, Kenya IJERTV2IS International Journal of Engineering Research & Technology (IJERT) ISSN: Vol. 2 Issue 8, August

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1 Some Inestigation Of Incompressible Iniscid Stead Flow In Engineering Sstems: A Case Stud Of he Bernoulli s Equation With Its Application o Leakage In anks Mutua, N. M 1, Wanama, D. S, iogora, P. R 3 1 Mathematics and Informatics, aita aeta Uniersit College, oi, 80300, ena Mathematics and Informatics, aita aeta Uniersit College, oi, 80300, ena 3 Pure and Applied Mathematics, Jomo enatta Uniersit of Agriculture and echnolog, Nairobi, , ena 780

2 Abstract During fluid spill incidents inoling damaged tanks, the amount of the product released ma be uncertain. Man accidents occur under aderse conditions, so determining the olume lost b sounding the tanks ma not be practical. In the first few hours, initial olume estimates often are based on isual obserations of the resulting leels, a notorious unreliable approach. his stud has described a computer based model b Bernoulli s equation that will help in responding to leakages in tanks. 1. Introduction Fluid storage tanks can be damaged in the course of their life and a substantial amount of the fluid lost through leakage. here is need therefore to calculate the rate at which the tank leaks in order to adequatel respond to the situation. he olume of a fluid escaping through a hole in the side of a storage tank has been calculated b the Bernoulli s equation which has been adapted to a streamline from the surface to the orifice. 1.1 Objecties he objecties of the stud are: i. o determine the elocit of the fluid through the opening in the tank. ii. o determine the olume flow rate through the opening. iii. o determine the mass flow rate through the opening. 1. Justification Fluid storage tanks e.g. water reseroirs & petroleum oil tanks are commonl used in our societ toda. his storage tanks are prone to accidents which when not adequatel responded to, great losses will be incurred in terms of mone and also pollution to the enironment. he olume of a fluid escaping through a hole in the side of a storage tank is calculated b the Bernoulli s equation calculator the results of which are useful for deeloping the intuitiel skills of responders and planners in spill releases. 1.3 Literature Reiew Castelli and onicelli (1600) were first to state that the elocit through a hole in a tank aries as square root of water leel aboe the hole. he also stated that the olume flow rate through the hole is proportional to the open area. It was almost another centur later that a Swiss phsicist Daniel Bernoulli (1738) deeloped an equation that defined the relationship of forces due to the line pressure to energ of the moing fluid and earth s graitational forces on the fluid. Bernoulli s theorem has since been the basis for flow equation of flow meters that epresses flow rate to differential pressure between two reference points. Since the differential pressure can also be epressed in terms of height or head of liquid aboe a reference plane. An Italian scientist, Gioanni enturi (1797), demonstrated that the differential pressure across an orifice plate is a square root function of the flow rate through the pipe. his is the first known use of an orifice for measuring flow rate through a pipe. Prior to Gioanni s eperimental demonstration, the onl accepted flow measurement method was b filling a bucket of known olume and counting the number of buckets being filled. he use of orifice plates as a continuous flow rate measuring deice has a histor of oer two hundred ears. Subsequent eperiments, Industr standards online in their demonstration showed that liquids flowing from a tank through an orifice close to the bottom are goerned b the Bernoulli s equation which can be adapted to a streamline from the surface to the orifice. he ealuated three cases whereb in a ented tank, the elocit out from the tank is equal to the speed of a freel bod falling the distance h -also known as orricelli s heorem. In a pressuried tank, the tank is pressuried so that product of grait and height gh is much lesser than the pressure difference diided b the densit. he elocit out from the tank depends mostl on the pressure difference. Due to friction the real elocit will be somewhat lower than these theoretic eamples. On leaking tank models, a recent literature reiew reeals numerous papers describing formulas for calculating discharges of non-olatile liquids from tanks Burgreen (1960); Dodge and Bowls(198); Elder and Sommerfeld (1974); Fthenakis and Rohatgi (1999); Hart and Sommerfeld (1993); oehler(1984); Lee and Sommerfeld (1984); Shoaei and Sommerfeld (1984); Simecek-Beatt et al. here are also computer models aailable in ship salage operations. hese tpes of models estimate the hdrostatic, stabilit, and strength characteristic of a essel using limited data. he models require the user to hae an understanding of basic salage and architectural principles, skills not tpical of most spill responders or contingenc planners. A simple computer model, requiring input of readil aailable data, would be useful for deeloping the intuitiel skills of responders and planners in spill releases. Mathematical formulas hae been deeloped to accuratel describe releases for light and hea oils. Dodge and Bowles (198); Fthenakis and Rohatgi (1999); Simecek-Beatt et al. (1997). Howeer, whether an of these models can describe the unique characteristics of fluids 781

