverging antiipated value of the upstream sill-referened energy head.) transition, Fane (1927) gave the following design rules: 't is better to have the throat as long as possible (L = 2H ), onsidering l max Table 2.1. Modular limits for a long-throated expense, and to have short upstream wing walls, say 0.10 m radius.' flume (nglis 1928) PLAN r l,, t L Bottom slope of Modular limit diverging transition (per ent) 5 to to to to 1 94 To measure and regulate irrigation water on Java, Romijn (1932) tested a broad-rested weir with the longitudinal profile shown in Figure 2.4. f-l.2 Hl max+l.2 Hl max---1j top of bank LONGTUDNAL SECTON CROSS SECTON ELEVATON ON A-A LOOKNG DOWNSTREAM top of wall opin~-= " CROSSSECTON B - B top of wall Figure 2.3. Type design for long-throated flume (after nglis, 1928) \ 3.2 Hjrnax \ \ \ \ \ \ \~ horizontal Figure 2.4. Longitudinal profile over a Romijn weir (1932) Although Romijn designed a ompat weir profile, the above reommendations of Fane yield a shorter struture. Romijn's weir rest was mounted on top of a vertially movable gate so that the rest elevation ould be hanged with respet to the upstream water level. The resulting struture was an exellent disharge measuring and

16 regulating devie whih is still widely used today. Later, in 1936, Palmer and Bowlus developed some trapezoidal flumes for sewer flow measurement. These flumes, whih still bear their name, were further refined by Arredi (1936) and by Wells and Gotaas (1958). Although earlier researhers have used urved onverging transitions, Palmer and Bowlus used plane transitions, whih have the merit of simple onstrution. Wells and Gotaas showed that the differene in performane between strutures having either a urved or an 1-to-3 plane onverging transition is negligible. n 1981, Bos and Reinink showed that a l-to-2 transition is suffiient to avoid flow separation at the leading edge of the throat. This, in fat, is the sole funtion of this transition (Setion 3.5.3). t is interesting to note that the latter development yielded a longitudinal setion over the struture similar to that of Bazin (Figures 2.2 and 2.5). ~horizontal----;1...=...:=-_...l ;;;. 0.2 Hl max,---r _-'A<; C alternative -, design.~ :g ;;; E~ ~~t~ designs ;;;. Hjrnax ~2t03Hlmax--71kiE;:--~--~ Disharge rating based on boundary layer development _ ' ~;;. Hl max *-2 to 3Pl *-' to 2 Hqmax -;*r ld = 6P :,! Figure 2.5. Longitudinal profile of a broad-rested weir or a long-throated flume (Bos, Replogle, and Clemmens 1984) n evidene of the growing importane being attahed to water ontrol in newly designed irrigation projets, further systemati experimental work on broad-rested weirs and long-throated flumes was onduted again after about 1955 (Wells and Gotaas 1956; Robinson and Chamberlain 1960; Hall 1962, 1967). Akers and Harrison (1963) applied the theory of boundary layer development to flow in the flume throat. They produed a general design method for flumes with a trapezoidal ontrol setion, inluding the two limiting ases, namely the retangular and triangular ontrol. Their paper laid the foundation for the head-disharge equation: (2.4) where: Cd disharge oeffiient (Setion 3.5); C v approah veloity oeffiient (Setion 3.6); C s a shape oeffiient whih orrets for the ontrol setion not being retangular; bottom width of ontrol setion; sill-referened head. This general design method introdued the boundary layer displaement depth, a shape oeffiient, and an iteration proedure to alulate a rating table with the exlusive use of struture dimensions. This method was aepted by the British Standards nstitution (1974) and by the nternational Standards Organization (1980) as a ornerstone for their standards on long-throated flumes. The above method of produing a rating table assumes that the veloity distributions at the gauging station and in the throat (ontrol) setion, redued by the displaement depths, are uniform. A non-uniform veloity distribution due to streamline urvature, however, an influene the flume rating by approximately as muh as the introdued boundary layer displaement depth. Replogle (1975) reported the Akers and Harrison method to be inonsistent in aurately prediting the laboratory alibration of a variety of arefully tested flumes. This prompted the development of a omputer model for making a rating table that uses both the boundary layer theory and a predition of the veloity distribution. Replogle (1978) states that this model for broad-rested weirs and long-throated flumes, having any arbitrary shape of the ontrol setion and being plaed in any hannel, produes the alibration with an error in the listed disharge of 2% or less.

17 Disharge rating based on H 1/L ratio As an expansion to the hydrauli theory presented by Jameson (1925) and to the method of allowing for the veloity of approah, C, as used by v the British Standards nstitution (1969), a series of head-disharge equations were developed (Setion 3.3). As shown in Figure 2.6, all equations use a disharge oeffiient, Cd' and either an approah veloity oeffiient, C, or a table to v determine the rate of the flow. n the pratie of irrigation, and of water management in general, the flows to be measured are within a ertain range. Bos (1976, 1977) and Clemmens, Bos, and Replogle (1984) found that within the range 0.1 < HlL < 1.0, one relationship between the disharge oeffiient, Cd' and the dimensionless ratio, ~/L, is suffiiently aurate for all long-throated flumes and broad-rested weirs (Setion 3.5.2) Bos (1977) also developed a generally valid proedure whih gives values of the approah veloity oeffiient for all ombinations of ontrol shape and approah hannel (Setion 3.6). With and Cv' produed. the equations as listed in Figure a rating table for the related 3.12 and the above values for C d ontrol setions an be with respet to the tailwater level (Chapter 4). This is true for any measuring struture in a stream with a flat hydrauli gradient. As mentioned when Table 2.1 was being introdued, the first systemati researh on the head loss requirement for modular flow was reported by Fane (1927). Subsequently, other researhers (Engel 1934; Wells and Gotaas 1956; Blau 1960; Landbouwhogeshool Wageningen 1964 to 1971; Harrison 1968; and Smith and Liang 1969) published data on the modular limit of individual strutures. No general system of estimating the modular limit beame available, and the guidelines published by the British Standards nstitution (1974) and by the nternational Standards Organization (1980, 1982) are in the same tabular form as those published by nglis in 1928 (Table 2.1.) n 1976, Bos published a method of estimating the modular limit of a struture having any arbitrary shape and being plaed in any hannel. This 16-step method was laboratory tested and heked against published data (Bos and Reinink 1981). A reent study on the performane of a large weir (16.45 m wide) and reent laboratory tests showed that the method is suffiiently aurate and reliable for the hydrauli design of broad-rested weirs and long-throated flumes (Replogle et al. 1983; Dodge 1982; Boiten 1983). A detailed desription of this method is given in Chapter Estimate of the modular limit n flat irrigated areas, the measurement and ontrolled distribution of flow over a number of suessive anal bifurations requires a onsiderable part of the available head in the anal system. An aurate estimate of this part of the available head results in a good knowledge of the available hydrauli gradient along the reahes of the anal system. For an individual struture, a orret estimate of the required head loss, as a funtion of the hydrauli design of that struture, is essential for determining the rest or throat elevation

18 The head -disharge relationship We may therefore onlude that if the shapes of the gauging setion and the ontrol setion are known, and the two orresponding water levels are measured, the two unknown average veloities, v and v, an be 1 determined from the following equations: Conservation of mass, if density hanges are negleted: Q = v A = v A 1 1 (3.1 ) Conservation of energy, if energy losses in the zone of aeleration are negleted: 3.1 BASC EOUATONS Figure 3.1 shows a short zone of aeleration bounded by the setion of the gauging station and the ontrol setion. Both setions are perpendiular to straight and parallel streamlines. n both ross-setions, the effet of streamline urvature on the piezometri level is negligible so that this level oinides with the water surfae levels. These water levels determine the areas A and A ' 1 2 a v /2g + (P/pg + Z) (3.2) Flow measuring strutures as desribed above, whih require that two water levels be determined and onverted into areas of ross-setion, are named Venturi flumes. The measurement and onversion of two heads, however, is time-onsuming and expensive, and should be avoided if possible. t will be shown that the measurement of one water level in the gauging setion is suffiient to determine the rate of flow, provided that the flow in the ontrol setion is ritial. To explain this ritial flow ondition, the onept of speifi energy will first be defined. 3.2 SPECFC ENERGY The onept of speifi energy was first introdued by Bakhmeteff in 1912, and was defined as the average energy per unit of weight of water at a hannel setion, with the hannel bottom serving as referene level. Sine the piezometri level oinides with the water surfae level, the piezometri head with respet to the hannel bottom is: Figure 3.1. Cross-setional area of flow at gauging station and ontrol setion P/pg + Z = y, the water depth (3.3)

19 So that the speifi energy head is: Sine da = Bdy, this equation beomes Substitution of v = Q/A i nto Eq. 3.4 yields: (3.4) H o (3.5) Where A, the ross-setional area of fl funtion ow, an also be of y, so that f expressed as a or a given hannel rossdisharge, the speifi setion and a onstant energy head is a funtion only. Plotting this t of the water depth wa er depth y i gi ves h ',aga nst the speifi en t e speifi energy u ergy, Ho' rve as shown in Figure 3.2. The urve sh h OWS t at, for a given disharge Ho' there are two 'alter t d ' Q2' and speifi energy, na e epths' of flow. flow and one for subriti 1 fl. one for superritial a ow. At point C th at its minimum for the i ' e speifi energy is g ven disharge and th oinide. This depth,e two alternate depths of flow is known as 'riti relationship between this i i a depth', y. The m n mum speifi ener h ritial depth is found b diff gy ead, H ' and the y erentiating Eq 3 5 t remains onstant. 0 y, while Q dh /dy = 1 o = (aq /ga )(da/dy) 2 (av /ga) (da/dy) Figure 3.2. The speifi energy urve dh /dy = 1 - o 2 av B/gA f water flows at ritial depth, the speifi energy head is at its minimum. Thus dh /dy = 0 and Eq. 3.7 beomes (Jameson 1925): o 2 Cl: v /2g = A /2B 3.3 HEAD-DSCHARGE EQUATONS (3.8) The ritial veloity, v, is the maximum speed for disturbanes to travel with respet to the flowing water. This implies that superritial flow is only influened by upstream onditions. Hene, the (superritial) rate of flow is independent of the tailwater level; the flow over the struture is then alled 'modular'. The follo~ing setions ~ill show that Eqs. 3.1, 3.2, and 3.8 allow the development of a head-disharge relationship for modular flow in any broad-rested weir or long-throated flume. The head-disharge equations in this setion are needed for two purposes: (i) for struture design; (ii) for rating table or rating urve prodution. When the struture is being designed, the values of h 1mi n, P' and h l max must be mathed to the antiipated flow rates Q mi n and Qmax. This mathing proess usually requires the alulation of h 1mi n h l max for one or two ontrol shapes and a variety of dimensions (Chapter 5). One the shape and dimensions of the ontrol setion have been 8eleted, the head-disharge equations are used again to produe a h1-q rating of the designed struture. Often, this rating is made after the weir or flume has been onstruted, so and that the atual dimensions of the ontrol setion an be used. f a programmable alulator is

20 available, the iteration method desribed in Setion 3.7 an be used to produe the rating table or urve ~--- =-.-:::=:...:: v ~ General equation for ideal flow A broad-rested weir, or the related long-throated flume, is an overflow struture with a horizontal rest in the diretion of flow. n the ontrol setion, the streamlines are pratially straight and parallel so that the effet of entripetal aeleration on the piezometri level an be negleted and the pressure distribution is hydrostati. To obtain this situation, the rest length, L, should be related to the sill- or rest-referened energy head, H' as: (3.9) so that urvature of streamlines does not signifiantly disturb the hydrostati pressure distribution in the ontrol setion (see also Setions and 4.3.3). f the measuring struture is so designed that the onverging transition leads the water into the throat (or above the rest), without signifiant flow separation and subsequent turbulene losses, there is a smooth flow pattern upstream of the ontrol setion. Negleting frition losses in this zone of aeleration we thus may write (Figures 3.1 and 3.3): L throat iength Figure 3.3. llustration of terminology Ld variable diverging transition length Combining Q = v A and Eq and assuming a pratially uniform veloity distribution, a = 1.0, gives: (3.12) n this equation for the ideal rate of flow, Qi' we an use Eq. 3.8 to alulate: Y = H - A /2B 1 The head-disharge equation of a struture, having any well-defined ontrol setion and being plaed in any hannel, an be derived from Eqs and 3.13, as will be done in the following setions. (3.13) or: 2 a v 2 H y + a v /2g where H equals the sill-referened energy head as shown in Figure 3.3. (3.10) (3.11) Retangular ontrol setion For a retangular ontrol setion in whih the flow is ritial, we may write A b Y and Bb. Hene: 1 (3.14) Y H - 2' Y or: 2 H (3.15) Y = 3

21 Triangular ontrol setion l~_u :>j Figure 3.4. Dimensions of a retangular ontrol setion For a triangular ontrol setion (Figure 3.5), we may write 2 e e i A = y tan -2 and B = 2 y tan -2. Substitution of these values nto Eq gives: (3.19) Substituting of this relationship and rewriting gives: A b y into Eq and Substitution of this Y value and of A = y 2 tan ~ into Eq gives (JamesOn 1925): (3.16) This equation for ideal flow over a broad-rested weir was first determined by Belanger in t is based upon a number of idealized assumptions suh as: absene of energy losses between the gauging and ontrol setions; uniform veloity distribution in both setions; and straight parallel streamlines at the gauging and ontrol setions. n reality these assumptions are not entirely orret, but deviations from them an be ompensated for by the introdution of a disharge oeffiient, Cd; Q = C Q d i Q = ~ (~g) 0.50 tan ~ H For the reasons explained in Setion 3.3.2, the introdution of v ompletes this equation to: (3.20) Cd and (3.21) Equation 3.16 then reads: Q (3.17) Figure 3.5. Dimensions of a triangular ontrol setion n a field installation, it is impratiable to measure the energy head, H 1, diretly. Common pratie therefore is to relate the disharge to the upstream sill-referened head, h 1 To orret for negleting the veloity head, a 1 v 1 2 / 2g, an approah veloity oeffiient, Cv' is introdued into Eq Hene: Q = C C ~ (~g)0.50 b h 1.50 d v whih is the final equation for a retangular ontrol further details on the Cd and 3.5 and 3.6 respetively. Cv values, referene is setion. For (3.18) made to Setions Trunated triangular ontrol setion For strutures with a trunated triangular ontrol setion (Figure 3.6), two head-disharge equations should be used: one for the onditions where flow is onfined within the triangular part of the ontrol setion, and the other, at higher stages, where the presene of the vertial side walls has to be taken into aount. The first equation is analogous to Eq. 3.21, being: (3.22)

22 A omparison between this equation and Eq shows that the flow through the triangular part of the ontrol setion is aounted for by 1 subtrating 2 \ from the sill-referened head. Flow through a trunated triangular ontrol thus equals the flow through a retangular Figure 3.6. Dimensions f o a trunated triangular ntrol setion This equation is valid if Y ( Hb SUbstitution of this limitation into Eq gives the limit of appliation of Eq for this ontrol shape as (Bos 1976): (3.23) A head-disharge equation for H ) 1.25 H or B i by) H 1 b was derived by os n 972 as follows: ontrol of similar width and with a sill referene loation at 0.5 R b above the invert of the triangle. This may be alled the equivalent retangular ontrol setion, and h - respet to 0.5 H b is the upstream head with the equivalent horizontal sill in the ontrol setion. (For other omplex ontrol setions, see Setion 3.4.) Trapezoidal ontrol setion For and 2 a trapezoidal ontrol setion (Figure 3.7) with A = by + zy B b + 2z Y, we may write Eq. 3.8 as for a = 1: A = B Y 1-2- B H = B (y b ( Not e th a t Y Ho is the average water depth in the ontrol setion.) Substitution of A d an B into Eq gives: (3.24) (3.28) 2 Sine for ideal fluid flow H = H v /2g + Y, we may write the = total sill-referened energy head as a funtion of the dimensions of the ontrol s~tion as = ~ 1 1 Y 3 H + (; \ and ~ - y = 3' (H - ~ \) so that Eq an also be written as: (3.25) or: (3.29) A (3.26) Substituting the Eqs and 3.26 into Eq and adding the and Cv values gives Cd Q C C 2 (~g) O d v 3' 3 B(h - 2' \) (3.27 ) b Y b Y z R R = H R B 1-- ""----==~=_=-_-T_~ tan 8/2=z" e / v----;./ <: Figure 3.7. Dimensions of a trapezotdal ontrol setion (3.30)

23 From this equation, it appears that the ritial depth in the ontrol setion is a funtion of the energy head, H' of the bottom width, b' and of the side slope ratio, z' of the ontrol setion. t also appears that, if Z is known, the ratio Y/Hl is a funtion of Hl/b ' Values of Y/Hl as a funtion of Z and the ratio H/be are shown in Table Substitution of A = b y + z y into Eq and the introdution of a disharge oeffiient give a head-disharge equation (Bos 1976): Q = Cd[b y + z Y ][2g(H l-y)j (3.31) For given values of H' b, and z, a value for the ratio y /H l an be derived from Table 3.1, so that y is known and the disharge an be alulated from Eq By varying H' the Q-H l relationship is obtained. This Q-H l relationship an be onverted into Q-h l as follows: table 3.1. Values of the ratio Y/Hl trapezoidal ontrol setions Side slopes of hannel, ratio of horizontal to vertial (z) 0.25:1 0.50:1 0.75: :1 as a funtion of Z and H/b for 1.5: : : :1 4: Estimate Al by assuming that h ~ H; Calulate h = H - alq /2gA ; l 3. Use this new h value to alulate A; 4. Repeat Step 2 to find a suffiiently aurate h value; 5. Plot Q-h urve or make Q-h rating table. l l top of bank i~ d : y h 1 ~ 1 p..' ~~.03..~. Y...:..1...~.. p 2 k lip: L.xx _ k la,,_ Lo :t- L '1

