Implementation of Spur Dikes to Reduce Bank Erosion of Temporary Diversion Channels During Barrages Construction
|
|
- Tyler Todd Palmer
- 5 years ago
- Views:
Transcription
1 Australian Jurnal f Basic and Applied Sciences, 3(4): , 2009 ISSN Implementatin f Spur Dikes t Reduce Bank Ersin f Temprary Diversin Channels During Barrages Cnstructin Ali Talaat, Karima Attia, Gamal Elsaeed, Mhammad Ibraheem 1 Department f Hydraulics and Irrigatin, Ain Shams University Department f Hydraulics and Irrigatin, Nile Research Institute, Natinal Water Research Center. 3 Department f Civil Engineering, Faculty f Engineering, Shbra, Banha University. 4 Department f Civil Engineering, Faculty f Engineering, Shbra, Banha University. 2 Abstract: This study was initiated t intrduce nn-submerged spur dikes as training structures t reduce ersin at the ppsite bank t diversin channel at Naga Hammadi barrage thrugh minimizing the velcity values near the banks. The length f the bank t be prtected is 450m. The width f diversin channel is 172m; hwever the average channel width at the regin under study is 450m. A tw dimensinal mathematical mdel were used t simulate many cases. T assure mdel validity, experimental results were used fr verificatin. The mdel simulated lngitudinal and transverse velcities as well as the spur wrking length. A financial ecnmic evaluatin as a functin f grin length is intrduced t help in selecting the ptimum grup with minimum cst. Eighteen runs (18) were executed where three (3) effective parameters were tested. These parameters were the cntractin rati, which is defined as the spur length t the channel width (L/B), the spur rientatin angle; and the spur spacing. The cntractin rati was varied between 0.1 and 0.2 while the used O O O rientatin angle are 60, 90 and 120 and the spacing was 2, 4, and 7 times as much as the spur length. The measurements cvered 60 grid pints alng fur lngitudinal lines (A, B, C, and D) crssed by 15 lateral crss sectins. The study cncluded that the maximum spur wrking length is ccurred with repelling spurs f 120 with a 0.2 cntractin rati at 2L r 4L spacing. On the ther hand, 7L spacing prduced the minimum wrking length in additin t its discntinuity. It was als fund that the wrking length is inversely prprtinal t the spur spacing but it is directly prprtinal t the spur length fr a fixed rientatin angle and spacing. The maximum and minimum values f lngitudinal velcity ccurred in the case f using a spur with an rientatin angle f 90 0 with a cntractin rati f 0.2. It was als nticed that changing the spur length, spacing, and rientatin angles did nt affect the maximum transverse velcities. Fr the tested cases, the maximum and minimum transverse velcities are lcated at the middle third f the channel. There is a clear similarity between the lngitudinal velcity in case f implementing repelling and straight spurs. Fr fixed spur length and spacing, using a grup f spurs at any rientatin angle, bth lngitudinal and transverse velcities decrease at the different crss sectins in the vicinity f the bank by 50% and 20%, respectively. Using a grup f 10% cntractin rati length presents mre ecnmic slutin frm the view f cst evaluatin when cmpared t 20% cntractin rati length. The study recmmended that 4 spur riented at 60 with 10% cntractin rati length and spacing f 4 times spur length can be used t prtect the attacked 450m at the bank facing the temprary diversin channel, while the repelling and straight types spur with 0.2 cntractin rati culd be implemented t prduce a deep channel. The scur assciated t spurs existence is discussed in a separate paper. Key wrds: Oriented Spur dike, mathematical mdel, velcity cmpnents, and wrking length. INTRODUCTION In rder t cnstruct a regulating structure like a barrage, a temprary artificial channel f smaller width is established after which cffer dams r diaphragm walls are cnstructed t dewater the cnstructin site t allw the wrkers and equipments t perate at the ftings and the main skeletn f the barrage. After the clsure f the cnstructin site, the full surge f water way is diverted t the artificial channel. On the ther hand, after pening the diversin channel the flw decelerates at the inlet due t the gradual cntractin. Hwever this phenmenn is reversed at the utlet due t the gradual enlargement. Cnsequently, the flw Crrespnding Authr: Gamal Elsaeed, Departmentf Civil Engineering, Faculty f Engineering, Shbra,Banha University 3190
2 exits the diversin channel with high velcity t strike the ppsite bank f the diversin channel thus causing its ersin. The implementatin f spur dikes t minimize the impacts n the ppsite bank f the diversin channel is investigated in this study. The spurs may be defined as a structure extending utward frm the bank f a stream fr the purpses f bank prtectin by deflecting the main current away frm critical znes (Klingeman, P.C., S.M. Kehe, 1984). This research was thus initiated in rder t define the ptimum grup f spurs that minimizing the bank ersin prblem. Many parameters are invlved t define the ptimum grup, the spur length, spacing, and rientatin angles. The spur implementatins cver bank length f 450 m, the number f spurs depends n the invlved parameters especially spur length and spacing. The effect f these parameters n the flw pattern and velcities in the diversin channels is studied. A tw dimensinal finite element mathematical mdel was develped by Mlinas and Hafez (2000) is used in this study. Fig. 1: General Layut Study Cases: A number f runs were simulated using the mathematical mdel; ne f which represented the flw pattern withut any spurs. This run was used as a reference t allcate the hydraulic perfrmance f spur dike implementatin at the ppsite bank f the diversin channel. The runs names are frmulated as spacing, functin f spur type, and cntractin rati. Fr example, 2A 10 means that the spur spacing is equal t 2L at O a 60 (attracting spur) with 10% cntractin rati, and 4S 20 means that the spur spacing is equal t 4L at a O O 90 (straight spur) with 20% cntractin rati, while 7R 10 means that the spur spacing is equal t 7L at a 120 (repelling spur) with 10% cntractin rati. Mrever, the spur lengths crrespnding t 10% and 20% cntractin rati are 45m and 90m respectively, as the average channel width is 450. It shuld be mentined that in all the tested cases the grup f grins cvered a channel length f 450m. This was achieved by changing the number f grins t fit the assigned 450m accrding t spur length and spacing. Table 1 shws the number f grins used fr each run and all ther details related t spur length, spacing, cntractin ratis and rientatin angles. 3191