3 accuratel is not known. Obserational data of these tpes of releases are needed to test eisting models, and probabl modif them in the case of a gien fluid. J. Irrig and Drain. Engrg (August 010) carried out eperiments under different orifice diameters and water heads. he dependence of the discharge coefficient on the orifice diameter and water head was analsed, and then an empirical relation was deeloped b using a dimensional analsis and a regression analsis. he results showed that the larger orifice diameter or higher water head hae a smaller discharge coefficient and the orifice diameter plas more significant influence on the discharge coefficient than the water head does. he discharge coefficient of water flow through a bottom orifice is larger than that through a sidewall orifice under the similar conditions of the water head, orifice diameter, and hopper sie. In this research work a simple computer model, based on Bernoulli s equation requiring input of readil aailable data, is used to inestigate leakage from essels or tanks: the case of two pipeline companies (Oil refineries and ena pipeline co.) in the Coast proince of ena. he results are of ital importance in responding to leakages to minimie losses. his template, created in MS Word 003 and saed as Word 003 doc for the PC, proides authors with most of the formatting specifications needed for preparing electronic ersions of their papers. All standard paper components hae been specified for three reasons: 1) ease of use when formatting indiidual papers, ) automatic compliance to electronic requirements that facilitate the concurrent or later production of electronic products, and 3) Margins, column wihs, line spacing, and tpe stles are built-in; eamples of the tpe stles are proided throughout this document. Some components, such as multileelled equations, graphics, and tables are not prescribed, although the arious table tet stles are proided. he formatter will need to create these components, incorporating the applicable criteria that follow. Use the stles, fonts and point sies as defined in this template, but do not change or redefine them in an wa as this will lead to unpredictable results. You will not need to remember shortcut kes. Just a mouse-click at one of the menu options will gie ou the stle that ou want.. Goerning Equations. 1 Oeriew he equations goerning the flow of an incompressible iniscid stead fluid through an orifice in a tank are presented in this chapter. his chapter first considers the assumptions and approimations made in this particular flow problem and the consequences arising due to these assumptions. he conseration equations of mass, momentum, energ to be considered in the stud are stated, Bernoulli s equation deried followed b a model description of the fluid flow under consideration. Finall a simple computer model, requiring input of readil aailable data is built which will be used in inestigating flow rate in chapter three.. Assumptions and approimations he following assumptions hae been made. 1. Fluid is incompressible i.e. densit is a constant and 0. Fluid is iniscid i.e. the fluid under inestigation is not iscous. 3. Flow is stead in that is if F is a flow ariable defined as F (,, t) then F 0 4. Flow is along a streamline. 5. he fluid speed is sufficientl subsonic mach Discharge coefficient C alue is tpicall between 0.90 and Consequences as a result of the assumptions he fact that as the water issues out of the orifice from the tank, the leel in it changes and the flow is, strictl speaking, not stead. Howeer, if A1 A, this effect (as measured b the ratio of the rate of change in the leel and elocit ), is so small that the error made is insignificant. he assumption of incompressibit would not hold at aring temperatures for a fluid like water which has differing densities at different temperatures. Howeer this is taken care of b our model which allows the user to enter determined alues of densities at arious temperatures..4 he Goerning Equations.4.1 Equation of conseration of mass Consider the fluid element of olume fied in space surrounded b a smooth surface S. If the densit of the fluid is and d is the olume element of at a point p in, then the total mass of the fluid in is gien b 78