24 Paraboli ontrol setion The relatively unommon paraboli ontrol setion (Figure 3.8) an be built from a setion of a prefabriated irrigation anal. f f is the 2 foal distane of the parabola, we an write A = 3 By and B = 2.f2fY. Figure 3.9. Dimensions of irular ontrol setion and: Figure 3.8. Dimensions of a paraboli ontrol setion Substitution of A into Eq yields: 1 8 y = -d (1 - os- 2 ) 2 Substitution of A and B into Eq. 3.8 gives 2 v d 28 = sin 8 8 sin 2 (3.36) (3.37) 2 Substitution into Eq of this Y value, A = 3 By' and B = 2.f2fY, and the introdution of Cd and Cv gives (Jameson 1925): Cirular ontrol setion (3.33) 2 and beause H = H = Y + V /2g, we may write a dimensionless form of the sill-referened energy head as: H 2 Y V sin e er= d+'2d sin 4 + e g 16 sin 2 (3.38) 2 e For eah value of the dimensionless ratio y /d = sin -4' mathing values of the ratios A /d 2 and Hl/d an be alulated with the above information. These values, and the additional values of the 2 dimensionless ratios, V /2gd and y/hl' are presented in Table 3.2. For a struture with a irular ontrol setion (Figure 3.9) we may write: For a irular ontrol setion, we an use the general head-disharge equation given earlier (Eq. 3.12) and write A! d 2 (8 - sin 8) 8 (3.34) (3.39) B (3.35) This equation an be written in terms of d ratios of Table 3.2 as (Bos 1976): and the dimensionless

25 Table 3.2. Ratios for determining the disharge Q of a broad-rested weir and long-throated flume with irular ontrol setion (Bos, 1976) 3.34, 3.36, and 3.38 into Eq yields: substitution of Eqs Q., {fee)} Cdd g (3.41) 2 2 Ye/ de V~/2gde 1l 1lde Ae/d~ Ye/H f( 0) Ye/de ve/2gde ll/de Ae/de Ye/H f( 0) e).5 ontrol setion. ee!e - sin is a shape fator for the where fee) 0) (8 sin 2: the related value of is set to a given value, fd is known and H value and the Cd Table 3.2. Substitution of this read from fee) an be iterative proedure of yields the disharge Q. The value into Eq. H -Q relationship into should be used to transform this Setion an hl-q relationship. values for the ontains olumns presenting dimensionless Table 3.2 also data will water depth, and related area of flow. These veloity head, Setion and in Chapter be used in U-shaped ontrol setion ontrol setion (Figure 3.10), strutures with a U-shaped For measuring for the onditions equations must be used: the first two head-disharge of the ontrol setion, where flow is onfined within the irular part of the vertial seond, at higher stages, where the presene and the equation is: be taken into aount. The first.31.1l side walls has to A C U Q d {2g(H l/de - Ye/de)} Cd -2 d O.13U U B021 is valid if Y Zd or if e <; 11. This equation (Eq 3.40) related ratio H /d '" 3.2 with this limitation shows the 1 Entering Table U-shaped ontrol is limited Hene, the use of Eq 3.40 for the r--' by H <; 0.70 d should be used B6 ~g f H ;J 0.70 d' the seond equation H1 - Ye A e t was derived by Bos in 1977 as follows: ~ de

26 < B =d Trunated irular ontrol setion For a struture with a irular ontrol setion that is trunated on the bottom (Figure 3.11), we may write the following relationships: A.. d 2 (<1> - sin <1»/8 (3.46) s At d 2 (e - sin e)/8 (3.47) Figure Dimensions of U-shaped ontrol setion and: B d (3.42) (3.43) and: B.. d sin e (3.48) 2' b d sin <1> (3.49) 2' P d (1 - os.2)/2 (3.50) 2 Substitution of this information into Eq gives for the ritial depth: (3.44) Combining Eqs. 3.12, 42, and 44, and adding the Cd and Cv oeffiients gives: (3.45) A omparison with Eq, 3.18 shows that h d in Eq is' the upstream head with respet to the equivalent horizontal sill in the ontrol setion. Y.. d (os ~ - os ~)/2 where: As.. area of sill; At.. total area of sill and wetted flow area at the ontrol setion; b sill width; P.. sill height at the ontrol setion. f the pipe is horizontal, note that P1 P (see Fig. 3.3). (3.51 )

27 Table 3.3. Shape fators f($, 8) of a broad-rested weir in a irular pipe. Cd = 1.0, a = 1.0, H = H P + H de Figure Dimensions of irular ontrol setion with trunated bottom The wetted area at the ontrol setion, A, A A s d 2 (8 - $ + sin$ - sin8)/8 is found from (3.52) Substituting the above A and B values into Eq. 3.8 gives: 2 v zg A d 2 (8 - $ + sin$ - sine).s; 2B (3.53 ) whih, in ombination with Eq. 3.13, yields: 8 + $ + sin$ - sin sin 2 (3.54 ) Substituting Eqs and 3.54 into Eq and introduing a Cd value gives (Clemmens, Bos, and Replogle 1984): or Q Q 1.50 d 2.50 O. SO... (..:;:.8_...:r...~=--:-~?~_ p + snp - sin8) Cd g 8(8 sin ~) (3.55) (3.56 ) To solve this equation for a given ombination of P and d (and thus for $ through Eq. 3.50), it should be noted that the angle 8 is defined if a y value is given in addition (Eq. 3.51). Hene, the angle e is 2 defined if (p + Y )/d is known. Adding V /2gd (from Eq. 3.52) to C Lnl () ~Q';l

28 this ratio yields: 1.+ P -d--- = e 8 sin 2' 5 sin e + e + ~ + sin ~ e 16 sin 2' (3.57) SHAPE OF CONTROL SECTON HEAD-DSCHARGE EO. TO BE USED HOWTO FND THE Ye-VALUE SOURCE OF BASC EQUATON Belanqer Thus for given values of relative sill height P /d and of (H + P )/d, the f(~, e) an be solved. Values for the shape fator f($, 0) have been omputed and are given in Table 3.3. Jameson, 1925 For a struture of known dimensions, p and d, and a given H value, the related dimensionless value an be obtained from Table 3.3, and Q an then be alulated from Eq Use Table 3.1 Bos, 1976 The resulting Q-H 1 relationship an be transformed into a Q-h 1 table or urve by using the method of Setion Then for any dimensionless water depth, Yl/dl' a orresponding value of A 2 an be found in 1/d1 Jameson, 1925 Table 3.2. n using Table 3.3, it should be noted that the veloity head is inluded and therefore h should not be onfused with H. Bos,1976 Jameson, Summary of equations n the above setions, head-disharge equations were derived for a variety of shapes of the ontrol setion. All these equations are based upon Eqs. 3.8, 3.12, and 3.13, while the assumptions that underlie the Cd and Cv oeffiients are idential in all ases. The derived o = Cdd~' vg [(e)] us. tabl. 3.2 to lind (e) Us. Tabl. 3.2 Bos, 1976 equations are summarized in Figure The Ye values are also summarized beause they are needed to estimate the modular limit (Chapter 4). f H1 " 0.70 de = Cdd~"vg (Hell us. table 3.2 to lind lie) Use Table Bos EQUVALENT SHAPES OF CONTROL SECTONS Bos 1977 An important property of the broad-rested or long-throated struture follows diretly from a ombination of the Eqs and The resulting equation: 0: Cdd~"vg [(~,e)) use table 3.3 to find f(tp, /') Y is variable Cremrnens. 80S and Replogl., 19B4 (3.58)

29 shows that the (ideal) disharge through a ontrol setion is determined by two variables only: A and B' n other words, all ontrol shapes that flow with the same water surfae have an arbitrarily shaped wetted area with the same disharge at the same rate. This property, whih was width, B' and A value, illustrated with the derivation of Eqs and 3.45, an be used for other ontrol shapes with omposite ross setions. The following two examples may further illustrate this. f--bc=1.50~ r d A=o. A=O.25m 2 1 ( f--b=1.50m~ : ~ (J.2~- O.16ir=ll1lllll11llllllaDlllllllllllllllllllllllll - --i6 P1=O.083 ~ O?j 25 m21 Figure Similarity in shape of ontrol setions with equal disharge Photo 3.1. Long-throated flume with omplex ontrol setion The left-hand side of Figure 3.13 shows setion of two long-throated flumes. the designs for the ontrol n both designs, the head under whih the lower flows are to be measured is inreased by narrowing the bottom to b = 0.50 m. f the ritial water depth at the omplex ontrol setion does not exeed 0.25 m, the head-disharge relationship of the idential trapezofdal parts of the ontrols is given by Eq. appliation of this equation an be derived from Eq. 3.29: The limit of Substitution of b = 0.50 m, Y = 0.25 m, and Z = 2.0 into that f H > m, no head-disharge equation is available for the two 1 omplex ontrol setions. The lower trapezoids, however, an be replaed by, respetively, a retangle and a trapezoid with B = 1.50 m and A = 0.25 m 2 The dimensions of these two areas are shown in the right-hand side of Figure As an be seen, the equivalent singular ontrol shapes have an imaginary invert at m and m respetively above the real sill level. These values must be subtrated from the real H values of the left-hand side ontrols if applied to the head-disharge equations of the equivalent singular ontrol Setions. The proedure of obtaining a rating urve for a omplex ontrol shape is illustrated below, with the ontrol shape at the top left of Figure 3.13 serving as an example: Determine the Y value for whih the lower part of the ontrol setion flows full (Y m in example). 2 Calulate the ~ value Whih orresponds with this Y value; Eq yields ~ m for the original ontrol shape.

30 Selet the relevant head-disharge equation from Figure 3.12 and alulate a rating urve for the lower part of the ontrol setion. 4. Determine the area of the lower part of the ontrol setion A = 0.25 m 2 and alulate the dimensions of the 'equivalent retangular area'. 5. Calulate the imaginary raise, 6Pl' of the sill-referene level of the 'equivalent singular ontrol' (6Pl = m in example). 6. Selet the head-disharge equation for the 'equivalent retangular ontrol'. Calulate the related rating urve. Corret the heads of this rating urve with the 6Pl of Step 5 (add ~Pl = m to imaginary head). 7. Convert the Q-H l rating into a Q-h l rating (Setion 3.3.5). 8. Summarize the rating urves as illustrated in Figure ~ 0.7 E.s o 0.1./ V /7-~ :>.../ ~fm 0.2./ / 0.3 ~ /'/ Figure Rating urves for a omplex ontrol shape ~ " v ~ 0.8 l;;j flow rate in m 3/s 3.5 DSCHARGE COEFFCENT, Cd Physial meaning As Eq. stated when the disharge oeffiient was being introdued in 3.17, its numerial value follows from: C orrets for the atual deviation from the following three d idealizing assumptions: * Absene of energy losses between gauging station and ontrol (3.59) setion; * Straight and parallel streamlines at gauging station and at ontrol setion; * Uniform veloity distribution at the gauging station and ontrol setion Cd values As mentioned in Setion 3.5.1, the value of the disharge oeffiient is mainly influened by energy loss due of veloities due to frition, and by an inrease to streamline urvature. Both phenomena an be related to the dimensionless ratio HlL. For heads that are low with respet to L, energy loss due to frition upstream of the ontrol setion is signifiant with respet to H' ausing Cd dereasing Hl/L. For high HlL ratios, the downward streamline to derease with urvature auses C to rise. d Laboratory data on 105 broad-rested weirs and long-throated flumes from 29 different researh papers (for list of authors, see legend of Figure 3.15) were used to alulate the Cd value as a funtion of the 8l/L ratio. The resulting points are plotted in Figure 3.15) Whih shows the relation between Cd and HlL for the wide variety of ~eirs and flumes that were tested. The dimensions and onstrution materials of these strutures differed onsiderably: the shape of the

31 -... J - ontrol setion ranged from a narrow (0 = 30 ) triangle to a wide (b = m) trapezoid; the throat length ranged from 0.04 m to 3.65 m; the onverging transition was made either of urved surfaes (rbottom 0.2 H l max) or of flat surfaes with a ontration ratio as low as l-to-4; approah veloity onditions ranged from two-dimensional to three-dimensional, while at Q the Froude number in the approah max hannel ranged from 0.1 to 0.5; the downstream diverging transition ranged from very gradual (lo-to-l) to fully trunated (O-to-l); flow towards the ontrol setion was aelerated by side ontration only, by a bottom sill only, or by a ombination of the two; strutures were built of glass, brass, PVC, sheet steel, wood, and onrete. The results of the following analysis thus apply to smoothly finished broad-rested weirs and long-throated flumes. Cd value A - A P A El fj D it it A TA, 11.& - tg; t# f t----iQJ1----f-=~_+--+_-_+--_ m m f----f f ! +-_--+ - O.86~-~ f -f -f_-f_-f -f -j---r f ! _----j1-_+-_ f---f _-----,-_+-_--+-_-+ --_-+-_--j ratio H 1/L ratio H1/L Figure 3.15 (ont.) Figure Laboratory tested Cd value plotted versus the ratio HlL

32 Cd value 1.10r---~-,---,-----r--,-----, ,-----r-----,------,--r-~ n Ji n m"m El fj ill jjl& JJ. rp Cd value ~". -~-- D DD :a n D D D ill w f--,1il m A m 0.90r--j---j---t--t--t--t---t---t r--t---j l--~ r--r j-----!--!--!--!--t r--t----t j--.J j Figure (ont.) [j]d D 1 D0 Tlr D D li J>. DB A {!]~. m J>. ] 0dP"', -Er A J>. AA 0 U ] a 1r.\1_ ri' rd.j l AAA J>. A "~A--- 1J _DO Aml!l Bm 1...~1lJ D!kJ~ A m~~~j>.~~aaa 'iij.la,.:'01!11!1 ~~1!\~ J>.7Jf' llo.t,l ~",~~- A 0.94 f---. l'a1" J>. A.D AAA filii A ~J~t--A~- 33 A! legend ll] o Smith and Liang 1969 i 01!i. l Pitlo and Smit ] 0w- WL {!] "-- "-- ---" 1---f-"" ---- ] rnrn " 0.82 o Figure (ont.) ratio H 1 /L

33 Cd value 1.10 r-,----, r--,-----,----,----,---.--,------,-~--~~ Cd value 1.10 ~----, ~----,---,--~-----,-~~--,--~--~----, r--t--t J r--t-----t f ~ j A ~ _-- 11 :r 1.04i-t-----t--t t J-----.j 1.02r--t--t----t J i i ~_ 11 ~ El m El 11_+-_-+-_ [i ratio H,/L o.mo ratio H 1/L Figure (ont.) Figure (ont.) The average value of Cd' and its standard deviation, for lassified values of HlL are listed in Table 3.4. The last olumn of this table also gives the perentage error of this average Cd value (95% onfidene level). Both the average Cd values (0) and the related 95% onfidene limits are presented in Figure 3.16.