3 Table 1: The Study Simulated Cases Run Name L/B Number f Grins Angle f Orientatin Spur Name 0 2A Attracting 4A A A A A S Straight 4S S S S S R Repelling 4R R R R R MATERIALS AND METHODS Mathematical Mdel: The develped mdel gverning differential equatins are in the Cartesian X-Y crdinates, alng and acrss the main flw directin, respectively. On the ther hand, the Navier Stkes equatins are used t describe mtin. The fluid is assumed t be incmpressible and fllws a Newtnian shear stress law, whereby, viscus frce is linearly related t the rate f strain. In the mdel, the hydrdynamics gverning equatins are the equatins f cnservatin f mass and mmentum. Cnservatin f mass equatin takes the frm f the cntinuity equatin while Newtn s equatins f mtin in tw dimensins express the cnservatin f mmentum. The cntinuity equatin is given as: (1) The mmentum equatin in the lngitudinal (X) directin is (2) The mmentum equatin in the lateral (Y) directin is (3) Where U = Lngitudinal surface velcity, V = Transverse surface velcity, P = Mean pressure, n e = Kinematics eddy viscsity, F x = Bdy frce in X directin, F y = Bdy frce in Y directin, g = Gravity acceleratin, q = Average water surface slpe, r = Fluid density, ô fx = Turbulent frictinal stresses in X- directin, ô = Turbulent frictinal stresses in Y-directin. fy The assumptins used in the hydrdynamic mdel are: The density is assumed t be cnstant (incmpressible fluid). 3 Flw cnditins are cnstant (discharge=2900m /s). The turbulent viscsity varies with the velcity gradient. Tw-dimensinal surface analysis. Free surface as a rigid lid. Pressure is cnsidered t be hydrstatic. Wind stresses are neglected. 3192
4 It shuld be mentined that cmplete details abut numerical slutin f the mdel gverning equatins, the bundary cnditins and the wrking flw chart is presented in Ebraheem (2005). List f Symbls: The fllwing symbls are used in this paper: L = Spur length [m] U = Lngitudinal surface velcity [m/s] V = Transverse surface velcity [m/s] 2 P = Mean pressure [kg/m ] 2 n e = Kinematics eddy viscsity [m /s] F x = Bdy frce in X directin = g sin è [kg.m/s 2 ] F y = Bdy frce in Y directin = 0.0 [kg.m/s 2 ] g = acceleratin due t gravity [m/s 2 ] S= spacing between spurs [m] q = Average water surface slpe [degrees] 3 r = Fluid density [kg/m ] 2 ô fx = Turbulent frictinal stresses in X-directin [kg/m ] 2 ô = Turbulent frictinal stresses in Y-directin [kg/m ] fy Mdel Testing, Validity and Verificatin: T verify the effectiveness f the numerical mdel fr flw simulatin, a previus experimental study, carried ut in the Hydraulics Research Institute (HRI) Ministry f Water Resurces and Irrigatin, Egypt fr Naga Hammadi Barrage, is used. A cmparisn between the numerical and physical results was achieved at tw crss sectins ut f ten (crss sectin 6 and 7, at 50 m and 51.6 m respectively), frm the experiment inlet, Figure 2. These 2 sectins represent sectins at 1500m and 1550m, respectively, in the field (prttype). 3 The results are presented fr a discharge f 1500m /s. The figure indicates gd agreement between the mdel results and the experiment data. This insures the capability f the current mdel t reprduce cnfident results. Fig. 2: Testing the Validity f the Used 2-D Numerical Mdel 3193
5 RESULTS AND DISCUSSION The fllwing sectins shw the results f the several executed simulatins. The Wrking Length: The spur wrking length is defined as the spur influence length which is extended upstream and dwnstream the spur lcatin. T investigate the wrking length by the aid f velcity vectrs, a finite element mesh was created. It cnsisted f mre than 7200 measuring ndal which requires a lng time in running the mdel. Figure 3 shws a part f the created mesh. Fig. 3: Part f the Created Finite Element Mesh The wrking length fr a grup f spurs is the summatin f bth separatin pint and reattachment lengths. Using a grup f spurs may perfrm a cntinuus r separated wrking length. The cntinuus is the mst favrable as it prvides a week regin f flw in frnt f the bank that shuld be prtected. This is shwn in Figures 4 (a, b, and c) where the arrws define the velcity vectrs in the channel. Fig. 4(a): Flw Pattern arund Attracting Type Spur 3194
6 Fig. 4(b): Flw Pattern arund Straight Type Spur Fig. 4(c): Flw Pattern arund Repelling Type Spur Table 2 summarizes the ttal wrking length fr the different simulated cases. Frm the table it culd be nticed that the maximum wrking length was btained in case f implementing repelling spurs f 120 with 0.2 cntractin rati and 2L r 4L spacing. It culd als be nticed that such spurs create a separatin pint length at the upstream in additin t the reattachment length at the dwnstream (which are the tw cmpnents f wrking length). This agreed with what was cncluded by Ebraheem (2005) and Attia (2006). It was als nticed that the wrking length is inversely prprtinal t the spacing between spurs. Fr fixed rientatin angle and spacing, the wrking length is directly prprtinal t the spur length. The abve table illustrates that the wrking length was discntinuus, fr all the simulated cases f spurs with spacing f 7L at any rientatin angle and cntractin rati. Frm Table 2 it is nticed that the ptimum grups fr bank prtectin are 2A and 2S as they present the lngest wrking length Velcities: The imprtance f velcity in defining the ptimum grup f spurs fr bank prtectin can nt be neglected. The velcity is cnsidered t be a fcal parameter fr flw characteristics which helps t indicate the psitins f scur and depsitin due t spurs existence. The velcity was measured at 60 lcatins distributed alng fur lines in the lngitudinal directin and at 15 crss sectins, 40m apart. It shuld be mentined that the lngitudinal lines (A and B) are distributed t cver the channel width in rder t define the flw pattern in the vicinity f spurs. As fr line C and D, they are used t define the behavir f the velcity at the middle f the channel and at the ppsite bank, respectively, Table 3 and Figure 4. It shuld be mentined that line (A) is lcated prir t grin tip by 5m and 50m fr grup with 10% and 20% cntractin rati respectively. Hwever line (B) is lcated prir t grin tip by 10m nly fr the grup f 20% cntractin rati. 3195
7 Table 2: The Wrking Length and Its Cntinuity Run Name Wrking Length (m) Wrking Length Functin Cntinuity f Wrking Length in Length (L) Basic A A A X 2A A X 7A X 2S S S X 2S S X 7S X 2R R R X 2R R X 7R X 20 Table 3: The Distance between Right Bank and Measuring Lines after Diversin Channel Line A B C D Distance Frm Right Bank (m) Fig. 5: Lcatin f Velcity Measurements A summary f the btained velcity values resulted frm the different simulatins is presented in tables 4 and 5, where the maximum and minimum lngitudinal and transverse velcities are given fr each run tgether with their lcatins with respect t the crss sectin number and line symbl. Lngitudinal Velcity: Table 4 shws that the maximum and minimum lngitudinal velcity (U max, and U min) that ccurred when 0 using a 90 (straight spur) with 20% cntractin rati. These results are in agreement with the results btained by Attia (2006). That assures the fact that using straight spurs with lng lengths, with spacing 4L r less, makes the grup f spurs acting as a firewall against flw which, by its turn, decrease the width f channel and increase the velcity at the middle f the channel and the ppsite bank, t the erected spurs, as well. This 3196