4 d 1 We let s be an element of the surface S. s, and this fluid is displaced a distance hen if the fluid flows outwards through after time equal to. hen the rate at which mass is leaing the olume element is gien b Lim s t s Lim 0 0 is taken to be speed. If nˆ is the unit normal ector to s, then Lim nˆ f ( f denotes 0 t elocit). hus Lim s s. fnˆ 0 3 his gies the rate of mass flu flowing out of. From 3, the total mass flu flowing out of through S is gien b fnˆ s s 4 From Gauss theorem, equation 4 can be written as s f fnˆ s d 5 From equation 1 the rate at which the mass is changing in olume is d 6 Appling the law of conseration of mass, we hae, Or f d d d f d d 0 f d 0 7 Since is an arbitrar olume, then for equation 7 to hold, we hae f 0 8 And this is the general equation of mass conseration. If is a constant, then equation 8 becomes f 0 9 his is the equation of continuit of an incompressible fluid flow. On the other hand, if the flow is stead i.e. the flow ariables don t depend on time, and then equation 8 reduces to f 0 10 his is the equation of continuit of a stead fluid flow..4. Equation of conseration of energ Consider the fluid element of shown below. ddd as Figure 1: Fluid Element B Fourier s law heat transferred through the face perpendicular to the - ais b conduction is gien b (11) dd he element of heat which leaes the olume element along the -ais is gien b ddd (1) Amount added to through conduction along ais = 783

5 ddd dd d (13) Similarl the amount added to along the - ais and - ais through conduction is ddd and ddd. otal heat added to b conduction ddd t Q (14) (Q is purel due to heat conduction) If we let e be the internal energ per unit mass, then total internal energ of the fluid element i.e. eddd e. (15) From this we hae ddd de de de (16) So dw ddd de ddd or dw de 1 (17) If the fluid is incompressible then 0 dw for incompressible fluids equation (17) reduces to de (18) Adding heat generation b frictional force to equation (18) we hae, de (19) where is known as the dissipation function gien b 3 w u w w u u w u (0) (19) is the general equation of energ of the fluid flow whose elocit components are u, and w if is as defined b (0) It is noted that if the fluid is incompressible = a constant and the internal energ E is a function of t alone, then equation (19) reduces to df (=temperature) df ) ( (1) If e is a function of alone then C f C e () substituting this in (1) we hae t C (3) (3) is the equation of energ of a non- iscous incompressible fluid with constant coefficient of conductiit..43 Equation of motion for compressible fluids Consider a control olume ABCD (of unit depth) in a -D flow field with its centre located at (, ). If the state of stress at (, ) in this -D flow field is represented b,, and, then the surface forces on the four faces of the C can be written in terms of these stresses and their deriaties using alor series. A few of these are shown in the figure below. 784

6 Figure : Control olume he net surfaces forces acting on this element in the - and -directions are easil seen to be F And F If surface,...1 surface, f and 5 force per unit mass, then f are the components of the bod F f And bod, F f bod, B Newton s law of motion..1 So that D Dt 8 And similarl D Dt f f D Dt f 9 D Dt and Dt D ma be epressed in terms of the field deriaties using the Euler acceleration formula which gies f t 30 With similar equations obtained from can now use the epression for p 30, we and (From Fluid Mechanics and its Applications b ija Gupta and Santosh Gupta page 150), we obtain, 31 And f f p p 3 For a general 3-D flow these components can be written in the ector form. f p 33 nown as Naier-Stokes equation. his contains three equations for,,.he LHS of equation 33 represents the fluid acceleration (local and conectie) and is referred to as the inertial term. he term on the right represents the bod force, the pressure and the iscous forces respectiel. In man flows of engineering interest, the iscous terms are much smaller than the inertial terms and thus can be neglected, giing. f p 785