34 Table 3.4. Average Cd values and ratios standard deviation for various l)/l Ratio Number of Average Standard 95% onfidene HlL data points, Cd value deviation, limit in per ent n s of Cd strutures whe re the tailwater hannel bottom deflets the jet upwards, the disharge oeffiient of a high weir (P2!H 1 > 0.75; Bos 1976) will be higher than that of a flat-bottomed flume. Corresponding lusters of Cd values for various types of strutures are indiated in Figure For general pratie in water management, Cd v~al~u~e -r-r- '- ' T T_T' pratial range of apljiation OS l:n = 1395 FLAT BOTTOMED.1. FLUMES 1.14L---J i---+--y-1- -, When the data on Cd were being proessed, it was assumed that for a given HlL ratio the oeffiient data were normally distributed with an average value Cd and standard deviation s. As stated in Setion 3.5.1, however, energy loss due to frition in the zone of aeleration and streamline urvature at the ontrol setion influene the Cd value: For the same area of flow of the ontrol setion, the wetted perimeter in a narrow ontrol setion is greater than the wetted perimeter in a wide ontrol setion. Consequently, frition losses are also greater, and a narrow ontrol setion has a lower disharge oeffiient than the wide ontrol setion. Further, beause streamline urvature at the ontrol setion an develop better above weirs with a high P2 value than above \ \ ratio H,/L Figure Cd va 1ues as a funtion of HlL for broad-rested weirs and long-throated flumes of all shapes and sizes

35 however. it is reommended that these systemati differenes be ignored. and that the average Cd versus HlL urve of Figure 3.16 be used instead. To limit the effet of roughness of the weir rest at low HlL values and the effet of variable streamline urvature at high HlL values. the following pratial limits of appliation are reommended: (3.60) t should be noted that this pratial range of validity is wider than the theoretial range of Eq The Cd versus HlL line. within the pratial limits of appliation shown in Figure losely orresponds with the following equation: (3.61) The error in the disharge oeffiient of Figure 3.16 or Eq was determined from the 95% onfidene limits. For a given value of the ratio HlL. this oeffiient error is: x (3.62) funtion of a onverging transition is to guide the flow into the ontrol setion without ausing flow separation to Our. To study the effet of differently shaped onverging transitions on the Cd value. tests were onduted (Bos and Reinink 1981) Tb d e ata points are plotted in Figure Tests Al and A5 were run on the model desribed in Setion This was a trapezoida1-throated flume with a transition in whih the bottom onverged 2-to-1 and the side slopes 1.50-to-1. The transition started at 0.30 m upstream of the throat entrane. n Tests B1 and B5. the transition was hanged to start at 0.45 m upstream of the throat entrane and the bottom 1 s ope was hanged to 3-to-1. The side slopes onverged 2.25-to-1. n Test C6. the sides onverged as in the Bl and B5 tests. but the bottom of the transition was flat. Cd 1.00r--,--, ,------,----, t-- n some speial ases. suh as a water balane study. aurate measurements in a wider range of flow ratios may be required. The measuring struture must then be alibrated either in the field or in a laboratory sale model nfluene of transition shapes on Cd As mentioned earlier. the Cd versus HlL relationship of Figure 3.16 is valid for all broad-rested weirs and long-throated flumes provided that there is no flow separation at the leading edge of their rest or throat. Suh flow separation an be avoided by properly shaped -..o ~in... t-r"n,dtions. As already mentioned in Setion the main 0.91 '-.. i ratio H, L Figure nfluene of shape of onverging transition on va 1 ue f C 0 d (WL 1980; Bos and Reinink 1981) -

36 Figure also plots the data points of a test onduted at the Hydrauli Laboratory, Delft (WL 1980, test run ). This test was run on a broad-rested weir with bottom ontration only and a rounded onverging transition with a radius of 0.2 H 1max (r = 0.20 m). On the basis of the data of Figure 3.17, there would seem to be no pratial differene between the effets of a plane transitions (2-to-1 slopes of Al and A5) and a rounded transition (r = 0.2 H of max WL 1980). For ratios of HlL greater than 0.5, streamlines beome inreasingly urved. n flat-bottomed flumes, Pt = P2 = 0, the disharging jet is supported by the bottom of the downstream transition; the streamline urvature is thus less than in flumes with elevated throats. This differene in Cd values is shown in Figure 3.18 for HlL values of 0.45 and 0.6 (Bos and Reinink 1981). B series; '_ Pl =P2=0.15 m J ~A f---. J 0.94 legend downstream transition 1:0 + 1; 1 x 1;2 o 1;4 1:6 A 1;10 C series; Pl =P2= ~+ijl 0.94 ~t 3.6 APPROACH VELOCTY COEFFCENT,, Physial meaning As stated in Setion 3.3.2, the approah veloity oeffiient orrets for the use of h instead of ~ in the head-disharge equation, and 2 thus for negleting a 1 v 1 12g. The exat value of Cv an be derived from Eqs. v 3.17 and n general terms for singular ontrols this is: where u equals the exponent of h in the head-disharge equation for the studied range of disharges Cv values for various ontrol shapes Substitution of V Q/A l into Eq gives: (3.63) 2 f the approah veloity V is small, the veloity head a 1 v 1 12g is small with respet to H' Hene H and h are almost equal and the C value is just slightly more than unity. Beause of the exponent 2 of v V in the veloity head, however, this head inreases rapidly with inreasing approah veloity ratio H 1/L ratio H 1/L (3.64) Figure nfluene of shape of downstream transition on the value of Cd The flare angle of the downstream transition seems to have no signifiant influene on Cd' The oeffiient error of Eq also inludes the effet of the throat elevation PZ' at values of HlL up to 1.0. The exat value of C for a given shape of the ontrol setion an be v found by substituting into this equation the appropriate equation for Q and the related u value for the studied range of disharges. ~tangular ontrol setion: For a retangular ontrol setion, u = 1.50, the disharge equals:

37 Thus Eq beomes: Substitution of this equation and u 2.0 into Eq gives: v b 2 h 3] (3.68) or: v (3.65) (3.69) Bos (1976) plotted the C value of various ontrol shapes versus the v dimensionless area ratio fl CdA*/A where A* would be the imaginary l l, area of the ontrol setion if the water depth were to equal h. For a retangular ontrol setion (Figure 3.19): Rewriting yields: _ / C 0.5 _ 1 C v 3.0SY v 2 (3.70) At< = b h 1 (3.66) Triangular ontrol setion: Substituting this A* into Eq and rewriting gives: C 2/3 v C 2 v Paraboli ontrol setion: For a paraboli ontrol setion, A* equation is: -~ 2.60"V~ C v (3.67) f h,and the disharge Q (Eq. 3.33) For a triangular ontrol setion, A* = h 1 2 tan ~, and the disharge equation is: (Eq. 3.21) Substitution of this equation and the related value u '" 2.50 into Eq, 3.64 gives: = v Whih, upon substitution of A*. reads: (3.71) B, C 0.4 v Rewriting yields: (3.72) _le = 3.49V _v':'-':2~- v (3.73)

38 Summary of Cv values Equations 3.67, 3.70, and 3.73 give the relationship between the area ratio and the approah veloity oeffiient. Substitution of various values of Cv into these equations yields the values of ~CdA*/A1 as given in Table 3.2 (Bos 1976, and C1emmens, Rep1og1e, and Bos 1984). Table 3.2. Table of values for plotting Cv versus la C A*/ A 1 d 1 Approah veloity oeffiient C v Area ratios alc for 3 ontrol shapes da*/a 1 Retangular Paraboli Triangular ~ ~C ~C 0.4_ v v 2 C C C v v v oeffiient of approah veloity Cv o 0.1 j/ triangular ontrol u= paraboli ontrol u= retangular ontrol u=1.5!".~ /'" ;f' ;f' /.{/ ~7/ "4'" ~' /~' :4'-' "",,,' ~~'.-~~-: * 0.8 area ratio vr, Cd A /A1 Figure Cv values as a funtion of the area ratio ~CdA*/A1 Bos 1977) (from l l l l l Plotting the values of Table 3.2 in a graph yields Figure 3.20, whih shows a remarkably lose plot of Cv values as a funtion of the dimension1ess area ratio. The explanation for this is that the imaginary area A* already expresses the ontrol shape. 3.7 ALTERNATVE RATNG BY TERATON Equations for ideal flow The general equations for ideal flow at ritial depth in the ontrol were given in Setion They are repeated here in a setting. For ideal flow at onstant rates through the weir 3.21, we an apply Eq. 3.5 to the gauging station. Hene, "i = l.0: (3.74) Q i is the ideal flow rate. were derived for ideal flow read: (Eq. 3.12)

39 F' y = H_ - A /2B -1. (Eq. 3.13) A (3.75 ) The ombination of these t wo equati ons gives: and (Eq. 3.58) This general equation is valid for all ar b itrarily shaped ontrol setions. As disussed in Setion 3.5, the effet of energy losses and streamline urvature in the ontro 1 setion are aounted for by the introdution of a disharge oeffiient, C. d' B b + 2 z y (3.76) The approah hannel may have any shape. Most irrigation and drainage anals, however, are usually trapezoidal, or may be assumed to be Hene: so. Q C Q d i (Eq. 3.59) (3.77) and for pratial purposes: in whih, as shown in Figure 3.21: (Eq. 3.61) (3.78) Thus, for eah ombination of approah hannel and ontrol setion shapes, the Eqs. 3.13, 3.58, and 3.74 have unknown Y' Qi' and h' f anyone of these three is given, the other two an be solved by iteration. sill zone of aelerolion Figure The energy level at gauging station and setion for ideal flow. the ontrol The iteration proedure starts with determining the range of h values for whih the appropriate disharges need to be omputed. Next, an initial guess is made for Y in terms of h' As an be seen in Figure 3.12, y ranges from 0.67 H for a retangular ontrol setion (z = 0) 1 to 0.80 H for a triangular ontrol setion (b = 0). f the 2 veloity head, V /2g, is negleted, an initial guess for Y ould be: 0.70 h (3.79) The rating proedure The ombined use of the above equations is easy if simple equations exist for A and B in terms of Y' For a trapezoidal ontrol setion these equations, for example, read: NO loser guess of Y is needed for different shapes of the ontrol setion, sine the iteration proess onverges rapidly. One y has been guessed, values of A, B, and Q an be omputed, followed by i those of H and y (from omputed Q value). f the new y value equals i the input y value then the omputed Q is the orret flow rate for an i ideal fluid mathing the set h value. Usually, however, the new

40 Y value will not equal the input value, and a new series of alulations will have to be made until the y values math. This iteration loop is illustrated in Figure The atual flow rate, Q, that mathes the set h value is found by using the last H value for the alulation of HlL and the related Cd value from Eq FinallY, Eq is used to alulate the atual flow Q. This method has the advantage of not requiring an estimate of C, v sine both H and h are used in the omputation, and the energy heads are balaned. A further advantage is that beause the method starts with h rather than H' a programmable alulator an be used for the diret development of head-disharge relationships. alulate A 1 initialize h,-value assume Y=0.70 h 1 alulate A and B Cd =0.93+ O.10H 1/L ". -"~Q ~. 72. Flow hart for the 1 1 i f a u at on 0 head-disharg~ (h _Q) 1

41 Required head loss over the struture -=..::::=-.~ ~- - - ~ v-~129- p proah hannel,~ g "'-- ~- Ql"iji ~ u_ L throat length variable diverging transition length 4.1 NTRODUCTON Figure 4.1. llustration of terminology. As stated when Eqs. 3.8 and 3.12 were being introdued, the water depth at the ontrol setion of a struture must be ritial to give a unique relation between the upstream sill-referened head and the flow rate in the struture. f the downstream sill-referened head is suffiiently low with respet to the upstream sill-referened head, modular flow will our. With high downstream heads, the flow at the ontrol setion annot beome ritial and the downstream sill-referened head influenes the upstream sill-referened head. f the submergene ratio, H is high, the flow is non-modular. 2/H 1, That ratio of H at whih flow at the ontrol setion an just 2/H1 beome ritial is alled the modular limit, ML, for the orresponding rate of flow. The loss of head, ~H, is aused by frition and turbulene losses in the struture and the adjoining hannel reahes from the upstream to the downstream head measurement setions. This loss of energy 'head an be related to the upstream head in terms of the submergene ratio by: (4.1) To design a struture with modular flow in a given hannel, the following variables must be seleted: (i) The elevation of the weir sill or flume throat; (ii) The shape and related width and depth of the ontrol setion; (iii) The expansion ratio and the length of the diverging transition. These design variables greatly influene the head loss requirement for modular flow, making the proess of mathing the struture to the (depth-disharge urve of the) hannel an iterative one. n this ontext, it should be noted that the hannel does not have a stable depth-disharge urve. f this were the ase, no disharge measuring struture would be required. The design proedure, however, means hoosing a measuring struture with an optimal stage-disharge relationship. For modular flow, the head-disharge equations of Figure 3.12 an be used. For non-modular flow, the atual disharge is less than that alulated by these equations. To orret for this redution in flow rate, a 'drowned flow redution fator', f, an be used so that: (4.2) Qnon-modu1ar fqmodular

42 submergene ratio H 2H, i... < >. > >>\..i < -r-- J~ >\\\i~ io.~ i ~N ~OQuJ9rJimit.../ ---'$ M ~ +' Cl> 0.7 ~»».....».i drowned flow redution fato r, f i> >i 0.6 Q =0.158 m 3;s / flume B4 0.5 e-» 0.4 i o Figure 4.2. Example of the relationship between drowned flow redution fator and level. submergene ratio that varies with a rising downstream water Figure 4.2 shows a typial urve giving f values as a funtion of the submergene ratio for a trapezoidal flume (B4) as tested by Bos and Reinink (1981) at a onstant flow rate of Q = m 3/s. The higher the value of the modular limit, the more the urve will move into the top right orner of the figure. n this thesis, the modular limit is numerially defined as the value of the submergene ratio H 2/H1 at whih the atual disharge deviates by 1% from the modular disharge (f = 100/101 ~ 0.99). Flumes and weirs with non-modular flow are not reommended for measuring disharge. The reasons are: 3. Errors in determining both H and H propagate in H / H n the example of Figure 4.2, an error of ± 3% in the submergene ratio auses the f value to vary from 0.82 to n pratie, the error in H 2/H1 often exeeds 3%. Espeially in ases where the modular limit is high, the f value annot be determined with suffiient auray; 4. Non-modular flow requires the measurement of two sill-referened heads (h and h Proessing these heads into energy heads and 2). ombining them with a drowned flow redution fator - a funtion of the Q to be measured - an be an expensive trial-and-error proedure. 4.2 THEORY The fundamental ondition for flow at the modular limit is that the available loss of head between the hannel ross-setions where the upstream head, H' and the downstream head, H, are to be determined, 2 is just suffiient to satisfy the requirement for ritial flow to our at the ontrol setion. This situation will be analyzed by dividing this minimum loss of energy head, H - H, into three parts 1 2 (Bos 1976): (1) The energy head loss, H - H between the upstream head ' measurement setion (gauging station) and the ontrol setion in the flume throat (Setion 4.2.1); (2) The energy losses, ~Hf' due to frition between the ontrol setion and the downstream head measurement setion (Setion 4.2.2); (3) The losses, ~Hd' due to turbulene in the diverging transition ( Se t ion ) 1. The drowned flow redution fator is unknown unless the given ombination of ontrol setion, diverging transition and tailwater hannel is tested in a hydrauli laboratory for the omplete range of relevant flow rates and downstream heads; Figure 4.3 indiates the lengths of those parts of the struture for whih these three energy losses are to be alulated. 2. The value of f for a given struture is not a funtion of H 2/H 1

43 "0., Cl s: + h 1,b Q hl hl,a Figure 4.3. Lengths of struture parts for whih H - H ' ~Hf' and ~Hd are to be alulated. Qb ~ flow rate Energy losses upstream of the ontrol setion 4.4. llustration of terms in Eqs. 4.4 and 4.5 The head-disharge relationship for a retangular, paraboli, or triangular ontrol setion, and shapes, an be written in the exponentional form: Q where K is a dimensional oeffiient, a onstant for a given weir or flume. u = for parts of all other ontrol setion The value of the exponent, u, an be alulated from: dq dh 1 =CdCKh u v 1 (4.3) (4.4) For the appliation of this equation, a rating urve of the onsidered ontrol setion should be available on linear paper (Figure 4.4). During the design proess, however, exponent, u, an then be approximated from: u = 10h h1,b - log hl,a suh a urve is not available. The (4.5) appliation of Eq. 4.5, the flow rates Q and Q must be a b from the valid head-disharge equation (see Chapter 3). of the appropriate values for the disharge oeffiient, Cd' disussed in Chapter 3. As stated when Cd was being introdued in 3.17, its value follows from the need to orret for: Energy losses between the gauging station and the ontrol setion; The effet of urvature of streamlines in the ontrol setion; The non-uniformity of the veloity distribution in both setions. heads that are low with respet to the throat length, the influene streamline urvature and of the non-uniformity of the veloity is negligible with respet to the energy losses (Akers 1963; Replogle 1975; Bos 1976; Bos and Reinink 1981). Consequently, it an be assumed that Cd only expresses the energy between the gauging station and the ontr01 setion. Ating on assumption and replaing ~ by H in Eq. 4.5 results in: (4.6)

44 Combining Eqs. 4.5 and 4.6 gives: whih an also be written as (Bos 1976): H - H = H_ (1 - C l/u) 1-1 d The right-hand member of this equation approximates the loss of hydrauli energy between the gauging and ontrol setions. This equation, however, is only valid if the influene of streamline urvature at the ontrol setion on the Cd value is insignifiant. This limitation is investigated in Setion Frition losses downstream of the ontrol setion (4.7) (4.8) Although flow is non-uniform in the diverging transition, the energy losses due to...,:1. (Le 0< So that: frition are estimated by applying the Manning equation to the three reahes shown in Figure 4.3: (1) Reah of the flume throat downstream of the ontrol setion; the length of this reah is held at L/3; (2) Length of the reah of the atual diverging transition of bottom and side walls, L d; (3) Length of a anal reah from the end of the transition to the measurement setion of the downstream sill-referened head 5 Y2) t>h =.!.L( nq )2 throat 3 A R 2/3 2 L n Q d ( A R 2/3 ) d d (4.9) (4.10) n the alulation of t>h and average area of flow, trans Ad = (A + A an be used. The n value in eah of the equations 2)/2 depends on the onstrution material of the related reah of the struture and anal. As stated in Setion 3.5.2, the struture is assumed to be smoothly. finished. The total energy losses due to t>h = t>h + t>h + t>h f throat trans anal frition, t>h f, between the ontrol setion and the setion where h 2 is measured then equals the sum of losses over the three reahes: n ontrast to hannel and the dimensions of the area of flow in the approah (4.12) the ontrol, the dimensions of the downstream area of flow depend on the unknown value of H 2 The alulation of the modular limit therefore requires the solution by iteration of an impliit funtion of the downstream head (Setion 4.2.5) Losses due to turbulene in the zone of deeleration n the diverging transition, part of the kineti energy is onverted into potential energy. The remainder is lost in turbulene. With flow at the modular limit, losses due to turbulene in the hydrauli jump are low (Peterka 1958) so the simple lassial expression of Borda for energy losses in an expansion of a losed onduit an be used: in whih:..:l...,aa nn t'ha 11n'ltnnT.7n A''''''~n''",,..._...:1 (4.13) the energy loss oeffiient, being a funtion of the expansion ratio of the diverging transition; derease in average flow veloity between the ontrol setion and the downstream head measurement setion the