8 Table 4: Lcatins f the Maximum and Minimum Lngitudinal Velcities Run Name Max. U (m/s) Lcatin Min. U (m/s) Lcatin Line X-Sec Line X-Sec Basic C D 5 2A C D 5 4A C D 4 7A C D 5 2A C A 6 4A C A 6 7A C A 6 2S C D 4 4S C A 8 7S C D 5 2S C A 9 4S C A 14 7S C A 5 2R C D 6 4R C D 4,5 7R C D 5 2R C A 8 4R C A 13 7R C D 5 7S C D 5 10 Table 5: Lcatins f the Maximum and Minimum Transverse Velcities Run Name Max. V (m/s) Lcatin Min. V (m/s) Lcatin Line X-Sec Line X-Sec Basic C C 14 2A C C 12 4A C C 13 7A C C 12 2A C C 10 4A C C 12 7A C C 15 2S C C 11 4S C C 12 7S C C 12 2S C C 10 4S C C 11 7S C C 15 2R C C 12 4R C C 13 7R C C 12 2R C C 10 4R C C 11 7R C C is used t maintain deep channels that are used in navigatin prcesses. In fact this is ne f the main purpses f using spurs. This agrees with the results cncluded by Ebraheem (2005), as well. The table als illustrates that fr all simulated cases, the maximum lngitudinal velcities are directly prprtinal t the spur length and is lcated at the middle third f the channel alng line C (200m frm right bank),especially, at crss sectins 1 and 2 at the mst cntracted regin (after the flw exits the diversin channel). Frm Table 4 it is nticed that the grup f 4A10 presents the ptimum cnditin fr bank prtectin as it presents the minimum values fr bth maximum and minimum lngitudinal velcities when cmpared t the ther cases. Als, it shuld be mentined that the lngitudinal velcity dminates the scur hles assciated t existence f grins, in ther wrds it can be said that the grup f 4A10 presents minimum bed mrphlgical changes. The investigated spacing agrees with what btained by Msselman (2000). Transverse Velcity: The maximum transverse velcities are slightly affected by changing the spur length, spacing, and rientatin angles, as shwn in Table 5. Hwever fr all simulated cases, the maximum and minimum transverse velcities are lcated at the middle third f the channel. This culd be attributed t the fact that as the flw exits the diversin channel, it impacts the right bank. This causes the flw, in behind, t be diverted away frm that regin. This als explains the negative value f the minimum transverse velcity. It was als 3197
9 nticed that, fr all the simulated cases, the repelling grup f spurs has higher values f the maximum transverse velcities than that in cases f using straight and attracting grups. This means that larger and deeper scur hles will ccur in frnt f spurs. Mrever, large amunts f dwnstream sediment ccur due t the dead zne f weak flw presented in terms f velcity. In ther wrds, it can be said that scur hles are inversely prprtinal t the rientatin angle measured frm the dwnstream. This agrees with the results btained by Melville (1992). The table als shws that fr all simulated cases, the maximum values f transverse velcity are inversely prprtinal t the spur length and are directly prprtinal t the spacing between spurs. Frm Table 5 it is nticed that the grup f 4A 10 presents the average values fr bth maximum and minimum transverse velcities which is valuable in preventing depsitin f the facing bank f grins erectin. Effects f the Orientatin Angles n Velcities: T test the effect f the rientatin angles n the flw pattern, the relatinships between the velcity and the rientatin angles are pltted fr the basic case and the simulated cases alng the different lines. The cntractin rati was kept cnstant during this investigatin. The rati 0.10 with spacing f 4L was selected. This rati was chsen based n different simulated cases. This ratin is the mst effective influencing parameter. Figure 6 illustrates that at line (A) there is a clear similarity in the trend f bth the lngitudinal and transverse velcities. Hwever, using a grup f spurs at any rientatin angle decreases the lngitudinal and transverse velcities by 50% and 20% respectively, at the different crss sectins when cmpared t basic case. As fr the peak values f the lngitudinal velcities, fr the repelling grup (120 rientatin angle), they were slightly higher at mst f the crss sectins. On the ther hand, the peak values f the transverse velcity, fr the attracting spurs (60 rientatin angle) are lcated just dwnstream the tip f spur. Fig. 6: Lngitudinal and Transverse Velcities at Line (A) fr 0.1 Cntractin Rati and 4L Spacing Fr Different Orientatin Angles 3198
10 Frm Figure 7, it can be seen that the lngitudinal and transverse velcities, fr line B (80m frm right bank), with attracting spurs shwed lwer values than in case f repelling and straight spurs while bth the repelling and straight spurs have almst equal values. Hwever, using spurs at an angle t the bank imprves the situatin, relative t the basic case, as it decreases the ersive velcity in the vicinity f the right bank. Frm the figure, it can als be cncluded that the lngitudinal velcity is directly prprtinal t the rientatin angle. Hwever, the transverse velcity, using spurs, des nt nticeably change relative t the basic case. Fig. 7: Lngitudinal and Transverse Velcities at Line (B) fr 0.1 Cntractin Rati and 4L Spacing Fr Different Orientatin Angles At the middle f the crss sectin f the channel, alng line (C), the lngitudinal and transverse velcities shw the same trend relative t the basic case using different rientatin angles. Hwever, fr the case f the attracting spurs, lwer values f lngitudinal velcities, relative t the basic case, were bserved. On the cntrary, the repelling and straight spurs gave the greater values relative t the basic case. This means that repelling and straight spurs maintain deep channel fr navigatinal purpses mre than the attracting spurs. Mrever it was nticed that the tested rientatin angles had the same trend and value f the transverse velcity, relative t the basic case. Als, it is nticed that the grup f 4A 10 presents the best slutin t disperse the velcity away frm the attacked bank. At line (D), alng the ppsite bank, the lngitudinal and transverse velcities fr the tested cases shw the same trend relative t the basic case. It shuld als be mentined that the tested cases have higher values relative t the basic case and are directly prprtinal t the crss sectin frm the pint f view f the lngitudinal velcity. On the cntrary, the transverse velcities, fr all the tested cases, are lwer relative t the basic case. They are als inversely prprtinal t the crss sectin. In additin t that, the lngitudinal velcity, in case f the attracting spurs, has a higher value than in case f the tested repelling r straight spurs. The attracting grup presented in 4A 10 prves effective perfrmance in preventing the depsitin at the ppsite bank. 3199
11 Fig. 8: Lngitudinal and Transverse Velcities at Line (C) fr 0.1 Cntractin Rati and 4L Spacing Fr Different Orientatin Angles Fig. 9: Lngitudinal and Transverse Velcities at Line (D) fr 0.1 Cntractin Rati and 4L Spacing Fr Different Orientatin Angles 3200