7 his is known as the Euler equation which is applicable to non-iscous flows and plas an important role in the stud of fluid motion..5 Bernoulli s Equation Bernoulli s equation states that the total mechanical energ (consisting of kinetic, potential and flow energ) is constant along a streamline. It is a statement of the conseration of energ in a form useful for soling problems inoling fluids. For a non-iscous, incompressible fluid in stead flow, the sum of pressure, potential and kinetic energies per unit olume is constant at an point. he form of Bernoulli's Equation we hae used arises from the fact that in stead flow the particles of fluid moe along fied streamlines, as on rails, and are accelerated and decelerated b the forces acting tangent to the streamlines. Bernoulli s equation has been obtained b directl integrating the equation of motion of an iniscid fluid. hus equation (34) is the Bernoulli s equation p p g g 34 i.6 Illustration of the fluid flow Fluids flow from a tank or container through a hole/orifice close to the bottom. he Bernoulli equation deried can be adapted to a streamline from the surface of the fluid to the orifice. Figure 3: Flow from a ank P1 1 g. h1 g. h Where P 0 35 h h 1 h 36 Since (1) and () s heights from a common reference are related as (36), and the equation of continuit can be epressed as (37), it is possible to transform (35) to (38). A A1 P1 P g. h A 1 A1 38 A special case of interest for equation (38) is when the orifice area is much lesser than the surface area and when the pressure inside and outside the tank is the same- when the tank has an open surface or ented to the atmosphere. At this situation (38) can be transformed to (39). g. h (39a) Due to friction, the real elocit will be somewhat lower than the theoretic elocit in (39). he actual elocit profile at A will depend on the nature of the orifice. A sharp-edged orifice will result in much -D effects than will a smooth one. In engineering practice, these non-ideal effects are usuall taken care of b introducing an eperimentall obtained correction factor termed the discharge coefficient C. hus (39a) can be epressed as (39b). he coefficient of discharge can be determined eperimentall. For a sharp edged opening it ma be as low as low as 0.6. For smooth orifices it ma be between 0.95 and b Cd. g. h If the tank is pressuried so that the product of grait and height (g.h) is much lesser than the pressure difference diided b the densit, (38) can be transformed to (40). hus the elocit out from the tank depends mostl on the pressure difference. Howeer in our stud, we hae thus concentrated on the ented tank. he pressuried tank will be dealt with in our subsequent studies.. P1 P 40 d In the case of the ented tank, the discharge rate is gien b Q Cd A. g. h 41 he source of error in the equation is the fact that as the water issues out of the orifice from the tank, the leel in it changes and the flow is, strictl A speaking, not stead. Howeer, if, this effect (as measured b the ratio of the rate of 1 A 786

8 change in the leel and elocit ), is so small that the error made is insignificant..7 Water flowing (discharging) from a ented tank, pond, reseroir containing water or other liquid Figure 4: Water discharging from a ented tank he Borda tpe is also known as a re-entrant since it juts into the tank.c alues were obtained from Dall et al. (1993) for circular orifices. Water (or other liquid) draining out of a tank, reseroir, or pond is a common situation. Our calculation allows ou to compute for final liquid depth gien the time the tank has discharged and the initial liquid depth of the fluid. his will be conenient for a tank that we know the initial liquid depth of the fluid but we don t know the final liquid depth. he final liquid depth will gie us the spout depth. (his works for high tanks that one can t climb to measure the fluid depth from the top of the tank). Alternatiel, the user can compute the time needed to lower the water from one depth to a lower depth or to empt the tank. he tank (or pond or reseroir) is open to the atmosphere and it can be clindrical or other crosssection but must hae the same cross-section for its entire height. he orifice can be circular or noncircular, but for our stud, we hae modelled the circular orifice. Hi, Hf, and h are measured erticall from the centerline of the orifice. Hdrostatic pressure will impart a elocit to an eiting fluid jet. he elocit and flow rate of the jet depend on the depth of the fluid. Gien the time the tank has discharged, the initial liquid depth of the fluid, tank diameter/side dimensions (which will gie us tank area), orifice diameter (will gie us orifice area) and discharge coefficient we will compute for final liquid depth which will gie us the spout depth. o calculate the jet elocit and flow rate (both olume and mass), enter the parameters specified on the calculator application. (An interaction of the fluid jet with air is ignored.).9 Equations used in the Calculation Cd. g. h Figure 5: Free discharge iew Q A jet jet CA spout jet.8 Design of Calculator Application In this stud, the free discharge orifice has been modelled. We hae studied on circular orifice geometr where B is orifice diameter. A pull-down menu allows ou to select an orifice tpe. Discharge coefficients for the four orifice tpes are built into the calculation. Built-in alues for orifice discharge coefficients are: Rounded Sharp-edged Short-tube Borda Or Q Cd A. g. h Note: he aboe equations are alid if both the tank and orifice are at the same pressure, een if the pressure is not atmospheric For a tank with a constant cross-sectional geometr A in the plan iew (i.e. as ou look down on it), substitute: dh Q A Integrate h from Hi to Hf and integrate t from 0 to t, then sole for time t, which is the time required for the liquid to fall from Hi to Hf: 787