45 nternational literature ontains few data that allow the measured total energy loss over flumes to be broken down into the above three parts and permit ~-values to be alulated. Blau (1960), Engel (1934), nglis (1929), and Fane (1927), however, published suffiient data on the geometry of strutures and hannels to allow the total head loss, ~H, to be broken down into a frition part and a turbulene part. The alulated ~ values that were obtained from this literature are shown in Figure 4.7. They orrespond with the ~ values for the Band C series of the experiments onduted by Bos and Reinink (1981). The results of these experiments are disussed in Setion Total energy loss requirement The total energy loss over a flume or weir at the modular limit an be estimated by adding the three omponent parts as disussed in the preeding setions: Rather sudden expansion ratios like 1 to 1 or 2 to 1 are not effetive beause the high veloity jet leaving the throat annot suddenly hange diretion to follow the boundaries of the transition. n the resulting flow separation zones, turbulene onverts kineti energy into head and noise. f for any reason the hannel annot aommodate a fully developed gradual transition of 6-to-1 it is reommended that the transition be trunated to L = H rather than to use a more sudden expansion d 1max ratio (see Figure 2.5). The end of the trunated expansion should not be rounded, sine it guides the water into the hannel boundary; a rounded end auses additional energy losses and possible erosion. The modular limit of a weir or flume an be sides of Eq by H' giving: found by dividing both 2 v 2)!2gH 1 (4.15) (4.14) For the onsidered rate of flow through the struture, this equation gives the minimum loss of energy head required for modular flow. That part of the above equation whih expresses the sum of the energy losses l!u due to frition, H (1 - Cd ) + ~Hf' beomes a large perentage of the total energy loss, H - H 2, when diverging transitions are long (high ~Hf values). This is mainly beause the relatively high flow veloities in the downstream transition are maintained over a greater length. On the other hand, very gradual downstream transitions 'have a favourable energy onversion (low ~ value). As a result, very gradual transitions may, as a whole, lose more energy than more rapid but shorter transitions. Sine, in addition, the onstrution ost of a very gradual transition is higher than that of a good 6-to-l. shorter one, there are arguments in favour of limiting the ratio of expansion to about Equation 4.15 is a general expression for the modular limit of any long-throated flume, and is also valid for the hydraulially similar broad-rested weir Proedure to estimate the modular limit Modularity of a disharge measurement struture in a given hannel implies that the required head loss for modular flow must be less than the available head loss. The required head loss, however, an only be estimated after the type and dimensions of the struture have been hosen. As will be explained in Chapter 5, this hoie is also governed by other onsiderations, suh as range of flows to be measured, and auray. An optimal solution to the design problem an only be found in an iterative design proedure (Setion 5.8). Part of this proedure is estimating the modular limit for Q and Q of the tentative max mi n design under onsideration in the relevant design loop.

46 n the following proedure to estimate the modular limit, it is assumed that the relationship between Q, h and Cd is known. f this 1, relationship is unknown, it an be derived as explained in Chapter 3. To estimate the modular limit of a weir or flume in a hannel of given ross-setion, both sides of Eq must be equalized as follows: 1. Determine the ross-setional area of flow at the station where h 1 One some experiene has been aquired, Eq an be solved with two or three iterations. Sine the modular limit varies with the upstream head, it is advisable to estimate the modular limit at both minimum and maximum antiipated flow rates and to hek if suffiient head loss (H - H is available in both ases (see also Setion 2) 5.3.1) is measured, and alulate the average veloity, v 1; 2 Calulate H 1 = h 1 + v 1 /2g; For the given flow rate and related head, note down the Cd value; 4.3 HYDRAULC LABORATORY TESTS Determine the exponent u; For a retangular (u 1.5), paraboli (u = 2.0), or triangular To verify the theory and related proedure of estimating the modular ontrol setion (u = 2.5), the power u is known from the limit (Setion 4.2), model tests were onduted in the hydrauli head-disharge equation. For all other singular or omposite laboratory of the University of Agriulture at Wageningen (Bos and ontrol shapes, use Eq. 4.4 or 4.5; Reinink 1981). l/u Calulate Cd ; Use Setion 3.3 and Figure 3.12 to find y at the ontrol setion. Note that Y is a funtion of H 1 and of the throat size and shape; Determine the ross-setional area of flow at the ontrol setion with the water depth, y, and alulate the average veloity, v ; Use Figure 4.7 to find an ~ value as a funtion of the angle of expansion; Estimate the value of h 2 that is expeted to suit the modular limit and alulate A 2 and the average veloity v 2; 2 Calulate ~(v - v 2) /2gH 1; Determine ~Hf = ~Hthroat + ~Htrans + ~Hana1 by applying the 1 Manning equation with the appropriate value of n to 3L of the throat, to the transition length, and to the anal up to the h 2 measurement setion (see Setion 4.2.2); Calulate ~Hf/Hl; 2 Calulate H 2 = h + v /2g; 2 2 Calulate H 2/H l; Substitute the values (5), (10), (12), and (14) into Eq. 4.15; f Eq does not math, repeat steps (9) through (15) Desription of model tests n a onrete-lined hannel setion with bottom b = b = 0.50 m and a l 2 side slope of -to-l, a trapezoida1 10ng-throated flume was onstruted (Figure 4.5). The flume throat was made of polyvinyl hloride (PVC) with a sill height P = P2 = 0.15 m, length L = 0.60 m, width b = 0.20 m, and a side slope Z = 1.0. This model was first used to study the effet on the Cd value of a -to-2 slope of the onverging transition versus the ommonly used -to-3 slope. The result of these A series of tests are given in Setion n a further series of tests, the B series, the bottom of the throat was again plaed 0.15 m above the bottom of the approah hannel bottom so that P = P2 = 0.15 m (see Figure 4.5). n eah test series, the flume was suessively fitted with six diverging transitions as shown in Table 4.1. During Test B4, some diffiulties arose with instability of the tai1water level, h To 2 solve this problem, a piezometer was plaed to measure h, and for Test 2 B5 the flume was moved 1.40 m upstream (see Figure 4.5).

47 (2.21) ~, ~p.45' <-'i : ) Measuring the modular limit To evaluate the effet of submergene at various flow rates on the related upstream sill-referened head of the tested flumes, the Q-H 1 relationship around the onsidered flow rate is written in the general form: Q (4.16) where: note: dimensions in between brakers refer to replaed model 7,' : 0.50= bl SECTON A-A for series A &B ~1 (' H 0.20=b SECTON OVER FLUME THROAT Figure 4.5. Dimensions of model, in metres (Bos and Reinink 1981) For the C series, the bottoms of the approah and were raised by 0.15 m so diret derivation of the loal energy head, h ' Table 4.1. Divergin Test number B1 B2 B3 B4 B5 B6 Bottom slope 0-to-1 1-to-1 2-to-1 4-to-1 6-to-1 10-to-1 transitions for tests of B series tailwater hannels that P = P2 = O. n this series, the flat-bottomed flumes thus needed no transition on the bottom. The ratios of divergene of the side wall transitions are the same as those in the B series. Piezometers were also installed in the bottom of the throat to allow a length of diverging transition, L d Side wall slope 0-to to to-l 2.9-to to-l 7-to-1 u 1.01 u R1(10l) the dimensionless power of H' the value of whih depends on the shape of the ross-setion of the flume throat and onsidered flow rates (see Setion 4.2.1); u 1.01 R 1(100) 2 h1(101) = R1(101) - V /2g the range of K* a dimensional oeffiient whose value depends on the size and shape of the flume (its dimension depends on u). Equation 4.16 implies that the log Q versus log H urve is straight. 1 This is true for all retangular, paraboli, and triangular ontrol setions, and it is at least a good approximation for all other ontrol setions if the studied range of Q is limited. For eah of a number of fixed flow rates, alulations were made of the head R 1(101) at whih the flow rate, as alulated by the head-disharge equation for modular flow, deviated by 1% atual flow rate in the test run: from the After R 1(101) had been alulated with this equation, the related limiting value of the upstream sill-referened head was found (4.17) (4.18) (4.19) from: (4.20)

48 Table 4.2. Modular limits and energy losses as a funtion of flow rate in twelve trapezoida1 flumes (Bos and Reinink 1981) Disharge, in ubi metres per seond Flume Data B1 h/h "2 /" H B2 h/h "/" " B3 h/h "/" " B4 h/h "/" " B5 h/h "/" " B6 h/h "/" " Cl h/h "/" " C2 h/h "/" " C3 h/h C4 "/" " h/\ "2 /" " C5 h/h "/" " This value of h 1(101) is the minimum value of h 1 that is required to preserve modu1arity at the prevailing head, h 2 For eah of the twelve tested flumes in the Band C series, the tests were run at flow rates as lose as possible to 0.10 m 3!s, m 3!s, m 3!s, and m 3!s respetively. The downstream water level was raised stepwise. When the flow pattern had rate was read on the flow meter, and Head loss H 1 - He Equation 4.8 was derived to between the gauging station and assumption of straight and stabilized, the atual flow all heads were measured with point gauges. This proess yielded the limiting downstream water level, h 2, whih aused the alulated value of h so that the limiting l(lol)' submergene ratio h 2!h1 ould be alulated. Table 4.2 lists the modular limits for eah ombination of flume and disharge in terms of both measured sill-referened heads, h 2!hl, and the alulated energy heads, H 2!Hl To evaluate the to alulate H 1 flow rates. The estimate the loss of hydrauli energy the ontrol setion, subjet to the parallel streamlines in the ontrol setion. validity of this assumption, laboratory data were used 2 2 = h + v!2g, H = Y + V!2g, Cd' and u for fixed resulting values allowed both sides of Eq. 4.8 to be alulated separately for twelve 10ng-throated flumes with trapezoida1 ross-setion (B and had C in Setion 4.3.1). Of these twelve flumes, six a bottom hump of P = P2 = 0.15 m; the others had a flat bottom (P P2 = 0). The diverging transition varied as shown in Table 4.1. Figure 4.6 shows that the energy loss upstream of the ontrol setion of the Band C flumes an be estimated by the right-hand member of Eq. 4.8 if this loss is less than about 5 mm. For the twelve tested flumes, this loss of 5 mm about 0.5. ourred at flow rates that aused an Hl!L value of C6 h 2/ h l "2 /" A" Note: With flumes Bl, 8Z. and B3, the h 1 value was measured at 1.90 m downstream of the throat, for flume B4 at 2.43 m, and for the other.,,~ ~.. _-. C"

49 Energy losses downstream of the ontrol setion H 1-H in mm o r o / /. 0/ ;/ o B series C series H 1 (1_C~/U) in mm As disussed in Setion 4.2, the energy head loss, ~H, for flow at the modular limit an be divided into three parts: H - H ~Hf' and ~Hd' ' Table 4.3 lists the measured values of ~H, the alulated values of H - H (by Eq. 4.8) and those of ~Hf (by Eq. 4.12), and the remaining energy head loss ~Hd' Beause of the approximate nature of the assumptions that underlie the appliation of both Eqs. 4.8 and 4.12, the number of signifiant figures given for H - H and ~Hf does not imply a orresponding auray. They serve merely to allow data to be ompared and to alulate ~d' As an be seen in Table 4.3, the total energy loss due to frition, (H - H + ~Hf' expressed as a perentage of the total energy loss ) over the flume, ~H, inreases with inreasing length of the diverging transition. For a flat-bottomed flume with a 10-to-1 transition (C6), perentage is already greater than 35. Beause of the relatively flow veloities in the diverging transition in a flat-bottomed flume (C series), the perentage of energy loss due to frition is larger than in a flume with an elevated throat (B series). rom the alulated ~Hd values of Table 4.3, and the related average eloities, V and v the energy loss oeffiient, F" for the tested 2' was alulated with Eq As shown in Figure 4.7, these orrespond with the F, values for the strutures tested by Fa (1927), nglis (1929), Engel (1934), and Blau (1960). Figure 4.6. Head loss due to frition between the gauging and ontrol setions (Bos and Reinink 1981) Hene Eq. 4.8 an be used to estimate H - H if the HlL ratio is less than 0.5. For higher values of HlL, are signifiantly urved, so streamlines at the ontrol setion that the onept of minimum speifi energy H - Y + v 2/ 2g, is no longer valid and Eq. 4.8 does not apply, - (see Setion 4.4).

50 Table 4.3. Energy losses over flumes flowing at their modular limit, in entimetres (Bos and Reinink 1981) Disharge, in ubi metres per seond Disharge, in ubi metres per seond Tested Tested flume flume Beause the inreasing frition losses in a more gradual expansion are only partly ompensated for by a lower ~ value, the required energy loss for modular flow, 6H, dereases little if the expansion ratio exeeds a ertain value. Weighing the onstrution ost of a more gradual expansion against the lower requirement of ~H yields a pratial upper limit of the expansion ratio, EM, of 6-to-l. 6H = Hi - H 2 Hi - H 6H f!lh d B1 B2 B Cl C2 C value of ( 1.5, , , , , o." ~ legenda 10 serle B /Pl =P2-0, 15) <D sene C (Pl =P2=0) & BLAU flume K V ENGEL NGLlS FANE flume 1 flume 2 flume 1 flume 2 flume u flume p ill 0.47 D fa 30 /s % 3J /s /s C B CS o expansion ratio EM of bottom and/or sides C Figure 4.7. Values of ~ as a funtion of the expansion ratio of downstream transition (Bos and Reinink 1981) To estimate the energy 108s onneted with onversion of kineti energy into potential energy in the diverging transition of a weir or flume, the use of the envelope of Figure 4.7 is reommended. This onservative ~ value is then substituted into Eq to estimate 6H d (see Setion 4.2.5).

51 EXPERMENTAL VERFCATON OF MODULAR LMT ESTMATE WTH RECENT TESTS To evaluate the presented method of estimating the modular limit of a long-throated flume, data from reent literature were available for use. From the atual dimensions of laboratory models (Boiten 1983; Dodge 1982; SO 1983; Smith and Liang 1969), and of a large prototype (Replogle et al. 1983) the modular limit was estimated. These results were plotted against the modular limits as measured by the above authors (Figure 4.8). For three ombinations of struture and flow rate, the method overestimated the modular limit. All three were weirs with bottom ontration only, plaed in a retangular laboratory flume and flowing at H1/L~0.5. Figure 4.8 shows that the method of estimating the modular limit is a suffiiently aurate approximation for the design of long-throated flumes and in Setion and the hydraulially related broad-rested weirs. As disussed 4.3.3, the related theory is valid, provided that streamline urvature at the ontrol setion is negligible; hene if HlL < With higher HlL ratios, the streamlines at the ontrol setion beome modular limit, inreasingly urved, whih has a negative effet on the As a onservative rule, it is assumed that if the H L ratio inreases 1 from 0.5 to 1.0, the modular limit dereases linearly from the value alulated to a value of y H where y is the ritial depth in the 1, ontrol setion. This rule annot be supported by the results of systemati experiments. t is supported, however, by observations made by Bos 1976, Bos and Reinink 1981, Boiten 1983, and SO estimated modular limit VSUAL DETECTON OF MODULAR LMT 0.90 ~-----f j =~~-----j ",,0.50 f the tai1water level is suffiiently low for a stable hydrauli jump to our downstream of the ontrol setion, this jump is learly visible (see top row of Photo 4.1). Beause of the hydrauli jump, flow must be ritial at the ontrol setion and thus be modular. 0.80l-----l----~~~---t------j With very high tailwater levels only minor undulations our (bottom row of Photo 4.1). Here, the non-modular flow pattern is obvious. For flows at, or around, the modular limit, even an experiened hydrauli engineer will have diffiulty in deiding whether flow is modular or not. The reason is that 'white water' at the surfae may be legenda 01 Boiten, 19B3 D,. Dodge, 1982 o Replogle et al., 1983 Smith and Liang, 1969 aused either by a hydrauli jump or by a stable surfae wave at subritial flow (seond and third rows of Photo 4.1). To aid in the visual detetion of the modular limit, the following suggestions are made: "".S.0., measured modular limit

52 ~ 'tl zr o M o "1... ~ o 0:: t> '1 Cl> xr '1 o Cl> 0. o '1 t> en M t> 0. t> -=... '1 Modulllr flow, m 3/s ( 18 May 1982) At modular limit, m 3/ s ( 21 May 1982) 'tl =r o M o l:- l:-...,... n o;:l M Just beyond modular limit, m 3/s (26 May 1982) Non-modul ar flow, m 3/s (28 June 1982)

53 # Flumes with side ontration: Whether flow through the flume is modular or non-modular an usually be seen from the way the jet leaves the flume throat. f the flow is modular, the flow pattern is almost symmetrial with respet to the entre line of the flume. f flow is non-modular, the jet moves either to the right or to the left, as shown in Photo 4.2. The side to whih the jet moves an be influened by disturbing or hanging the flow pattern in the approah hannel. By disturbing the flow pattern and observing the jet movements, one an test whether the flow is modular or not. E o'"..1 E ev '"? er Photo 4.2. Non-modular flow; jet has moved to the left (Bos and Reinink 1981; photo University of Agriulture, Wageningen) Flumes (weirs) with bottom ontration: With modular flow, the water surfae at the downstream end of the throat urves downward. f the water surfae urves upward at this loation, flow is non-modular. At the modular limit, the water surfae is horizontal (see Figure 4.9). The modular limit is easier to detet if the end of the throat is marked on the side walls of the struture. Figure 4.9. Visual detetion of modular limit (two-dimensional flow)