12 Tables 6 and 7 summarize the average lngitudinal and transverse velcities, respectively, fr a grup f spurs with 10% cntractin rati and 4L spacing at different rientatin angles and velcity lines. Als, the percentage f reductin r increase relative t the basic case is given in the same table. It shuld be nted that the negative sign refers t the reductin in value. Table 6: Average Lngitudinal Velcities at Different Orientatin Angles Angle Line Average Lngitudinal Velcities (m/s) % Basic Case Basic A B C D Table 7: Average Transverse Velcities at Different Orientatin Angles Angle Line Average Lngitudinal Velcities (m/s) % Basic Case Basic A B C D Frm the abve tables, it can be cncluded that, at mst f the velcity lines, bth repelling and straight spurs have apprximately similar values f transverse velcity. Line (C) represents the impact f spur implementatin n the velcity at the middle f the channel. The attracting spurs (60 ) reduced the average lngitudinal velcity, while the straight and repelling spurs prduced greater values relative t the basic case. Therefre, implementing repelling spurs will be useless as it culdn't create a slack flw upstream, while the attracting grup f 4A10 acts efficiently at the attacked bank. It maintains the depth at the middle f the channel and prevents the depsitin at the left bank. Als, it shuld be mentined that using the grup f 4A 10 decreases the velcity in the vicinity f the 450m erded bank by apprximately mre than 65% as an average value. As fr straight spurs, they can be used fr the purpses f bank prtectin and t increase the depth at the middle f channel fr navigatinal aims. Cst Evaluatin Test: The ttal number f grins in each simulatin case plays an imprtant rle in chsing the ptimum slutin fr minimizing bank ersin prblem in the diversin channel. The number shuld prvide enhancement in bank prtectin, at the same time the cnstructin cst shuld be reasnable taking int accunt a fewer numbers f grins never refers t lwer cst. The ttal number f grins is a functin f grin length and spacing such t cver the 450m frm the bank under study. In ther wrds, the ttal number f grins is inversely prprtinal t grin length and spacing. As the angle f rientatin desn't impact n the number f grins; in Figure 10, the symbls A, S, and R are replaced by symbl (G). The present cst evaluatin test fr the simulated cases is a rugh estimatin fr cst as it's presented as a functin f ttal length fr different runs. The ttal length is presented by multiply the grin length by number f grins fr each case. Fig. 10: Ttal Length f Grins fr Different Simulatin Cases 3201
13 Cmbining Table 1 and Figure 10 clearly indicates that, the maximum length was fund fr the grup f 20% cntractin rati and 2L spacing; hwever the number f grins fr that grup is 3 which isn't the maximum ne that indicates the higher cst. Mrever, using a grup f 10% cntractin rati length presents mre ecnmic slutin when cmpared t 20% cntractin rati length. After discussing the technical parameters f wrking length and cntinuity clearly was that, fr different rientatin angles, nly the grups f 10% length with 2 and 4L spacing was technically succeeded in bank prtectin. Hwever, the grup f 4L spacing had the mst ecnmical cst. Cnclusin and Recmmendatins: This research investigated the effect f spur installatin n different parameters. Fr the wrking length it was fund that using repelling spurs (120 with 0.20 cntractin rati with spacing less than 4L) prduced the lngest wrking length. Hwever t keep the wrking length cntinuus it is preferred t use spurs with length less than 10% f the channel width with spacing less than 4L. It was fund that the maximum velcity fr the tested cases is similar t the basic case velcity. On the ther hand, using attracting spurs (0.10 cntractin rati and 60 rientatin angle with spacing f 4L) prved t be the best case fr bank prtectin and sedimentatin prcesses. All maximum lngitudinal velcities are lcated at the middle third f the channel and all minimum lngitudinal velcities are lcated near the channel sides. The maximum and minimum transverse velcities are lcated at the middle third f the channel; als the maximum values f transverse velcities are inversely prprtinal t spur length and are directly prprtinal t the spacing between the spurs. Fr fixed spur length and spacing, it was fund that using a grup f spurs at any rientatin angle decreases the velcity at the different crss sectins in the vicinity f the bank by 50% and 20%, fr the lngitudinal and transverse velcities respectively. At the middle f channel it was fund that nly the attracting spurs shw lwer values than the basic case fr lngitudinal velcities, while at the ppsite bank f erectin it was fund that the tested cases have higher values than the basic case. This means that using attracting spurs is prtecting the bank ptimally due t the impact f diversin channel. Hwever bth repelling and straight spurs maintain deep channel. Hwever, testing the ecnmic cst prved that this case is nt the least cst frm the ecnmical pint f view. The study recmmended that similar study shuld be cnducted using submerged spurs rather than emerged spurs. A checklist shuld be created after simulating mre cases t define the suitability f each type accrding t the tackled prblems. A cmplete ecnmical study shuld be cnducted and evaluated relating t the ptimum technical evaluatins. REFERENCES Attia, K.M. and G. Elsaid, The Hydraulic Perfrmance f Oriented Spur Dike Implementatin in Open Channel Paper presented t Tenth Internatinal Water Technlgy Cnference, Egypt. Ebraheem, M.M.M., Hydrdynamic Behavir f Bank Prtectin Structures (Grins) Thesis Submitted t Faculty f Engineering, Banha University fr partial Fulfillment f the Requirements fr Master Degree f Science in Civil Engineering (Irrigatin & Hydraulics), Egypt, Nvember. Klingeman, P.C., S.M. Kehe and Y.A. Owusu, Stream Bank Ersin Prtectin and Channel Scur Manipulatin Using Rck Fill Dikes and Gabins, (N. WRRI-98), Oregn state University, Water Resurces Research Institute, Crvallis, Oregn, USA. Mlinas, A. and Y.I. Hafez, Finite Element Surface Mdel fr Flw arund Vertical Wall Abutments, Jurnal f Fluid and Structures, 14: Msselman, E., Technical Memrandum n Gryne Length and Spacing, Delft Hydraulics Lab. Cmmunicatin, Delft, The Netherlands. Melville, B.W., Lcal Scur at Bridge Abutment, Jurnal f Hydraulic Engineering, 118(4):
THE HYDRAULIC PERFORMANCE OF ORIENTED SPUR DIKE IMPLEMENTATION IN OPEN CHANNEL
Tenth International Water Technology Conference, IWTC10 2006, Alexandria, Egypt 281 THE HYDRAULIC PERFORMANCE OF ORIENTED SPUR DIKE IMPLEMENTATION IN OPEN CHANNEL Karima Attia 1 and Gamal El Saied 2 1
More informationExaminer: Dr. Mohamed Elsharnoby Time: 180 min. Attempt all the following questions Solve the following five questions, and assume any missing data
Benha University Cllege f Engineering at Banha Department f Mechanical Eng. First Year Mechanical Subject : Fluid Mechanics M111 Date:4/5/016 Questins Fr Final Crrective Examinatin Examiner: Dr. Mhamed
More informationAssume that the water in the nozzle is accelerated at a rate such that the frictional effect can be neglected.
1 HW #3: Cnservatin f Linear Mmentum, Cnservatin f Energy, Cnservatin f Angular Mmentum and Turbmachines, Bernulli s Equatin, Dimensinal Analysis, and Pipe Flws Prblem 1. Cnservatins f Mass and Linear
More informationPressure And Entropy Variations Across The Weak Shock Wave Due To Viscosity Effects
Pressure And Entrpy Variatins Acrss The Weak Shck Wave Due T Viscsity Effects OSTAFA A. A. AHOUD Department f athematics Faculty f Science Benha University 13518 Benha EGYPT Abstract:-The nnlinear differential
More informationEXPERIMENTAL STUDY ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE
EXPERIMENTAL STUD ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE Tmnbu Gt, Masaaki Ohba, Takashi Kurabuchi 2, Tmyuki End 3, shihik Akamine 4, and Tshihir Nnaka 2
More informationFall 2013 Physics 172 Recitation 3 Momentum and Springs
Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.
More informationAircraft Performance - Drag
Aircraft Perfrmance - Drag Classificatin f Drag Ntes: Drag Frce and Drag Cefficient Drag is the enemy f flight and its cst. One f the primary functins f aerdynamicists and aircraft designers is t reduce
More information(1.1) V which contains charges. If a charge density ρ, is defined as the limit of the ratio of the charge contained. 0, and if a force density f
1.0 Review f Electrmagnetic Field Thery Selected aspects f electrmagnetic thery are reviewed in this sectin, with emphasis n cncepts which are useful in understanding magnet design. Detailed, rigrus treatments
More informationENGINEERING COUNCIL CERTIFICATE LEVEL THERMODYNAMIC, FLUID AND PROCESS ENGINEERING C106 TUTORIAL 5 THE VISCOUS NATURE OF FLUIDS
ENGINEERING COUNCIL CERTIFICATE LEVEL THERMODYNAMIC, FLUID AND PROCESS ENGINEERING C106 TUTORIAL 5 THE VISCOUS NATURE OF FLUIDS On cmpletin f this tutrial yu shuld be able t d the fllwing. Define viscsity
More information2D Turbulent Jets on Rough and Smooth Boundaries
IOSR Jurnal f Envirnmental Science, Txiclgy and Fd Technlgy (IOSR-JESTFT) e-issn: 39-,p- ISSN: 39-399.Vlume, Issue Ver. I (April. ), PP 7- www.isrjurnals.rg D Turbulent Jets n Rugh and Smth Bundaries Shazy
More informationBuilding to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.
Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define
More informationAnalysis of Curved Bridges Crossing Fault Rupture Zones
Analysis f Curved Bridges Crssing Fault Rupture Znes R.K.Gel, B.Qu & O.Rdriguez Dept. f Civil and Envirnmental Engineering, Califrnia Plytechnic State University, San Luis Obisp, CA 93407, USA SUMMARY:
More informationCHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India
CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce
More information3. Design of Channels General Definition of some terms CHAPTER THREE
CHAPTER THREE. Design f Channels.. General The success f the irrigatin system depends n the design f the netwrk f canals. The canals may be excavated thrugh the difference types f sils such as alluvial
More informationNGSS High School Physics Domain Model
NGSS High Schl Physics Dmain Mdel Mtin and Stability: Frces and Interactins HS-PS2-1: Students will be able t analyze data t supprt the claim that Newtn s secnd law f mtin describes the mathematical relatinship
More informationChapter 39. A GUIDE TO THE DESIGN OP AIR BUBBLERS FOR MELTING ICE Simon Ince Hydraulics Section, National Research Council Ottawa, Canada
Chapter 39 A GUIDE T THE DESIGN P AIR BUBBLERS FR MELTING ICE Simn Ince Hydraulics Sectin, Natinal Research Cuncil ttawa, Canada INTRDUCTIN The use f air bubblers fr maintaining ice-free areas in lakes
More informationModule 4: General Formulation of Electric Circuit Theory
Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated
More informationUnit code: H/ QCF level: 5 Credit value: 15 OUTCOME 3 - STATIC AND DYNAMIC FLUID SYSTEMS TUTORIAL 3 - VISCOSITY
Unit 43: Plant and Prcess Principles Unit cde: H/601 44 QCF level: 5 Credit value: 15 OUTCOME 3 - STATIC AND DYNAMIC FLUID SYSTEMS TUTORIAL 3 - VISCOSITY 3 Understand static and namic fluid systems with
More informationDetermining the Accuracy of Modal Parameter Estimation Methods
Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system
More informationEffects of piezo-viscous dependency on squeeze film between circular plates: Couple Stress fluid model
Turkish Jurnal f Science & Technlgy Vlume 9(1), 97-103, 014 Effects f piez-viscus dependency n squeeze film between circular plates: Cuple Stress fluid mdel Abstract U. P. SINGH Ansal Technical Campus,
More informationSurface and Contact Stress
Surface and Cntact Stress The cncept f the frce is fundamental t mechanics and many imprtant prblems can be cast in terms f frces nly, fr example the prblems cnsidered in Chapter. Hwever, mre sphisticated
More information7.0 Heat Transfer in an External Laminar Boundary Layer
7.0 Heat ransfer in an Eternal Laminar Bundary Layer 7. Intrductin In this chapter, we will assume: ) hat the fluid prperties are cnstant and unaffected by temperature variatins. ) he thermal & mmentum
More informationStudy Group Report: Plate-fin Heat Exchangers: AEA Technology
Study Grup Reprt: Plate-fin Heat Exchangers: AEA Technlgy The prblem under study cncerned the apparent discrepancy between a series f experiments using a plate fin heat exchanger and the classical thery
More informationmaking triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=
Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents
More informationPhysics 2010 Motion with Constant Acceleration Experiment 1
. Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin
More informationSediment Basin (SB) Description. Appropriate Uses. Design and Installation
Descriptin A sediment basin is a temprary pnd built n a cnstructin site t capture erded r disturbed sil transprted in strm runff prir t discharge frm the site. Sediment basins are designed t capture site
More informationKinematic transformation of mechanical behavior Neville Hogan
inematic transfrmatin f mechanical behavir Neville Hgan Generalized crdinates are fundamental If we assume that a linkage may accurately be described as a cllectin f linked rigid bdies, their generalized
More information, which yields. where z1. and z2
The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin
More informationTHE TOPOLOGY OF SURFACE SKIN FRICTION AND VORTICITY FIELDS IN WALL-BOUNDED FLOWS
THE TOPOLOGY OF SURFACE SKIN FRICTION AND VORTICITY FIELDS IN WALL-BOUNDED FLOWS M.S. Chng Department f Mechanical Engineering The University f Melburne Victria 3010 AUSTRALIA min@unimelb.edu.au J.P. Mnty
More information1.2.1 Vectors. 1 P age. Examples What is the reference vector angle for a vector that points 50 degrees east of south?