54 5 Demands plaed on a struture in an irrigation and drainage system 5.1 NTRODUCTON f a struture is to funtion properly, the designer must list all the demands that will be made of the struture and math these demands to the properties of appliable strutures. To aid in this mathing proess, the following demands will be disussed: Funtion of the struture (Setion 5.2); Head loss for modular flow (Setion 5.3); Range of disharges to be measured (Setion 5.4); Error in the measurement of flow (Setion 5.5); Restrition of bakwater effet (Setion 5.6); Capaity to transport sediment (Setion 5.7). A step-by-step design proedure is given in Setion Measurement of flow rate All broad-rested weirs and measuring the rate of flow. To deide on what long-throated flumes are strutures for type of struture ought to be used, one must know for how long a period measurements are needed and how often they are to be taken. Together with information on the size and type of the hannel in whih the flow is to be measured, this will lead to the hoie of: A portable and re-usable flume for the measurement of flow up to about 90 l/s (Clemmens, Bos, and Repogle 1984; see Photo 5.1). A temporary weir built of suffiiently durable sheet-material to last the antiipated measuring ampaign (See Photo 5.2 for an example weir with a apaity of 1.5 m 3/s); A permanent weir or flume that measures the disharge in drainage anals and 5.3). As an be seen from streams, or the flow rate in irrigation anals (see Photo Photos 5.1 to 5.3, the mere measurement of flow does not require a struture with movable parts. The upstream head is 5.2 FUNCTON OF THE STRUCTURE rrigation and drainage demand three basi funtions of a struture: Measurement of flow; Controlled regulation of flow; Control of upstream water level. Photo 5.1. Small portable RBC-flume in a drainage hannel

55 measured with referene to the rest of the fixed sill. A proessor an be installed with the head reorder to onvert heads into flow rates. This proessor an also integrate the flow rates to flow volumes per interval of time Controlled regulation of flow rate When water is tapped from a river or reservoir or when an irrigation anal splits into two or more branhes, a struture is needed that an both measure and regulate the flow. This alls for a weir whose sill is movable in vertial diretion (Photo 5.4). With a near onstant upstream water level, the upstream sill-referened head an be adjusted so that the required flow passes over the weir. f automated, the weir sill will be able to follow variations in the upstream water level and thus maintain a pre-set h value and a orresponding flow over the weir. Photo 5.2. Temporary weir, ustom-built of sheet steel Photo 5.4. Weir with movable sill at a anal bifuration

56 Upstream water level ontrol Example The upstream water level an be ontrolled by a weir whose sill is either stationary or movable. Stationary sill: During the design phase, fixed values for y and lmin Ylmax an be seleted for the antiipated flow range. The ontrol setion is then designed so that these water depths our at the orresponding Q mi n and Qmax. Movable sill: ndependent of the flow in the hannel, the upstream water surfae an be maintained at a ertain level, or this level may be varied to suit a water management program. Given: A onrete-lined irrigation anal has a maximum design flow of 0.90 m3/s. The anal has l-to-l side slopes, 0.60 m bottom width, a depth of 1.00 m, and a bottom slope of sb= Required: Selet a weir or flume to measure the flow range Q = 0.10 m3/s to Q 0.90 m 3/s with a maximum allowable min max upstream water depth Yl= 0.90 m. Use the Manning equation to determine the relationship between Q and As the present study is onerned only with flumes and with weirs that have stationary sills, weirs with movable sills will not be further onsidered. 5.3 HEAD LOSS FOR MODULAR FLOW The available head loss at the measuring site follows from flow onditions in the downstream hannel and the highest water level that is tolerated in the approah hannel. This available head loss, at a given rate of flow, is a determining fator for the hoie of the ross-setional shape of the struture's ontrol setion and the expansion ratio of its diverging transition. On the other hand, the shape of the ontrol setion and of the downstream diverging transition influene the head losses at the required modular flow rates. These required head losses must be less than the head loss that is available at the measuring site, a requirement that must be met for the whole antiipated flow range. This interrelationship between the available head loss, the required head loss, and the shape of the struture will be illustrated in the following example. where A and R are funtions of the water depth, yz' and Z Z i s expressed in m l / 3/ s. l/n (5.1) The hydrauli resistane, n, determines the water depth, yz' at whih a ertain flow passes through a hannel with a ertain ross-setion and bed slope. The value of n is not expeted to be onstant beause it is influened by a variety of fators: erosion, sedimentation, deposition of trash, growth of weeds or algae, deterioration of lining, lak of maintenane, and these fators on so on. To illustrate the influene of some of the (tail)water depth, let us assume n = 0.014, a value ommonly used for a onrete-lined irrigation anal under field onditions (USBR 1957; Chow 1959). With this n value, the flow rate an be alulated for eah water depth. The resulting yz-q urve is shown in Figure 5.1 as the dashed line. The onrete bottom of the anal, however, may be overed with sediment. f so, the n value will be higher. f a 0.05 m sediment layer overs the bottom and n = 0.016, the Y2-Q urve beomes the dotted line of Figure 5.1. f the hydrauli roughness is signifiantly higher beause of negleted maintenane, the n value an beome 0.020, resulting in the solid line of Figure 5.1. Suh a line ould be onsidered a onservative estimate of water levels for the given range

57 water depth Y2 in m.9 o o.8 -> o 'h :; o 0.1 Figure 5.1 Range of possible water levels for a given flow in an example anal V....., ~ ' ' ol?:... ~o()'v ~o()~. --- " t>'\....> o o o o o.6 ~ O\~.~"Ol, O. 2.f/ / / V.'.' /' -: /' -: ~... ". /..----,,:~;., '.' O\A "----~O..../'''..----!//.1'/ / 1~ ~= r,m -T- - t. Y2=0.05m z= 1 ~ :ol."y ~ b2= flow rate in m 3/s of flow rates. To study whether flow over a struture will be modular, it is reommended that suh a onservative upper limit be used for the possible tailwater levels. n this ontext, it should be noted that tailwater levels an also be influened by the operation of gates, by bakwater effets, and so on. n pratie, it is suffiient to make a onservative estimate of the tailwater levels at the minimum and maximum flows that are to be measured and to hek the struture for modular flow at these extreme flow rates. For this example, the solid line of Figure 5.1 is used. The maximum flow rate, Q = 0.90 m 3/s, orresponds with Y2 = 0.80 m. The following step in the proedure is to find, by trial and the shape of the ontrol setion, the sill height, and - error, the expansion ratio of the diverging transition, so that, at any flow rate to be measured: As was shown in Chapter 4, the modular limit, ML, depends, amongst other things, on the downstream flow veloity and ratio (EM to 1) To meet the ondition of Eq. downstream sill (high P2 value) and (5.2) 5.2, a wide ontrol setion with a high low head (h) is appropriate. An example of suh a struture is shown in Figure 5.2A. The head-disharge relationship for this weir, with P = P2 = 0.45 m and b = 1.50 m, must then be determined as was explained in Chapter 3. This reveals that Q = 0.90 m 3/s at a head h l = 0.42 m. Figure 5.2A shows the hl-q max relationship of the weir and that between the upstream water depth, Yl = h + P' and Q. For Q = 0.90 m 3/s, it shows that Yl < 0.90 m, thus meeting the postulated demand. With the method explained in Chapter 4, the orresponding modular limit, ML = 0.89, is found. The maximum allowable tailwater depth for modular flow is then Y2max = (0.89 x 0.42) ~ 0.82 m, whih is 0.02 m above the depth Y 2 = 0.80 m. of the diverging transition. on the expansion For other rates of flow, the related values of head (h) and modular limit (ML) an be alulated, again yielding an allowable value Y2 max Figure 5.2A also shows a urve of Y versus 2max Q. For a ontinuous hannel bottom, P = P2' as in this example, differene between the Y l head loss. Between the Y l read. the urve and Y 2max urve yields the required urve and Y 2 urve, the atual head loss is For modular flow to our, the atual head loss must be the required head loss. Thus, y 2-Q urve of Figure 5.2A. greater than the Y 2max - Q urve should be above the As shown above, the margin between the required and atual head loss is 0.02 m at Q 0.90 m 3/s, but it inreases with dereasing flow max

58 rate. n this example the sill height P = Pz = 0.45 m and the atual head loss equals 0.Z9 m for Q i = 0.10 m 3/s, whereas only 0.04 m is mn required. f the value of h at ~in is too low to meet the auray requirement with whih ~in is to be measured, the bottom of the ontrol setion must be narrowed and lowered so that h l mi n will inrease as will be shown in Setion 5.5. To obtain an optimal auray at all flow rates, a flume an be designed with the ontrol setion shaped in suh a way that the Y1-Q urve follows the YZ-Q urve throughout the antiipated flow range. Suh a flume, whih has a omplex trapezoidal ross-setion, is shown in Figure 5.ZB (P = P2 0). As an be seen, Y1 does not exeed 0.90 m if Q equals 0.90 m 3/s. n this flume, with p = Pz = 0 and b = 0.10 m, the ondition of Eq. 1 s.z an only be met if the modular limit, ML, is high. Figure s.2b shows two diverging transitions: 1: EM = O. An abrupt diverging transition. The modular limit at Q 0.90 m 3/s equals ML = 0.86 and the maximum tailwater depth is Y2 = 0.76 m. This value is below the atual tailwater depth so max that the flow is non-modular. n fat, Figure s.2b shows that flow beomes non-modular above 0.15 m 3/s. Z: EM = 6. f a diverging transition with EM = 6 is added to the same flume throat, the modular limit inreases to 0.91 and thus for Q 0.90 m 3/s y = 0.82 m, whih is above the atual y value. For max 2 lower rates of flow, too, the Y2 urve lies above the Y2-Q urve max and flow remains modular at all antiipated rates. equivalent singular retangular ontrol setion (Figure S.2C). A omparison of Figures 5.2B and 5.ZC shows that the two Yl-Q urves almost oinide whereas the design of the Figure 5.2C struture is less ompliated and less ostly. The flume of Figure 5.ZC has a diverging transition with EM whih is needed for modular flow to our at this low P value. = 6 flare, A struture that has less than 0.10 m bakwater effet at the maximum flow rate (Yl < 0.90 m at Q = 0.90 m 3/s and Y2= 0.80 m), and does not need a diverging transition, an be realized only if P2 inreases at the ost of h (see Eq. S.2). f the head, h' dereases, however, width of the ontrol setion must inrease to obtain suffiient disharge apaity at Y l = 0.90 m. The lowest possible sill that an funtion with an abrupt diverging transition (EM = 0) the is shown in Figure S.2D. With respet to the design of Figure 5.ZC, the sill has been raised from O.lS to 0.30 m and the width of the ontrol setion has been inreased from 0.80 to 1.10 m. Beause of the inrease of P by 0.15 m at the ost of h' the measurement of flow will be less aurate (see Setion S.S) Another dimension that varies with the upstream sill-referened head in the four designs of Figure S.2 is the throat length, L. n this example the ratio H /L ( 0.7S, so that L varies from 0.60 m in Design A to max 1.20 m in Design B. This length is another fator that influenes the onstrution ost of the weir or flume. A omparison between the weir (P = 0.45 m) of Figure 5.2A and the flume (p = 0, EM = 6) of Figure 5.2B shows the flume to be a relatively ostly onstrution. A signifiant part of its ost is related to the riterion of auray, whih implies that the sill-referened head must be as high as possible at low flows. This riterion requires that P = 0 and b = 0.10 m. f this riterion an be relaxed, the lower trapezotd of the omplex ontrol setion an be replaed by its

59 water depth Or head in m 1.0, , , ,------, , A water depth or head in m required 0.8 f head 10ss-+-=-""""'=----+-~~--1 _ m 0.7 ~s.o ~\.--atual ,.L.1i--,.~ 6- -head 10ss-:7o<C j /a-:"~s../~1' - appro;>manal 0.4 ~+----_+_re:..---_ :l=---~= Ollgiludi nalsl'clion l----t ;;;,L l----+r:..."L+-+-;;-L' j f.----~4:;;l--- ;T~r------t---- l:=o_80~ 0.3 ~5 b 1-O.60 l' r-1 /./ WfR(Pl=O,45 m ) o water depth or head in m flow rate in m 3/s 0.9 ~~\i \\~~ 0.8~ _+---_t--_r :_: ~?>~s. ~'):~~1.// 0.7.4" / LP -/ /..-- B 0.1 o water depth or head in m t :;;>".L"--+~.,----j 0.7 D flume with EM=O flows non-modular T~; o,"j'. r oo f..--if'----7"'+-----t------t--- FLUME!Pl O,30; b=1,10m) 0.1 o o Figure 5.2. Alternative weirs and flumes for flow measurement in a onrete-lined anal Figure 5.2. (ont.)

60 RANGE OF DSCHARGE TO BE MEASURED Generally, the flow rate in an open hannel varies with time. The range between Q i and 0 through whih the flow is to be measured, m n "max strongly depends on the type of hannel in whih the struture is plaed. rrigation anals, for example, onvey a onsiderably narrower range of disharges than do natural streams. The antiipated range of disharges to be measured an be lassified by the ratio: exeeds 35, so that narrow-bottomed trapezotdal, triangular, or omplex ontrol setions are appropriate. f y.. ~ax/~in exeeds 350, a speially shaped ontrol setion, with a noth in its bottom, an be used. Although a rating table an be produed for the upper and lower ranges of head in suh a ontrol shape (see Setion 3.4), suh strutures are ommonly alibrated in a hydrauli laboratory. y.. Q Q i max m n (5.3) 5.5 ERROR N THE MEASUREMENT OF FLOW For retangular, paraboli, and Q y triangular ontrol setions, the headdisharge relationship an be expressed in the form: atual u value an be determined from Eq. 4.4 or 4.5. (Eq. 4.3) The disharge oeffiient, Cd' an be derived from Figure 3.16 for 0.1 ( HlL ( 1.0. For Q max the ratio HlL" 1.0 and Cd ; for Q mi n the ratio HlL" 0.1 and Cd t follows that the orresponding range of flows that an be measured by a ertain ontrol setion is: As was disussed in Chapter 4, (5.4) the exponent, u, depends on the shape of the ontrol setion perpendiular to the diretion of flow. For a retangular ontrol setion, u.. 1.5, and thus y.. 35; for a triangular ontrol setion,u and y For other shapes of the ontrol setion (trapezotdal, omplex, et.) the exponent u varies from 1.6 to 2.4 depending on the ratio B b. The n irrigation anals, the ratio y.. Q Q i is well below 35 and a max m n retangular (or trapezoidal) ontrol an measure all antiipated flow rates. n drainage anals and natural streams, y = Q maxqm i n usually The allowable error in the measurement of flow has an important bearing on the relation between the (average) width and of the ontrol setion of a flume or weir. depth The auray to whih a flow rate an be measured depends on: The auray with whih a rating table an be made for the struture. The perentage error in the disharge oeffiient is given in Eq as X.. ± (3 Hl/L _ ) per ent; The auray with whih the upstream sill-referened head, h, an 1 be determined. The resulting perentage error in h is denoted as ~l; The exponent, u, in the head-disharge equation (see Setion ). f the sill-referened elevation of the head measurement devie has been determined with suffiient auray, so that this soure of systemati error is removed, the value of X Q for modular flow is: (5.5) This X should not exeed a ritial value to be hosen by the user of Q the flow data. Usually one value is hosen for XQmin and another for XQm The relative magnitude of both values depends on the ax shape of the hydrograph, i.e. on the rates of flow that pass the struture during high or low flow periods. For a given value of X Q and derived values of X (Eq ) and u (Eq. 4.4 or 4.5), the allowable error in h an be alulated from:

61 For the h value, whih is related to (5.6) the onsidered flow rate, the maximum allowable reading error, ~hl' in h an be alulated from: (5.7) Usually, the hosen value of X will lead to a smaller ~h value Qmin 1 than the one that results from the postulated X value. As a result, Qmax the ~hl value at Q beomes a determining fator in the design of mi n the ross-setion of the ontrol and head-measuring devie. in the seletion of a n pratie, the total error in the sill-referened head onsists of two omponents: one due to a faulty referene level and the th Ah o er, u l' due to reading or registration errors. The systemati error due to a faulty referene level depends on the stability of the head-measuring devie with respet to the sill referene point, on the are with whih the proedure of zero-setting the devie to and on the growth of algae and the referene point is done the deposit of sediment in the ontrol. f the struture is properly maintained, the related error in h1 an be limited to 1 mm (Brakensiek, Osborn, and Rawls 1979; Bos, Replogle, and Clemmens 1984). Any attempt at auray will fail if the struture is not srupulously maintained. The reading error, ~h1' whih is related to the head-measuring devie, an be based upon information from instrument manufaturers, laboratory researh (Landbouwhogeshool, Wageningen 1968), and (Bos, Replogle, and Clemmens 1984). field experiene One the head-measurement method has been deided upon, ~hl an be determined. The requirement for h 1min for keeping the error be1ow Qmin is then: (5.8 ) At this low head, the bottom width of the ontrol setion an be approximated with a simplified modifiation of Eq (b and h lmin in metres, Q in ubi metres per seond): mi n (5.9) Equation 5.7 shows that for a ertain value of the reading error, ~, 1 the perentage error in the sill-referened head will derease as the head, h' inreases; it follows from Eq. 5.5 that the perentage error in the mathing flow rate dereases aordingly. 5.6 RESTRCTON OF BACKWATER EFFECT The water depth, Y l ' n the ontrol setion, flow is ritial: Fr v.. r;;:tb "V g"fd (5.10) To provide an upstream water surfae that is suffiiently stable to allow the sill-referened head to be measured, Fr l 0.5. in the hannel upstream of a weir or flume equals the 'undisturbed' water depth, plus a bakwater effet reated by the struture. To avoid overtopping of the hannel at Q,and to minimize max sedimentation problems, this bakwater effet is limited, Y l not being allowed to exeed a pre-determined value at maximum flow. The Q max at this water depth, Y,an be haraterized by the Froude number at l max the gauging station: (5.11) To reate Fr = 1.0, the flow must be aelerated towards the ontrol setion; this is done by ontrating the hannel. The degree of Contration an be desribed by the ratio A*/A l, where A* should not exeed is the area of the ontrol setion below the upstream water level (see also Setion

62 3.6). As shown in Figure 5.3, the upper limit of the area ratio, A*/A l, inreases with inreasing Fr l value. 5.7 SEDMENT TRANSPORT CAPACTY Design rule :; o The empirial urve of Figure 5.3 is the envelope of the alulated relationship between Fr l and A*/A l for modular flow in a variety of strutures. To illustrate the harater of this relationship, data points are shown for four ontrol setions: the retangular ontrol setion of Figure 5.2D, a triangular ontrol (P ~ 0, e ~ 90 ) in the same approah hannel, the (P ~ Figure 5.3. Approximate upper limit of A*/A l as a 0.25 m) trapezoidal ontrol of Figure 5.5, and the retangular-throated weir of Figure 5.6. To determine the required area A*, o one must know the dimensions of the approah hannel and the allowable water depth, Y,at 0 Upon l max "max alulation of the related value of Fr the orresponding ratio l, A*/A l an be read from Figure 5.3. f a struture is designed with a lower A*/A l ratio, this struture may ause more than the postulated bakwater effet. f a struture is designed with a higher A*/A ratio than that derived l from Figure 5.3, the upstream water depth at Q will be lower than max Yl max ~ 0.5 r ,------,------r ,-----,-----,------, ,---(:,---, E o "0; s "5 0.4 s: ~ e. ~.s 1] E '0 '" ~,g o fig. 5.2D V shape in fig. 5.1 (:, fig fig. 5.6 weir j----=.-/"" f funtion of Fr l 0,9 0,7 0.8 _ 1>.'1>.1 upper limit of the ratr The most appropriate method of avoiding sediment deposition in the hannel reah upstream of the struture is to avoid a derease in the hydrauli gradient. To ahieve this, the struture should be designed in suh a way that it does not reate a bakwater effet. With respet to the average approah hannel bottom, this means that the Q versus (h + P) urve of the ontrol must oinide with the water depth-disharge urve (Q versus Y urve) of the hannel upstream of l the struture. This near oinidene should our for those antiipated flows that are liable to transport bed-load. The effet of this design rule on the shape of the weir or flume an be illustrated by onsidering a onrete-lined irrigation anal whih transports sediment that may originate from the diverted river, from runoff into the anal, and from wind erosion. The dimensions of the anal are b l ~ 3.0 m, zl = 1.5, d l = 1.20 m, and s = The design flow rate of the anal is Q = 6.1 m 3/s, whih is transported max at a water depth of about Yl = 1.0 m, so that the related maximum value of the Froude number is For suh irrigation anals (see also Photo 4.1) the rougness of the onrete side slopes is less than that of the overed bottom. As dereasing water depth. Q with Y l in metres and Q in ubi metres per seond The above design rule requires a drop in the anal bottom that is suffiient to guarantee modular flow (here taken at 0.20 m), and (5.15) ontrol setion that has a apaity of 6.10 m 3/s at the undisturbed Water depth, Y l = P + h = 1.00 m. The simplest ontrol that meets this demand is a horizontal weir sill of P = a result, the Manning n value inreases with The water depth versus flow-rate relationship of this anal is shown in Figure 5.4. t an be approximated by: 0.25 m height a

63 f no bakwater effet is allowed for flows below 6.1 m 3/s, a flume with zero bottom sill (P = 0) is the only solution. Beause of the power ~ 2 of Yl in Eq. 5.15, the shape of the ontrol setion must approah that of a parabola (u = 2.0) with a foal distane of f = 1.00 m (see Figure 3.12). The h1-q urve of the omplex trapezoidal ontrol, with double break in the sides, oinides with the Y-Q urve of the hannel (see Figure 5.4). To eonomize on the onstrution ost of the flume, the ontrol setion an be simplified to a trapezoid with a single break in the sides. As shown in Figure 5.4, the bakwater effet of suh a flume is negligible. Figure 5.5. shows that the weir is simpler, and therefore heaper, than the flume a, flow rate in m 3/s Figure 5.4. Yl versus Q urve for a onrete lined irrigation anal and (P + h) versus Q urves of suitable strutures (see Figure 5.4). At 50% of the design disharge, this weir auses a bakwater effet of 0.07 m. This effet an further be redued if a weir sill height of P = 0.20 m is seleted. The y -Q urve of this weir is shown as a dotted line in Figure 5.4. t reveals a bakwater effet of only 0.02 m at 3.0 m 3/s, and a drawdown of 0.04 m at 6.1 m 3/s. With flows below 3 m 3/s, the bakwater effet inreases, whih may ause sedimentation if the flow veloity, v' in the undisturbed hannel is suffiient to transport sediment. For lower flows, however, th~ water depth in the undisturbed hannel, and the related v' will derease, and eventually the transport of bed will ease. 4 load! ~ sale i - H -- flow weir i! i PLAN --, - A WER Pl=D.25 m ~ Figure 5.5. Dimensions of a weir and, 11=:+===6 ~1 flume ~ B ' SECTON ~~~ 1 50 f.--- b1' FLUME P =0

64 Laboratory experiments At first glane, the flume of Figure 5.5 appears superior to the weir in its apaity to pass sediments. Available field experiene, however, reveals no sediment problems with weirs that meet the design rule on the restrition of the bakwater effet of Setion 5.7.2; all sediment that ould be transported by a hannel passed the weirs. To evaluate this field experiene and to generate systemati information on the influene of the transport of sediment on the h1-q relationship, some exploratory laboratory tests were run to ompare a broad-rested weir with a long-throated flume. The dimensions of the two strutures are shown in Figure 5.6. glass-sided =" tailwater level was suffiiently low for flow to be modular. n these exploratory tests, the sediment diameter and Froude number were so hosen that, after a hange in the regime, steady-state onditions were reahed within an aeptable period. While flow remained onstant at Q = m 3/s, the sediment load was inreased for eah test run (D = m, D = m). During eah run, the sediment transport was allowed to stabilize before final data were measured on approah hannel elevation, sill-referened head, h' and total energy head, H. During the tests, the total sill-referened energy head remained stable at ~ = m for the weir and H = m for the flume. As a result of the inreasing sediment transport, the average elevation of the approah hannel bottom inreased as shown in Figure 5.7. No deposit of sediment was observed on the weir rest or in the flume throat, so that the referene level did not hange (Photo 5.5). FLUME horizontal 0=0.660 m 3/s ~ Figure 5.6 Dimensions of the tested weir and flume r' '-----*~ L:060m ~ WER horizontal P2:0.30 m.s. <J 16 '~ '" ~ 0; 0; 12 s: '" s: '"o C-. 8 '" : Q) '" '" : s: " oweir... flume Both strutures were plaed in a glass-sided laboratory hannel (b 1 = b 2 = 1.50 m, z = 0, and s = ). They were dimensioned in suh a way that, without sediment, the Froude number in the approah hannel was equal to 0.45, so that Q = m 3/s and Y1 = h. + P = m. As a result, flow onditions upstream of the gauging stations of the weir and flume were idential. Figure 5.7. shows that they remained idential with inreasing sediment load. The o sediment transport in kg/hour (weighed under water) Figure 5.7. Change in approah hannel bottom elevation with sediment load (Bos and Wijbenga, in prep.)

65 dereaseof h1 (mm) o 2 4 ~o-~ flume oweir 195% onfidene limit -r-~ Photo 5.5. Weir flow with Q = m3/s and a sediment load of 800 kg/hour (photo Delft Hydraulis Laboratory) 14 o sediment transport in kg/hour (weighed under water) The resulting derease of the water depth at the gauging stations of the weir and flume aused v 1 2/2g to inrease at the ost of h (see Setion 3.2). The measured dereases of h are shown in Figure 5.8 as a funtion of the sediment load. The variation of h data is due to the hanging elevation of the sand dunes. The related 95% onfidene limits are shown. The derease of sill-referened head beause of an inrease in the approah veloity an be foreast aurately by applying the theory of Setion 3.6. Figure 5.8 shows the derease in h flume. Beause the h that, for the same sediment transport, is signifiantly greater for the weir than for the value of the weir is 0.10 m less than that of the flume, the perentage redution of h is even more signifiant, espeially beause of the exponent u = 1.5 of h in the h-q equation Figure 5.8. Derease of sill-referened head beause of hange in Pt related to sediment transport (Bos and Wijbenga, in prep.) of both strutures. For example, a sediment transport of 700 kg/h auses an error of 4.9% in the measured weir flow against an error of 2.0% in that of the flume. Hene, in sediment-laden flow, a flat-bottomed flume performs better than a weir. An example of suh a flume, with minimum bakwater effet (see Setion 5.7.2), is shown in Photo 5.6. This prototype flume has performed satisfatorily sine 1970.

66 Beause laboratory models are usually designed with n yl > ~a' the sale onditions of Eqs and 5.13 an only be met if n Fr 1 < 1. Hene, the Froude number in the model is larger than that in the prototype. Photo 5.6. Flat-bottomed flume in the High Shool Wash, Arizona Tu son, A prototype that would math the laboratory tests is a hannel with a water depth of 2 m and an average bed-load diameter of 3.5 mm. Suh a hannel ould be a river or a large irrigation anal. The test data ould also apply to a smaller onrete-lined irrigation anal, whih transports sediments that originate from wind inblow. The results of these exploratory tests warrant further researh, being appliable to hannels of shallower depth. n suh experiments, however, onsiderably more time will be required before steady-state onditions are attained. Researh on strutures in trapezoidal hannels is also reommended. 5.8 DESGN PROCEDURE FOR A STRUCTURE The results of the laboratory experiments an be applied to a prototype by use of (de Vries 1973): (5.12) where: veloity sale; partile diameter sale. This sale ondition on the sediment-transport proess usually influenes the Froude sale ondition: n the above setions, the designer of a 10ng-throated flume or broad-rested weir has been given a number of guidelines to selet the dimensions for a struture in a ertain hannel. The design proedure is an iterative proess whih leads from a detailed desription of the measurement site to a number of suitable strutures. The number of strutures that an serve a given site satisfatorily depends on the hannel in whih the struture is to be plaed and on the postulated hydrauli demands. The steps in the design proedure are: where: Froude number sale; water depth sale. (5.13) 1. Obtain data on the hydrauli dimensions and boundary onditions of the hannel at the measuring site and make a onservative estimate of the Q-yZ relationship. 2. Depending on the period that a struture is to be used and on Q,deide whether a portable, temporary, or permanent max

67 struture is needed, and, if a weir, whether it should have a stationary or movable sill (see Setion 5.2). 3. Deide on the allowable error in the measurement of Q and min ML = 0.85 for a struture in an ongoing hannel; for a struture dispensing into a wide hannel or reservoir, use ML = n a final phase of the design proess, the modular limit (ML) must be estimated with the proedure of Setion Determine the ratio, y = Q Q i ' and tentatively selet the ~x mn shape of the ontrol setion (retangular, trapezoidal, omplex, et.). The atual dimensions will be seleted in Step 6 (see Setion 5.4.) 5. Determine the maximum permitted water depth in the upstream hannel (Ylmax) and alulate the related values of ~ and Fr. Use Figure 5.3 to find the ratio A*/A l Calulate A*. 11. Compare the value of h of Step 8 with the h value of lmi n lmi n Step 10. f the head required to measure Q (Step 8) mi n is equal to, or greater than, the head required for modular flow (Step 10), proeed to Step 12. Otherwise, raise the invert of the weir rest or flume throat. To meet the demand on A* of Step 5, make the ontrol setion wider. With these new dimensions of the ontrol setion, return to Step Make a first tentative hoie of the dimensions of the ontrol setion, using the shape of Step 4 and the area A* of Step Make a preliminary estimate of Hand H Determine the lmin lmax flow-wise length of the throat, L, in suh a way that ( HlL ( 0.1. f the available head loss is a limiting fator, try HlL ( Use Setion 5.5 to alulate the allowable reading error, 6h lmin and 6h l,for the given Q i and Q f no pratial head max m n max measuring devie is available to meet the demanded value of 6h ' redue the width of the ontrol setion (see also Eq. 5.9) and 10. Use Chapter 3 to alulate h and h for the given range of min lmax flows to be measured by the ontrol setion of Step 6. return to Step 7. Note that the area A* of this new ontrol setion must again equal the value of Step 5. Use the ondition P2 + (ML x h) > Y2 to determine the values of h i and h that are required for modular flow at Q and m n max min Q max (see Eq. 5.2). For a first trial, use preliminary values of 12. Compare the value of h of Step 8 with the h of Step 10. f lmax lmax the head required for modular flow (Step 10) is less than the head required to measure Q (Step 8), a struture an be seleted max that will meet all of the design riteria and will operate aurately. This, however, does not guarantee the best or most effiient struture. f struture is aepted, proeed to Step 13. f the head required for modular flow is greater than that required to measure Qmax' a struture annot be seleted that will perform as desired, regardless of the width of the ontrol setion. n this ase, the designer has various options: a) nrease the allowable measurement error; b) Use a more aurate head detetion method; ) nrease the allowable upstream water level by raising the anal walls or reduing the freeboard requirements; d) Redue the required head loss by adding a diverging transition; e) Choose a loation where more head loss is available. Then repeat Steps 1 through 11, as appropriate.

68 Return to Step 10 to ensure that the modular limit at Q and min Q max was estimated with the proedure of Setion f so, proeed to Step 14. Summary 14. Return to Chapter 3 to alulate the hl-q relationship of the struture. Plot this relationship with the Yl-Q and graph (see Figure 5.2). Y2-Q urves in one The above design proedure is an iterative proess, with a number of trials before a final design is seleted. Although this proedure appears to be fairly omplex, the various iterations onverge rapidly. The only diffiult part of the proedure is estimating the flow onditions prior to the plaement of the struture. Vital for effetive water management are strutures that an measure the rate of flow in a wide variety of anals and streams. Chapter 1 of this thesis introdues the long-throated flume and the broad-rested weir; it explains why this family of strutures an meet the boundary onditions and hydrauli demands of most measuring sites. Chapter 2 reords the history of long-throated flumes and broad-rested weirs. t desribes how the hydrauli theory of flumes and weirs, and their design, developed separately over the last hundred years. The hapter onludes by reporting reent attempts to develop a generally valid theory for any long-throated flume or broad-rested weir in any hannel. The remainder of the thesis explains the steps that were taken to arrive at a proedure (Setion 5.8) that an yield the hydrauli dimensions and the rating table of the appropriate weir or flume to measure the flow rate in any hannel. The major steps taken over the hydrauli theory of the flow of water through ontrol setions of different shapes and dimensions (Chapter 3), the theory and proedure of estimating the head loss required for modular flow (Chapter 4), the boundary onditions of the hannel in whih flow is to be measured, and the demands plaed on the struture with respet to the range and auray of its measurements (Chapter 5). [ Chapter 3 gives two basi equations: Q i = A 2g(H l- Y) (Eq..12) and y = H l- A /2B (Eq. 3.13), whih are valid for ritial flow of an