1.2.1 Vectrs Definitins Vectrs are represented n paper by arrws directin = magnitude = Examples f vectrs: Examples What is the reference vectr angle fr a vectr that pints 50 degrees east f suth? What is
More informationSimulation of the Coating Process
Jsef Dembický Technical University f Liberec Studentská 2, 461 17 Liberec, Czech Republic E-mail: jsef.dembicky@tul.cz Simulatin f the Cating Prcess Abstract Cating prcesses play a significant rle in the
More informationCHAPTER 8b Static Equilibrium Units
CHAPTER 8b Static Equilibrium Units The Cnditins fr Equilibrium Slving Statics Prblems Stability and Balance Elasticity; Stress and Strain The Cnditins fr Equilibrium An bject with frces acting n it, but
More informationSection 6-2: Simplex Method: Maximization with Problem Constraints of the Form ~
Sectin 6-2: Simplex Methd: Maximizatin with Prblem Cnstraints f the Frm ~ Nte: This methd was develped by Gerge B. Dantzig in 1947 while n assignment t the U.S. Department f the Air Frce. Definitin: Standard
More informationSOLUTION OF THREE-CONSTRAINT ENTROPY-BASED VELOCITY DISTRIBUTION
SOLUTION OF THREECONSTRAINT ENTROPYBASED VELOCITY DISTRIBUTION By D. E. Barbe,' J. F. Cruise, 2 and V. P. Singh, 3 Members, ASCE ABSTRACT: A twdimensinal velcity prfile based upn the principle f maximum
More informationFebruary 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA
February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA Mental Experiment regarding 1D randm walk Cnsider a cntainer f gas in thermal
More informationMODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards:
MODULE FOUR This mdule addresses functins SC Academic Standards: EA-3.1 Classify a relatinship as being either a functin r nt a functin when given data as a table, set f rdered pairs, r graph. EA-3.2 Use
More informationPhys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1
Phys101 Final Cde: 1 Term: 1 Wednesday, May 1, 014 Page: 1 Q1. A car accelerates at.0 m/s alng a straight rad. It passes tw marks that are 0 m apart at times t = 4.0 s and t = 5.0 s. Find the car s velcity
More informationChE 471: LECTURE 4 Fall 2003
ChE 47: LECTURE 4 Fall 003 IDEL RECTORS One f the key gals f chemical reactin engineering is t quantify the relatinship between prductin rate, reactr size, reactin kinetics and selected perating cnditins.
More informationIntroductory Thoughts
Flw Similarity By using the Buckingham pi therem, we have reduced the number f independent variables frm five t tw If we wish t run a series f wind-tunnel tests fr a given bdy at a given angle f attack,
More informationBuoyancy Effect on the Fully Developed Air Flow in Concentric Inclined Annulus
Internatinal Jurnal f Mechanical & Mechatrnics Engineering IJMME-IJENS Vl:3 N:0 46 Buyancy Effect n the Fully Develped Air Flw in Cncentric Inclined Annulus Asmaa Ali Hussein Lecturer Fundatin Of Technical
More informationDepartment of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets
Department f Ecnmics, University f alifrnia, Davis Ecn 200 Micr Thery Prfessr Giacm Bnann Insurance Markets nsider an individual wh has an initial wealth f. ith sme prbability p he faces a lss f x (0
More informationBootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) >
Btstrap Methd > # Purpse: understand hw btstrap methd wrks > bs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(bs) > mean(bs) [1] 21.64625 > # estimate f lambda > lambda = 1/mean(bs);
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationRotating Radial Duct
Internatinl Jurnal f Rtating Machinery 1995, Vl. 2, N. 1, pp. 51-58 Reprints available directly frm the publisher Phtcpying permitted by license nly (C) 1995 OPA (Overseas Publishers Assciatin) Amsterdam
More informationAdvanced Heat and Mass Transfer by Amir Faghri, Yuwen Zhang, and John R. Howell
6.5 Natural Cnvectin in Enclsures Enclsures are finite spaces bunded by walls and filled with fluid. Natural cnvectin in enclsures, als knwn as internal cnvectin, takes place in rms and buildings, furnaces,
More informationNumerical Simulation of the Flow Field in a Friction-Type Turbine (Tesla Turbine)
Numerical Simulatin f the Flw Field in a Frictin-Type Turbine (Tesla Turbine) Institute f Thermal Pwerplants Vienna niversity f Technlgy Getreidemarkt 9/313, A-6 Wien Andrés Felipe Rey Ladin Schl f Engineering,
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationCHAPTER 6 WORK AND ENERGY
CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS 16. REASONING AND SOLUTION A trapeze artist, starting rm rest, swings dwnward n the bar, lets g at the bttm the swing, and alls reely t the net. An assistant,
More informationSections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.
Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage
More informationInterference is when two (or more) sets of waves meet and combine to produce a new pattern.
Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme
More informationMath Foundations 20 Work Plan
Math Fundatins 20 Wrk Plan Units / Tpics 20.8 Demnstrate understanding f systems f linear inequalities in tw variables. Time Frame December 1-3 weeks 6-10 Majr Learning Indicatrs Identify situatins relevant
More informationCurvature Effects on Thermal Buckling Load of DWCNT Under Axial Compression Force
Jurnal f Slid Mechanics Vl. 3,. (0) pp. -8 Curvature Effects n Thermal Buckling Lad f DWCT Under Aial Cmpressin Frce A. Ghrbanpur Arani,,*, M. Mhammadimehr, M. Ghazi Department f Mechanical Engineering,
More informationModeling the Nonlinear Rheological Behavior of Materials with a Hyper-Exponential Type Function
www.ccsenet.rg/mer Mechanical Engineering Research Vl. 1, N. 1; December 011 Mdeling the Nnlinear Rhelgical Behavir f Materials with a Hyper-Expnential Type Functin Marc Delphin Mnsia Département de Physique,
More informationarxiv:hep-ph/ v1 2 Jun 1995
WIS-95//May-PH The rati F n /F p frm the analysis f data using a new scaling variable S. A. Gurvitz arxiv:hep-ph/95063v1 Jun 1995 Department f Particle Physics, Weizmann Institute f Science, Rehvt 76100,
More informationChapter VII Electrodynamics
Chapter VII Electrdynamics Recmmended prblems: 7.1, 7., 7.4, 7.5, 7.7, 7.8, 7.10, 7.11, 7.1, 7.13, 7.15, 7.17, 7.18, 7.0, 7.1, 7., 7.5, 7.6, 7.7, 7.9, 7.31, 7.38, 7.40, 7.45, 7.50.. Ohm s Law T make a
More informationChapter 2 GAUSS LAW Recommended Problems:
Chapter GAUSS LAW Recmmended Prblems: 1,4,5,6,7,9,11,13,15,18,19,1,7,9,31,35,37,39,41,43,45,47,49,51,55,57,61,6,69. LCTRIC FLUX lectric flux is a measure f the number f electric filed lines penetrating
More informationINVESTIGATION OF B-JUMP NEGATIVE STEP IN RADIAL STILLING BASINS
Seventh Internatinal Water Technlgy Cnference Egypt 1-3 April 003 INVESTIGATION OF B-JUMP NEGATIVE STEP IN RADIAL STILLING BASINS A.M. Negm 1, G. M. Abdel-Aal 1, T.M. Owais and A.A. Habib 3 1 Assciate
More informationVane geometry effect on lubrication conditions between vane tip and cam-ring in hydraulic vane machines
Internatinal Jurnal f Mechanical Engineering and Applicatins 015; 3(1-): 1-10 Published nline Nvember 3, 014 (http://www.sciencepublishinggrup.cm/j/ijmea) di: 10.11648/j.ijmea.s.01503010.11 ISSN: 330-03X
More informationNUMERICAL SIMULATION OF CHLORIDE DIFFUSION IN REINFORCED CONCRETE STRUCTURES WITH CRACKS
VIII Internatinal Cnference n Fracture Mechanics f Cnete and Cnete Structures FraMCS-8 J.G.M. Van Mier, G. Ruiz, C. Andrade, R.C. Yu and X.X. Zhang (Eds) NUMERICAL SIMULATION OF CHLORIDE DIFFUSION IN REINFORCED
More information3. Mass Transfer with Chemical Reaction
8 3. Mass Transfer with Chemical Reactin 3. Mass Transfer with Chemical Reactin In the fllwing, the fundamentals f desrptin with chemical reactin, which are applied t the prblem f CO 2 desrptin in ME distillers,
More informationTechnical Bulletin. Generation Interconnection Procedures. Revisions to Cluster 4, Phase 1 Study Methodology
Technical Bulletin Generatin Intercnnectin Prcedures Revisins t Cluster 4, Phase 1 Study Methdlgy Release Date: Octber 20, 2011 (Finalizatin f the Draft Technical Bulletin released n September 19, 2011)
More informationSPH3U1 Lesson 06 Kinematics
PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.
More informationACCELEROGRAPH RECORDINGS OF THE M USA EARTHQUAKE 16 SEPTEMBER, 1972
115 ACCELEROGRAPH RECORDINGS OF THE M USA EARTHQUAKE 16 SEPTEMBER, 1972 B.Gauir SUMMARY On 16 September, 1972 at 04 15 09.8 UT an earthquake f magnitude ML 5.0 ccurred in sutheast Papua within abut 20
More informationAnalysis of Hydrodynamics and Heat Transfer in a Thin Liquid Film Flowing Over a Rotating Disk by the Integral Method
S. Basu B. M. Cetegen 1 Fellw ASME Mechanical Engineering Department, University f Cnnecticut, Strrs, CT 06269-3139 Analysis f Hydrdynamics and Heat Transfer in a Thin Liquid Film Flwing Over a Rtating
More informationA Study on Pullout Strength of Cast-in-place Anchor bolt in Concrete under High Temperature
Transactins f the 7 th Internatinal Cnference n Structural Mechanics in Reactr Technlgy (SMiRT 7) Prague, Czech Republic, August 7 22, 23 Paper #H-2 A Study n Pullut Strength f Cast-in-place Anchr blt
More informationROUNDING ERRORS IN BEAM-TRACKING CALCULATIONS
Particle Acceleratrs, 1986, Vl. 19, pp. 99-105 0031-2460/86/1904-0099/$15.00/0 1986 Grdn and Breach, Science Publishers, S.A. Printed in the United States f America ROUNDING ERRORS IN BEAM-TRACKING CALCULATIONS
More informationChapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Tw Dimensins; Vectrs Vectrs and Scalars Additin f Vectrs Graphical Methds (One and Tw- Dimensin) Multiplicatin f a Vectr b a Scalar Subtractin f Vectrs Graphical Methds Adding Vectrs
More information1. INTRODUCTION. In many polymer processing operations, molten polymers. emerge from dies into a stress field which deforms the
. NTRODUCTON. Histrical ntes f melt spinning prcess n many plymer prcessing peratins, mlten plymers emerge frm dies int a stress field which defrms the melt int a final fabricated shape. This is the case
More informationChem 115 POGIL Worksheet - Week 8 Thermochemistry (Continued), Electromagnetic Radiation, and Line Spectra
Chem 115 POGIL Wrksheet - Week 8 Thermchemistry (Cntinued), Electrmagnetic Radiatin, and Line Spectra Why? As we saw last week, enthalpy and internal energy are state functins, which means that the sum
More informationSuggested reading: Lackmann (2011), Sections
QG Thery and Applicatins: Apprximatins and Equatins Atms 5110 Synptic Dynamic Meterlgy I Instructr: Jim Steenburgh jim.steenburgh@utah.edu 801-581-8727 Suite 480/Office 488 INSCC Suggested reading: Lackmann
More informationCourse Stabilty of Structures
Curse Stabilty f Structures Lecture ntes 2015.03.06 abut 3D beams, sme preliminaries (1:st rder thery) Trsin, 1:st rder thery 3D beams 2:nd rder thery Trsinal buckling Cupled buckling mdes, eamples Numerical
More informationENGI 4430 Parametric Vector Functions Page 2-01
ENGI 4430 Parametric Vectr Functins Page -01. Parametric Vectr Functins (cntinued) Any nn-zer vectr r can be decmpsed int its magnitude r and its directin: r rrˆ, where r r 0 Tangent Vectr: dx dy dz dr
More informationTHE PARTITION OF ENERGY INTO WAVES AND CURRENTS
THE PARTITION OF ENERGY INTO WAVES AND CURRENTS W. Perrie, C. Tang, Y. Hu and B.M. DeTracy Fisheries & Oceans Canada, Bedfrd Institute f Oceangraphy, Dartmuth, Nva Sctia, Canada 1. INTRODUCTION Ocean mdels
More information. (7.1.1) This centripetal acceleration is provided by centripetal force. It is directed towards the center of the circle and has a magnitude
Lecture #7-1 Dynamics f Rtatin, Trque, Static Equilirium We have already studied kinematics f rtatinal mtin We discussed unifrm as well as nnunifrm rtatin Hwever, when we mved n dynamics f rtatin, the