69 ideal fritionless liquid in any long-throated flume and broad-rested weir. With these equations, the H versus Q relationship an be i derived for those ontrol setions whih have well-defined expressions for their A and B. Setion 3.3 presents this relationship for singular retangular, triangular, trapezoidal, paraboli, irular, and trunated-irular ontrol shapes, and for the omposite trunated-triangular and U-shaped ontrol setions. For other omposite shapes, a proedure by whih the H versus Q i relationship an be found is given in Setion 3.4. This proedure is based on the property of these flumes and weirs that the ideal flow rate Q _ ' i - g A B,is the same through all shapes of ontrol setions that flow with the same B and have the same area A t is explained how the H versus Q relationship of an equivalentcsingular i ontrol shape an be used for ertain omposite ontrol setions. To onvert the ideal into the real flow rate, a disharge oeffiient is used: Cd = Q/Qi (Eq. 3.59). This Cd value is assumed to be influened mainly by frition along, and the flume streamline urvature above, throat or weir rest (with length L). An analysis of laboratory data on 105 flumes and weirs of different shapes and and made from sizes different onstrution materials produed a urve that gives the average Cd value as a funtion of HlL. Within the limits of appliation, 0.1 < HlL < 1.0, the Cd value of any long-throated flume or broad-rested weir has an error of less than 5% limit). (95% onfidene To onvert the sill-referened energy head into a water level head, an approah veloity oeffiient is used: Cv = (H 1/h1)u (Eq. 3.63). This Cv value was alulated for three ontrol shapes with different values of the exponent u: retangular u = 1.5, paraboli u = 2.0, and triangular u = 2.5. C was alulated as a funtion of the v dimensionless ratio la Cd A*/A where A* i s t he area of the ontrol 1 1, ross-setion below the water level in the approah hannel. For these different ontrol setions, the funtions were found to be nearly idential. Consequently, for general water management pratie, the same empirial relationships for Cd and Cv an be used for all shapes of the ontrol setion. The hapter onludes with an iteration the proedure by whih a programmable alulator an be used to produe rating table of a long-throated flume or broad-rested weir. Chapter 4 explains the onept of modularity and Chapter 5 disusses the demands imposed by irrigation and drainage pratie and how these demands influene the design of a flume or weir. The struture may have three funtions: (ii) ontrolled regulation of flow rate; and (i) measurement of flow rate; (iii) ontrol of the upstream water level. Considering the period over whih data need to be olleted and the value of Q,it must be deided whether a temporary m~ or permanent flume or weir should be used (Setion 5.2). Setions 5.3 through 5.6 disuss the interrelation between the upstream freeboard requirement, the available head loss at the measuring site, the range w rates to be measured (Q Q ), the allowable error in the of flo max min measurement of the flow rate, the redution of losses in a downstream diverging transition, and the related proedure of estimating the required head loss over a struture to maintain a unique relationship between the upstream sill-referened head and flow rate; i.e. the head loss required for the equations of Chapter 3 to remain valid. The approah followed is based on the assumption that this head loss an be divided into three parts: (i) the energy loss between the upstream head measurement setion (gauging station) and ontrol setion; (ii) the energy loss due to frition between the ontrol setion and the downstream head measurement setion; and (iii) the losses due to turbulene in the diverging transition. Setion 4.2 i for these S epa r a t e parts of the required head loss gives express ons and for the total head loss. Laboratory tests were used to verify the above theory. Reently published laboratory data on measured modular limits of flumes and weirs were ompared with the values estimated by this proedure. The omparison shows that the proedure gives good results if the ratio HlL ( 0.5. Photographs and water surfae profiles are given as an aid in the visual detetion of the modular limit (setion 4.5). the onstrution ost of the flume or weir. Setion 5.6 also presents a relationship between the postulated value the the

70 of Fr l at maximum flow and the area ratio A*/A This relationship is l of speial importane for a first tentative hoie of a flume or weir that will be modular at the design maximum flow while meeting the postulated freeboard requirement. Setion desribes exploratory laboratory tests on the influene of sediment on the head-disharge relationship of a flume and a weir. Both strutures onveyed sediment equally well, but in the flume the head-disharge relationship was less disturbed than in the weir. Samenvatting The final setion of this thesis (Setion 5.8) gives a l4-step iterative proedure for the design of long-throated flumes and broad-rested weirs. Based on the theory of Chapters 3 and 4, this proedure leads to a flume or weir that fits the seleted measuring site and satisfies the demands of irrigation and drainage pratie. Ten behoeve van een effektief waterbeheer zijn kunstwerken nodig waarmee het debiet in een grote versheidenheid van kanalen en beken kan worden gemeten. n Hoofdstuk 1 worden de meetgoten met lange keel en de lange overlaten geintrodueerd; hier wordt uitgelegd waarom deze familie van kunstwerken kan voldoen aan de eisen die voortvloeien uit de omgeving en hydraulia van de meeste meetlokaties. Hoofdstuk 2 geeft een historish overziht van de meetgoten met lange keel en de lange overlaten. Het beshrijft hoe de hydraulishe theorie van deze kunstwerken en hun vormgeving zih, afzonderlijk van elkaar, ontwikkelden. Het hoofdstuk besluit met een bespreking van reente pogingen tot het ontwikkelen van een theorie die algemeen geldig is voor elke meetgoot met lange keel of lange overlaat in ombinatie met een willekeurige waterloop. De overige hoofdstukken behandelen de onderdelen van een ontwerpproedure (Paragraaf 5.8) die, voor elke willekeurige waterloop, leidt tot de hydraulishe afmetingen en bijbehorende Q-h relatie van l een geshikte meetgoot of meetoverlaat. De belangrijkste onderdelen van deze proedure worden behandeld, namelijk de theorie van stromend water door kanaalvernauwingen van vershillende vorm en afmetingen (Hoofdstuk 3), de theorie en proedure benodigd om het verval, dat nodig is voor modulaire stroming, te voorspellen (Hoofdstuk 4), de randvoorwaarden die gerelateerd zijn aan de waterloop waarin het debiet

71 moet worden gemeten, en de eisen die aan het kunstwerk worden gesteld met betrekking tot het trajet waarover het debiet moet worden gemeten met een gevraagde nauwkeurigheid (Hoofdstuk 5). Hoofdstuk 3 geeft twee fundamente1e verge1ijkingen: Q = A [2g(H 1-y )]0,50 (vlg. 3.12) en y = H - A 12 B (v1g. 3.13), i die a1gemeen ge1dig zijn voor kritishe stroming van een idea1e v1oeistof door elke meetgoot met 1ange keel of over e1ke over1aat. Met gebruik van deze verge1ijkingen kan de H1-Q re1atie worden afge1eid voor a11e vernauwingen waarvoor eenduidige verge1ijkingen bestaan voor A en B Paragraaf 3.3 geeft zu1ke re1aties voor enke1voudig rehthoekige, driehoekige, trapeziumvormige, parabo1ishe, irkelvormige, en afgeknot-irkelvormige vernauwingen en voor de samengestelde afgeknot-driehoekige en U-vormige vernauwingen. Voor and ere vormen van een samengestelde vernauwing geeft Paragraaf 3.4 een proedure, waarmee deze H1-Q re1atie kan worden gevonden. Deze proedure is gebaseerd op de algemene eigenshap van deze familie meetgoten en overlaten, namelijk dat het ideale debiet Q i = g' A ' B ' gelijk is voor elke vernauwing met een willekeurige vorm, mits waterspiege1breedte B en de natte doorsnede A gelijk zijn. Het blijkt dat de H Qi relatie van een equivalente 1- enkelvoudige vernauwing kan worden gebruikt voor bepaalde vernauwingen van samengestelde vorm. Het idea1e debiet wordt omgezet in een re~el debiet door gebruik te maken van een afvoeroeffiient, C = Q/Q (vlg. 3.59). Hierbij is d i aangenomen dat de waarde van Cd hoafdzakelijk wordt bepaald door wrijving langs en kromming van de stroomlijnen boven de keel van de meetgoot of de kruin van de overlaat (met lengte L). Een analyse van laboratoriumgegevens voor 105 meetgoten en overlaten van vershillende vormen en afmetingen en geonstrueerd van vershi1lende materia1en, resulteerde in een grafiek voor de gemidde1de Cd waarde a1s een funktie van HlL. Deze grafiek kan worden toegepast onder de voorwaarde dat 0,1 ~ HlL' 1,0, waarbij de fout in de waarde van Cd kleiner dan 5% is (95% betrouwbaarheidsinterval). Door een toestroamsne1heidsoeffiient Cv (H1/h1)u (v1g. 3.63) in te voeren kan, in p1aats van de energiehoogte H, een overstorthoogte h worden gebruikt voor het bepa1en van de afvoerrelatie van een meetgoot of over1aat. De waarde van C werd berekend voor drie vormen van de vernauwing v waarvoor vershillende u-waarden gelden: rehthoekig: u = 1,5, parabolish: u = 2,0 en driehoekig: u = 2,5. C werd berekend als v funktie van de dimensieloze verhouding ai Cd A*/A 1, waarin A* gelijk is aan de oppervlakte van de vernauwing onder de waterspiegel in het toestromingskanaal. De C waarden voor deze drie vormen bleken v nagenoeg gelijk te zijn. Ten gevolge hiervan mogen, voor algemene toepassingen bij waterbeheer, dezelfde relaties voor Cd en Cv worden gebruikt, ongeaht de vorm van de vernauwing. Dit hoofdstuk besluit met een iteratieve proedure, waarbij een programmeerbare zakrekenmahine kan worden gebruikt om de hl-q tabel te berekenen. Hoofdstuk 4 behandelt het begrip modulair stromen en de daarbij behorende proedure om het verval over een kunstwerk te berekenen. Kennis van dit verval is nodig voor het vaststellen van het bestaan van een eenduidige relatie tussen overstorthoogte en debiet en daarmee voar de geldigheid van de vergelijkingen van Hoofdstuk 3. De hierbij gevolgde methode is gebaseerd op de veronderstelling dat dit benodigde verval kan worden gesplitst in drie delen: (1) het energieverlies tussen de doorsnede waar de overstorthoogte wordt gemeten en de doorsnede van de vernauwing waar het water kritish gaat stramen, (2) het energieveries ten gevolge van wrijving tussen deze laatste doarsnede en de doarsnede waar de benedenstroamse waterstand (indien nadig) wardt gemeten en turbulentie in het vertragingsgebied. (3) het energieverlies ten gevolge van Paragraaf 4.2 geeft vergelijkingen voor deze drie delen van het benodigde energieverval en vaar het in totaal benodigde verval. Laboratorium- onderzoek werd verriht om deze methode te toetsen. Verder werden reent gepublieerde laboratoriummetingen van de modulaire limiet van vershillende meetgoten en overlaten vergeleken met de volgens bovengenoemde proedure berekende limiet. Deze vergelijking bevestigde dat de proedure goede resultaten geeft, voor HlL ~ 0,5. Foto's en lengteprofielen van de waterspiegel zijn toegevoegd als hulpmiddel bij de visuele detetie van limiet (Paragraaf 4.5). deze modulaire

72 Hoofdstuk 5 bespreekt de eisen die de irrigatie- en drainagepraktijk aan een debietmeetkunstwerk ste1t en hoe meetgoot of over1aat betnvloeden. Het hebben: debiet en deze eisen het ontwerp van een kunstwerk kan drie funkties (1) meten van het debiet, (2) geontro1eerde beheersing van het (3) beheersing van het bovenstroomse pei1. Gelet op de periode waarin debieten moeten worden gemeten en op de waarde van Q max' moet worden beslist een tijdelijk dan wel een permanent meetkunstwerk te gebruiken (Paragraaf 5.2). De paragrafen 5.3 tot en met 5.6 bespreken de samenhang van de benodigde bovenstroomse waking, het beshikbare verva1 bij de meet1okatie, het meetbereik van de meetgoot of overlaat: Q Q,de toe1aatbare fout in de debietmeting, de max min be perking van het energiever1ies in de vertragingszone en de bouwkosten van de meetgoot of over1aat. Verder geeft Paragraaf 5.6 het verband tussen de gewenste waarde van Fr 1 bij maximaal debiet en de opperv1akte verhouding A*/A 1 Dit verband is een belangrijke shakel in de eerste keuze van een meetgoot of overlaat, die zowe1 modulair stroomt bij het maxima1e ontwerpdebiet a1s de vooropge1egde waking niet beperkt. Paragraaf beshrijft een verkennend laboratoriumonderzoek naar de inv10ed van sediment transport op de h1-q re1atie van een meetgoot en een over1aat. Beide kunstwerken verwerkten het aangevoerde sediment even goed, de h1-q relatie van de meetgoot werd ehter minder verstoord dan die van de over1aat. De laatste paragraaf (5.8) van dit proefshrift geeft een, uit 14 stappen bestaande, iteratieve proedure voor het ontwerpen van meetgoot met lange keel of een lange over1aat. Gebaseerd op de in de Hoofdstukken 3 en 4 behande1de theorie, 1eidt deze proedure naar een meetgoot of overlaat die bij de gekozen meet10katie past en vo1doet aan de eisen uit de irrigatie- en drainagepraktijk. een Bibliography Akers, P., and Harrison, A.J.M Critial depth flumes for flow measurements in open hannels. Hydrauli Researh Paper pp. Department of ndustrial and Sientifi Researh, Hydrauli Researh Station, Wallingford, U.K. Arredi, F Disussion of Adaptation of Venturi flumes to flow measurements in onduits' by H.K. Palmer and F.D. Bowlus. Proeedings of the Amerian Soiety of Civil Engineers. Vol 62: 4: pp Ba1loffet, A Critial flow meters (Venturi flumes). Proeedings of the Amerian Soiety of Civil Engineers. Vol 81: Paper 743. Bazin, H.E Exp~rienes nouvelles sur l'~oulement en d~versoir. Annales des Ponts et Chauss~es. M~moires et douments, 6 s~rie, 16, 2 semestre, pp , p Paris. Bazin, H.E Exp~rienes nouve1les sur l'~oulement en d~versoir. Annales des Ponts et Chauss~es. Vol. 7, pp Paris. B~langer, J.B Notes sur le ours d'hydraulique. M~moires Eole Nat. des Points et Chauss~es. pp Paris. Blau, E Die modelm~ssige Untersuhung von VenturikanM1en vershiedener Gr~sse und Form. Ver~ffent1ihungen der Forshungsanstalt fur Shiffahrt, Wasser und Grundbau 8. Akademie-Verlag, Berlin, German Demorati Republi. Boiten, W The trapezoidal-profiled broad-rested weir. S170-X, April. 66 pp. Waterloopkundig Laboratorium, Delft.

73 Bos, M.G The Romijn movable measuring/regulation weir. n: Small hydrauli strutures. rrigation and Drainage Paper 26: Food and Agriulture Organization, Rome. Bos, M.G. (Ed.) Disharge measurement strutures. 2nd ed. 464 pp. Publiation 20, mprovement (LR), Wageningen. nternational nstitute for Land Relamation and Bos, M.G. 1977a. The use of long-throated flumes to measure flows in irrigation and drainage anals. Agriultural Water Management, Vol 1: 2: pp Elsevier, Amsterdam. Bos, M.G. 1977b. Disussion of Venturi flumes pp. for irular hannels' by M.H. Diskin. Journal of the rrigation and Drainage Division, Amerian Soiety of Civil Engineers. Vol 103: R3: pp Bos, M.G Standards for irrigation effiienies of CD. Journal of the rrigation and Drainage Division, Amerian Soiety of Civil Engineers. Vol 105: R1: pp Bos, M.G. and Reinink, Y Head loss over long-throated flumes. Journal of the rrigation and Drainage Division, Amerian Soiety of Civil Engineers. Vol.107: R1: pp Bos, M.G., Replogle, J.A., and Clemmens, A.J Flow measuring flumes for open hannel systems. 321 pp. John Wi1ey, New York. Brakensiek, D.L., Osborn, H.B., and Raw1s, W.J. (Coordinators) Field manual for researh in agriultural hydrology. Agriultural Handbook pp. U.S. Government Printing Offie, Washington, D.C. British Standards nstitution Methods of measurement of liquid flow in open hannels. Part 4: Weirs and flumes; 4B: Long-base weirs. British Standard pp. London. British Standards nstitution Methods of measurement of liquid flow in open hannels. Part 4: Weirs and flumes; 4C: Flumes. British Standard Chow, V.T. 52 pp. London Open-hannel hydraulis. 680 pp. MGraw-Hill, New York. Clemmens, A.J., Bos, M.G., and Rep10g1e, J.A RBC broad-rested weirs for irular sewers and pipes. n: The Ven Te Chow Memorial Volume. (G.E. Stout and G.H. Davis, Eds.). Journal of Hydrology, Vo1 68: 1: pp Clemmens, A.J., Replogle, J.A., Bos, M.G Retangular flumes for lined and earthen hannels. Journal of rrigation and Drainage Engineering, Amerian Soiety of Civil Engineers. Vol 110: 2: pp Clemmens, A.J., Replogle, J.A., and Bos, M.G FLUME: a omputer model for estimating flow rates through long-throated measuring flumes. U.S. Dept. of Agriulture (in press). Clemmens A.J., Bos, M.G., and Replogle, J.A Portable RBC-flumes for furrows and earthen hannels. Transations of the Amerian Soiety of Agriultural Engineers (in press). Cone, V.M A new irrigation weir. Journal of Agriultural Researh, 13 Marh: pp U.S. Dept. of Agriulture, Washington, D.C. Cone, V.M The Venturi flume. Journal of Agriultural Researh, Vol 4: 4: pp U.S. Dept. of Agriulture, Washington. D.C. Cornell University Experiments of U.S. Deep Waterways Board. n: Weir experiments, oeffiients and formulas. R.E. Horton, 1907: pp U.S. Government Printing Offie, Washington, D.C. Cornell University 1903, Experiments on model similar to Merrima River Dam at Lawrene, Mass. n: Weir experiments, oeffiients and formulas. R.E. Horton, 1907: pp U.S. Government Printing Offie, Washington, D.C. Delft Hydraulis Laboratory The V-shaped broad-rested weir. S170-V, Jan. 105 pp. Waterloopkundig Laboratorium, Delft. Diskin, M.H Venturi flumes for irular hannels. Journal of the rrigation and Drainage Division, Amerian Soiety of Civil Engineers. Vol. 102: R3: pp Dodge, R.A Ramp flume model study progress summary. 22 pp. U.S. Bureau of Relamation, Denver. Engel, F.V.A.E The Venturi flume. The Engineer. Vol. 158, August 3: pp ; August 10: pp Fane, A.B Report on flume experiments on Shirhing Canal. Punjab rrigation Branh, Paper 110: pp , plate A-G. Punjab Engineering Congress, Bombay. Food and Agriulture Organization Agriulture towards 2000 a normative senario. FAO, Rome.