More informationA Few Basic Facts About Isothermal Mass Transfer in a Binary Mixture
Few asic Facts but Isthermal Mass Transfer in a inary Miture David Keffer Department f Chemical Engineering University f Tennessee first begun: pril 22, 2004 last updated: January 13, 2006 dkeffer@utk.edu
More informationMath Foundations 10 Work Plan
Math Fundatins 10 Wrk Plan Units / Tpics 10.1 Demnstrate understanding f factrs f whle numbers by: Prime factrs Greatest Cmmn Factrs (GCF) Least Cmmn Multiple (LCM) Principal square rt Cube rt Time Frame
More informationES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER
ES201 - Examinatin 2 Winter 2003-2004 Adams and Richards NAME BOX NUMBER Please Circle One : Richards (Perid 4) ES201-01 Adams (Perid 4) ES201-02 Adams (Perid 6) ES201-03 Prblem 1 ( 12 ) Prblem 2 ( 24
More informationAnalysis on the Stability of Reservoir Soil Slope Based on Fuzzy Artificial Neural Network
Research Jurnal f Applied Sciences, Engineering and Technlgy 5(2): 465-469, 2013 ISSN: 2040-7459; E-ISSN: 2040-7467 Maxwell Scientific Organizatin, 2013 Submitted: May 08, 2012 Accepted: May 29, 2012 Published:
More information^YawataR&D Laboratory, Nippon Steel Corporation, Tobata, Kitakyushu, Japan
Detectin f fatigue crack initiatin frm a ntch under a randm lad C. Makabe," S. Nishida^C. Urashima,' H. Kaneshir* "Department f Mechanical Systems Engineering, University f the Ryukyus, Nishihara, kinawa,
More information3D FE Modeling Simulation of Cold Rotary Forging with Double Symmetry Rolls X. H. Han 1, a, L. Hua 1, b, Y. M. Zhao 1, c
Materials Science Frum Online: 2009-08-31 ISSN: 1662-9752, Vls. 628-629, pp 623-628 di:10.4028/www.scientific.net/msf.628-629.623 2009 Trans Tech Publicatins, Switzerland 3D FE Mdeling Simulatin f Cld
More informationPhysics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018
Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and
More informationLeast Squares Optimal Filtering with Multirate Observations
Prc. 36th Asilmar Cnf. n Signals, Systems, and Cmputers, Pacific Grve, CA, Nvember 2002 Least Squares Optimal Filtering with Multirate Observatins Charles W. herrien and Anthny H. Hawes Department f Electrical
More informationSupporting information
Electrnic Supplementary Material (ESI) fr Physical Chemistry Chemical Physics This jurnal is The wner Scieties 01 ydrgen perxide electrchemistry n platinum: twards understanding the xygen reductin reactin
More informationNUMBERS, MATHEMATICS AND EQUATIONS
AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t
More informationEquilibrium of Stress
Equilibrium f Stress Cnsider tw perpendicular planes passing thrugh a pint p. The stress cmpnents acting n these planes are as shwn in ig. 3.4.1a. These stresses are usuall shwn tgether acting n a small
More informationWRITING THE REPORT. Organizing the report. Title Page. Table of Contents
WRITING THE REPORT Organizing the reprt Mst reprts shuld be rganized in the fllwing manner. Smetime there is a valid reasn t include extra chapters in within the bdy f the reprt. 1. Title page 2. Executive
More informationYeu-Sheng Paul Shiue, Ph.D 薛宇盛 Professor and Chair Mechanical Engineering Department Christian Brothers University 650 East Parkway South Memphis, TN
Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Prfessr and Chair Mechanical Engineering Department Christian Brthers University 650 East Parkway Suth Memphis, TN 38104 Office: (901) 321-3424 Rm: N-110 Fax : (901) 321-3402
More informationJIRI GALAS Czech Technical University, Engineering, Prague.
Magnetic Separatin News, Vl. 2, pp. 119-136 Reprints available directly frm the publisher Phtcpying permitted by license nly 1988 Grdn and Breach, Science Publishers, Inc. Printed in the United Kingdm
More informationSolution to HW14 Fall-2002
Slutin t HW14 Fall-2002 CJ5 10.CQ.003. REASONING AND SOLUTION Figures 10.11 and 10.14 shw the velcity and the acceleratin, respectively, the shadw a ball that underges unirm circular mtin. The shadw underges
More informationLecture 5: Equilibrium and Oscillations
Lecture 5: Equilibrium and Oscillatins Energy and Mtin Last time, we fund that fr a system with energy cnserved, v = ± E U m ( ) ( ) One result we see immediately is that there is n slutin fr velcity if
More informationFree Vibrations of Catenary Risers with Internal Fluid
Prceeding Series f the Brazilian Sciety f Applied and Cmputatinal Mathematics, Vl. 4, N. 1, 216. Trabalh apresentad n DINCON, Natal - RN, 215. Prceeding Series f the Brazilian Sciety f Cmputatinal and
More informationGeneral Chemistry II, Unit I: Study Guide (part I)
1 General Chemistry II, Unit I: Study Guide (part I) CDS Chapter 14: Physical Prperties f Gases Observatin 1: Pressure- Vlume Measurements n Gases The spring f air is measured as pressure, defined as the
More informationNumerical Simulation of the Thermal Resposne Test Within the Comsol Multiphysics Environment
Presented at the COMSOL Cnference 2008 Hannver University f Parma Department f Industrial Engineering Numerical Simulatin f the Thermal Respsne Test Within the Cmsl Multiphysics Envirnment Authr : C. Crradi,
More informationLecture 17: Free Energy of Multi-phase Solutions at Equilibrium
Lecture 17: 11.07.05 Free Energy f Multi-phase Slutins at Equilibrium Tday: LAST TIME...2 FREE ENERGY DIAGRAMS OF MULTI-PHASE SOLUTIONS 1...3 The cmmn tangent cnstructin and the lever rule...3 Practical
More informationMODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b
. REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but
More informationRelationship Between Amplifier Settling Time and Pole-Zero Placements for Second-Order Systems *
Relatinship Between Amplifier Settling Time and Ple-Zer Placements fr Secnd-Order Systems * Mark E. Schlarmann and Randall L. Geiger Iwa State University Electrical and Cmputer Engineering Department Ames,
More informationOn Huntsberger Type Shrinkage Estimator for the Mean of Normal Distribution ABSTRACT INTRODUCTION
Malaysian Jurnal f Mathematical Sciences 4(): 7-4 () On Huntsberger Type Shrinkage Estimatr fr the Mean f Nrmal Distributin Department f Mathematical and Physical Sciences, University f Nizwa, Sultanate
More informationThe ultra-high energy cosmic rays image of Virgo A
The ultra-high energy csmic rays image f Virg A Radmír Šmída Karlsruhe Institute f Technlgy, Germany E-mail: radmir.smida@kit.edu Ralph Engel Karlsruhe Institute f Technlgy, Germany Arrival directins f
More informationThermodynamics Partial Outline of Topics
Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)
More informationHomology groups of disks with holes
Hmlgy grups f disks with hles THEOREM. Let p 1,, p k } be a sequence f distinct pints in the interir unit disk D n where n 2, and suppse that fr all j the sets E j Int D n are clsed, pairwise disjint subdisks.
More information