74 Forhheimer, P Hydrau1ik, Teubner, Leipzig and Berlin. Gravelius, H Herrn Basin's neue Untersuhungen Uber den Abfluss an Ueberfallen. Zeitshrift fur Gew~sserkunde, Vol. 3: 3: pp Leipzig. Gulhati, N.D rrigation in the world : a global review. 130 pp. nternational Commission on rrigation and Drainage, New Dehli. Hall, G.W Analytial determination of the disharge harateristis of broad-rested weirs using boundary layer theory. Proeedings of the nstitution of Civil Engineers, London. Vol. 22: Paper 6607: pp Harrison, A.J.M. 1967a. Boundary-layer displaement thikness on flat plates. Journal of the Hydraulis Division, Amerian Soiety of Civil Engineers. Vol. 93: HY4: pp ; Closure: Vol. 95: HY3: pp Harrison, A.J.M. 1967b. The streamlined broad-rested weir. Proeedings of the nstitution of Civil Engineers, London. Vol. 38: pp Harvey, W.B Harvey's irrigation outlet. Punjab rrigation Branh, Bombay. Horton, R.E. 1907, Weir experiments, oeffiients, and formulas. U.S. Dept. of the nterior, U.S. Geologial Survey. pp.195. U.S. Government Printing Offie, Washington, D.C. nglis, C.C Notes on standing wave flumes and flume meter falls. 35 pp. Tehnial Paper 15. Publi Works Department, Bombay. nternational Standards Organization Liquid flow measurement in open hannels using flumes. Draft Standard SO/DS pp. SO, Geneva. nternational Standards Organization Liquid flow measurement in open hannels : round-nose horizontal rest weirs. Standard pp. SO, Geneva. nternational Standards Organization First draft proposal for an SO standard on liquid flow measurement in open hannels by weirs and flumes : trapezoida1 profile weirs. By ndia. SO/TC 113/SC 2N 329, 332, and 333. SO, Geneva. James, D.W., Hanks, R.J., and Jurinak, J.J Modern irrigated soils. 235 pp. John Wi1ey, New York. Jameson, A.H The Venturi flume and the effet of ontrations in open hannels. Transations of the nstitution of Water Engineers, London: 30 June: pp Jameson, A.H The development of the Venturi flume. Water and Water Engineering: Marh 20: pp Kinghorn, F.C Draft proposal for an nternational Standards Organization standard on the alulation of the unertainty of a measurement of flow rate. Doument SO/TC 30/WG 14:24 E. SO, Geneva. Kraijenhoff van de Leur, D.A Hydraulia : 285-2C. 105 pp. Agriultural University, Wageningen. Landbouwhogeshool Aanvul1end onderzoek V-vormige lange overlaat. Laboratorium voor Hydraulia en Afvoerhydrologie. Nota 35, April. 11 pp. Agriultural University, Wageningen. Landbouwhogeshool Debietmeting in een rioolbuis met behulp van een U-vormige vernauwing. Laboratorium voor Hydraulia en Afvoerhydrologie. Nota 41, Otober. 36 pp. Agriultural University, Wageningen. Lindley, E.S Canal falls and their use as meters. Punjab Engineering Congress, Lahore. Vol. 1: pp Lindley, E.S Measuring irrigation deliveries in the Punjab. Proeedings of the Amerian Soiety of Civil Engineers. Vol. 37:2: pp Mahbub, S.., and Gu1hati, N.D rrigation outlets. 184 pp. Atma Ram and Sons, Delhi. De Marhi, G Dispositivi per la misura della portata dei anali on minime perdite di quota. Parte ll: Risultati delle esperienze. Vol. 14: pp l'energia Elettria, Milano. Meijer-Peter, E., and Muller, R Formulas for bed-load transport. Proeedings seond meeting of the nternational Assoiation for Hydrauli Researh, Vol. 2, No. 2, pp , Stokholm, Sweden. Palmer, H.K., and Bowlus, F.D Adaptations of Venturi flumes to flow measurements in onduits. Transations of the Amerian Soiety of Civil Engineers. Vol. 101: pp Parshall, R.L The improved Venturi flume. Transations of the Amerian Soiety of Civil Engineers. Vol. 89: pp

75 Peterka, A.J (revised 1964). Hydrauli design of stilling basins and energy dissipators. 222 pp. U.S. Department of the nterior, Bureau of Relamation, Washington. D.C. Pitlo, R.H., and Smit, M. weir' by C.D Disussion of Triangular broad-rested Smith and W.S. Liang. Journal of the rrigation and Drainage Division, Amerian Soiety of Civil Engineers. Rafter, G.W On the flow of water over dams. Proeedings of the Amerian Soiety of Civil Engineers. Vol. 26: 3: pp Replogle, J.A Flow meters for water resoure management. Water Resoures Bulletin: Vol. 6: 3: pp Replogle J.A Critial flow flumes with omplex ross-setion. Amerian Soiety of Civil Engineer. Speialty Conferene Proeedings : rrigation and Drainage in an Age of Competition for Resoures. Logan, Utah, U.S.A. Aug , pp Replogle, J.A. 1977a. Disussion of 'Venturi flumes for irular hannels' by M.H. Diskin. Journal of the rrigation and Drainage Division, Amerian Soiety of Civil Engineers. Vol. 103: R3: pp Replogle, J.A. 1977b. Compensating for onstrution errors in ritial flow flumes and broad-rested weirs. n: Flow measurement in open hannels and losed onduits. (L.K. Erwin, Ed.) National Bureau of Standards, Speial Publiation 434: Vol. 1: pp U.S. Government Printing Offie, Washington, D.C. Replogle, J.A Flumes and broad-rested weirs: mathematial modeling and laboratory ratings. n: Flow measurement of fluids. (H.H. Dijstelberger and E.A. North Holland Publishing Company, Spener, Eds.): pp Amsterdam. Rep1ogle, J.A., and Bos, M.G Flow measurement flumes: appliation to irrigation water management. n: Advanes in rrigation: Vol. 1: pp (D. Hillel, Ed.). Aademi Press, New York. Replogle, J.A., and Clemmens, A.J Broad-rested weirs for portable flow metering. Transations of the Amerian Soiety of Civil Engineers. Vol. 22: 6: pp Rep1ogle, J.A., Clemmens, A.J., Tanis, S.W., and MDade, J.H Performane of large measuring flumes in main anals. Amerian Soiety of Civil Engineers. Speialty Conferene Proeedings: Advanes in rrigation and Drainage : Surviving External Pressures. Jakson, Wyoming, July 20-22, pp Robertson, A..G.S Reprinted The magnitude of probable errors in water level determination at a gauging station. TN 7. Water Resoures Board, Reading. U.K. Robinson, A.R and Chamberlain. A.R Trapezoidal flumes for open-hannel flow measurement. Transations of the Amerian Soiety of Agriultural Engineers. Vol. 3: 2: pp Robinson. A.R Water measurement in small irrigation hannels using trapezoida1 flumes. Transations of the Amerian Soiety of Agriultural Engineers. Vol. 9: 3: pp and 388. Robinson. A.R Trapezoida1 flumes for measuring flow in irrigation hannels. 15 pp. U.S. Dept. of Agriulture. ARS U.S. Government Printing Offie, Washington. D.C. Romijn. D.G Een rege1bare meetoverlaat a1s tertiaire aftapsluis. De Waterstaatsingenieur. No. 9. Bandung. Romijn, D.G Meets1uizen ten behoeve van irrigatiewerken hand1eiding door De Vereniging van Waterstaats ngenieurs in Neder1andsh ndie'. 58 pp. Batavia. Rouse. H and ne. S History of hydraulis. 269 pp. owa nstitute of Hydrauli Researh. State University of owa. Ann Harbor. Singer. J.C Disussion of Adaptation of Venturi flumes to flow measurements' by H.K. Pa1mer and F.D. Bowlus. Transations of the Amerian Soiety of Civil Engineers. Vol. 101: pp Skogerboe. G.V Hyatt M.L Anderson R.K. and Egg1eston K.O., et al Design and alibration of submerged open hannel flow measurement strutures. Part 3: Cut-throat flumes. Report WG Utah Water Researh Laboratory, Utah State University. Smith. C.D and Liang. W.S Triangular broad-rested weir. Journal of the rrigation and Drainage Division. Amerian Soiety of Civil Engineers. Vol. 95: R4: pp ; Closure: Vol. 97: R4: 1971: pp

76 - J.JJ - Smith, C.D Open hannel flow measurement with the broad-rested weir. Annual Bulletin, nternational Commission on rrigation and Drainage. pp CD, New Delhi. Stevens, J.C The auray of water-level reorders and indiators of the float type. Transations of the Amerian Soiety of Civil Engineers. Vol 83. Thomas, C.W Common errors in measurement of irrigation water. Journal of the rrigation and Drainage Division, Amerian Soiety of Civil Engineers. Vol. 83: R2: pp U.S. Bureau of Relamation Hydrauli and exavation tables. 11th edition. 350 pp. U.S. Dept. of the nterior. U.S. Government Printing Offie, Washington, D.C. Vierhout, M.M On the boundary layer development in rounded broad-rested weirs with a retangular ontrol setion. Laboratorium voor Hydraulia en Afvoerhydrologie, Rapport pp. Agriultural University, Wageningen. Vlugter, H De regelbare meetoverlaat. 8 pp. Waterloopkundig Laboratorium, Bandung. Vries, M. de Appliation of physial and mathematial models for river problems. 24 pp. Publiation 112. Delft Hydraulis Laboratory. Voortgezet onderzoek van registrerende waterstands meters, Hydraulia Laboratorium Voortgezet onderzoek van registrerende waterstands meters. Nota pp. Agriultural University, Wageningen. Wells, E.A., and Gotaas, H.B Design of Venturi flumes in irular onduits. Transations of the Amerian Soiety of Civil Engineers. Vol. 123: pp Woodburn, J.G Tests of broad-rested weirs. Proeedings of the Amerian Soiety of Civil Engineers. Vol. 56: 7: pp Also Transations of the Amerian Soiety of Civil Engineers. Vol. 96: 1932: pp A A* a B b Cd C v D D a d E EM F Fr f List of symbols f subsripts are omitted, see list of subsripts at end of symbol list ross-setional area perpendiular to flow (flow area) imaginary ross-setional area at ontrol setion for water depth at same elevation as in approah anal entrifugal aeleration of water partile = water surfae or top width of flow bottom width = disharge oeffiient approah veloity oeffiient average or hydrauli depth harateristi partile diameter anal depth total energy head of partile with referene to an arbitrary elevation expansion ratio of diverging transition anal freeboard entrifugal fore Froude number = foal distane for paraboli ontrol shape frition oeffiient aeleration of gravity energy head of flow referened to weir sill height of triangle in omplex shape ontrol loss in energy head over flume or weir energy loss due to frition over throat

77 L'.H energy loss due to frition over diverging transition trans L'.H = energy loss due to frition over part of tailwater hannel anal L'.H f energy loss due to frition over downstream part of struture L'.H d energy loss due to turbulene in the diverging transition h L'.h L a ML n p P L'.p q R r u v head referened to weir sill hange in sill referened flow depth aross flume differene between measured and throat length true value of h length = distane from gauging station to start of onverging transition = length of onverging transition length of diverging transition length of tailwater hannel from developed flow (Setion 2) modular limit Manning roughness oeffiient pressure on water partile sill height relative to hannel bottom = hange in sill height atual flow rate or disharge flow rate for an ideal fluid hange in flow rate = disharge per unit width transition to fully hydrauli radius (flow area/wetted perimeter) radius of streamline urvature hydrauli gradient = hannel bottom slope sediment transport apaity = exponent of head in the head versus disharge equation atual veloity of water partile average veloity of flow X error in disharge from equations or rating tables error in disharge oeffiient error in upstreamsill referened head y Ysub Ysuper Z z a: y P Ps v e Subsripts atual water depth flow depth at subritial flow = flow depth at superritial flow elevation of water partile anal wall sideslope (horizontal to vertial) veloity distribution oeffient ratio of maximum to minimum flow rate to be measured with a struture angle made from enter of pipe to edges of water surfae in irular hannel energy loss oeffiient for downstream transition ripple fator pi = mass density of water relative density mass density of sediments kinemati visosity of fluid angle of opening for prismati hannels 1 orresponds to head measurement setion or gauging station 2 orresponds to setion in tai1water hannel downstream from struture orresponds to ontrol setion within weir or flume throat min max orresponds to minimull design or antiipated flow rate orresponds to maximum design or antiipated flow rate = errror in measured flow rate flow parameter for sediment transport

78 Subjet index Auray of measurement, 50, 52, 98, 103 Approah hannel, 2 Froude number in, 105 Approah veloity oeffiient, 24, for various ontrol shapes, 55, 58 physial meaning, 55 Bakwater effet, 105, 107 Boundary layer, 14 Broad-rested weir (see also long-throated flume) harateristi of, 2 omparison with flume, 2, 98, 109 design proedure, 115 head-disharge equation, 21 history of, 5 limits of appliation, 52, 102 water surfae profile, 89 Control setion, 3, 18 bottom width of, 105 omplex, 40 equivalent shapes of, 40, 42 Froude number at, 105 shapes of, 23 singular, 41 Critial depth, 20 Critial veloity, 21 Curvature of streamlines, 22 Cut-throat flume, 8 Design proedure, 115 Disharge oeffiient, 24 average values, 50 equation for, 52 error in, 52 physial meaning, 43 values, 43, S Drowned flow redution fator, 65 Energy-loss due to frition, 70, 81 due to turbulene, 71, 82, 83 total required, 72 upstream of ontrol setion, 68, 79 Flume (see also long-throated flume) Amerian harateristis, 7 ut-throat, 8 10ng-throated, 1, 3, 5 Parsha1l, 8 RBC, 97 Venturi, 10, 19 Head sill-referened, 2, 104 speifi energy, 20 Head-disharge equation, 21, 59 irular ontrol setion, 30 omplex ontrol setion, 40, 42 paraboli ontrol setion, 30 singular ontrol setion, 41 summary of, 38 retangular ontrol setion, 23 trapezoida1 ontrol setion, 27 triangular ontrol setion, 25 trunated irular ontrol setion, 35 trunated triangular ontrol setion, 25 U-shaped ontrol setion, 33

79 Head loss atual, 97 available, 94 for modular flow, 11, 64, 94 minimum required, 11, 64 deal flow, 22, 59 Long-throated flume advantages of, 3, 112 bakwater effet by, 105 demands plaed on, 90 design proedure, 115 funtion of, 90, 93 head-disharge equation, 21, 59 history of, 5 lay-out of, 1, 12, 97 limits of appliation, 52, 102 portable RBC, 91 Manning' n, 95 Measurement of flow, 1, 115 error in, 51, 103 range of, 102 reason for, 91 Modular limit, 16, 64 estimate of, 73 laboratory tests on, 75, 84 measuring the, 77 required head-loss at, 13, 72 theory for flow at, 67 verifiation of, 84 visual detetion of, 85, 89 Parshall flume, 8 Piezometri level, 19 Rating proedure, 21, 60 RBC flume, 91 Sediment transport apaity, 107 experiments on, 110 Speifi energy, 19 urve, 20 Transition onverging, 1, 14, 53 diverging, 2, 71 downstream,, 54 upstream,, 68 Venturi flume, 10, 19 Water level ontrol, 93 Weir broad-rested, 2 with movable sill, 13, 94 with stationary sill, 94 Zone of aeleration, 18

80 -... L - Curriulum vitae Marinus Gijsberthus Bos was born in 1943, Marh 16 in Ede, The Netherlands. After ompleting his seondary eduation at the Marnix College at Ede, he studied ivil engineering at the University of Tehnology, Delft, graduating (M.S.) in irrigation, with hydraulis and onrete onstrution as minor subjets. He subsequently joined the Food and Agriulture Organization of the United Nations (FAO, Rome), for whom he designed irrigation and drinking water systems in Uganda, irrigation systems in ran, and regional water supply systems in Cyprus and Lebanon. n August 1971 he joined the nternational nstitute for Land Relamation and mprovement (LR) at Wageningen, where he has a remained ative in development aid, working on short assignments in South Ameria, Afria, and the Middle East. With LR, he is engaged in researh on two subjets: the effiieny of irrigation water use and the hydrauli design of disharge measuring and regulating strutures. He oordinates his researh on irrigation effiienies with that of the nternational Commission on rrigation and Drainage (CD) at New Delhi. Sine 1976 he has been hairman of the CD Working Group on rrigation Effiieny. Whilst employed with FAO, he was onfronted with the problems surrounding the measurement and regulation of flow in irrigation anals. mmediately after joining LR, he started to work on this subjet through the informal 'Working Group on Small Hydrauli Strutures', a ooperative effort by the Delft Hydrauli Laboratory, the University of Agriulture at Wageningen, and LR.Sine 1979, he has been ollaborating on researh in this subjet with the U.S. Water Conservation Laboratory, Phoenix, Arizona.

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