9 A t H i H f ac g If the tank is circular in plan iew (i.e. looking down on it): A D 4 If the orifice is circular: d a 4 Our calculation allows ou to sole for an of the ariables: a, A, Hf, or t. he orifice and tank can be either circular or non-circular. If noncircular, then the diameter dimension is not used in the calculation. 3.3 Effect of Discharge coefficient on Eit elocit able : Effect of Discharge coefficient on Eit elocit Discharge coefficient Eit elocit Spout Depth Eit elocit 3 Results AND Discussion 3.1 Oeriew his section details the results of our work in form of graphs together with discussion of the results obtained. 3. Effect of Spout Depth on Eit elocit able 1: Effect of Spout Depth on Eit elocit Figure 3b: Effect of Discharge coefficient on Eit elocit Orifices with higher orifice coefficients gie higher eit elocities. his implies that the tpe of orifice will affect the orifice eit elocit. In our case rounded orifice tpe will gie the highest eit elocit followed b short-tube, sharp-edged then finall borda in decreasing elocities. 3.4 Effect of spout depth on discharge rate able 3: Effect of spout depth on discharge rate Spout Depth Discharge Figure 3a: Effect of Spout Depth on Eit elocit Spout eit elocit decreases with decrease in the depth of the spout. his is due to hdrostatic pressure which imparts a elocit to an eiting fluid jet but this pressure decreases when the fluid leel drops. hus the elocit of the jet depends on the depth of the fluid. 788

10 b Ginger Hepler, Jeff Simon & Daid Bednarck) 3.6 Effects of Discharge coefficient on discharge/flow rate able 5: Effects of Discharge coefficient on discharge/flow rate Discharge coefficient Flow rate Orifice area Discha rge Figure 3c: Effect of spout depth on discharge rate he highest depth of spout gies the highest discharge. Decrease in the depth of the spout reduces the rate of discharge. Hdrostatic pressure reduces on reduction of fluid leel imparts a elocit to an eiting fluid jet. hus the elocit and flow rate of the jet depend on the depth of the fluid. 3.5 Effects of Orifice area on Discharge able 4: Effects of Orifice area on Discharge Figure 3e: Effects of Discharge coefficient on discharge/flow rate Orifices with higher orifice coefficients gie higher discharge rates. his implies that the tpe of orifice will affect the discharge rate. In our case rounded orifice tpe will gie the highest discharge rate followed b short-tube, sharp-edged then finall borda in decreasing discharge rate. 3.7 Effects of densit on mass flow rate able 6: Effects of densit on mass flow rate Fluid densit Mass Flow rate Figure 3d: Effects of Orifice area on Discharge he larger the orifice area the larger the rate of discharge and ice ersa. Howeer, increasing orifice sie beond the carring capacit of the sstem has no effect on the flow rate. (From the paper Flow Rate as a Function of Orifice Diameter Figure 3f: Effects of densit on mass flow rate 789

11 Higher fluid densities cause higher mass flow rates. hus the rate of mass flow of a fluid from the tank is directl proportional to the fluid densit 4. Conclusions Man phenomena regarding the flow of liquids and gases can be analed b simpl using the Bernoulli equation. Howeer, due to its simplicit, the Bernoulli equation ma not proide an accurate enough answer for man situations, but it is a good place to start. It can certainl proide a first estimate of parameter alues. We analed the effects of spout depth, orifice area, friction coefficient on the fluid flow rate in a ented tank. he Bernoulli s equation that modelled the fluid flow was obtained b directl integrating the equation of motion of an iniscid fluid. he effect of a certain parameter alue on another was inestigated b aring the parameter and obsering the behaior of the other. In this stud the pressure is constant that is both the tank and orifice are at the same pressure, (een if the pressure is not atmospheric), in that the eiting fluid jet eperiences the same pressure as the free surface. he major analsis is made on orifice geometr more than on tank geometr. A change in orifice geometr in terms of spout depth and tpe affected the flow rate. nowing the duration the tank has leaked enables one to determine the current fluid depth in cases where tanks are too large and the depth can t be determined phsicall. his wa will know whether the tank is empt alread or not. In conclusion, the eit elocit of the fluid is affected b the significant changes in spout depth, orifice area discharge coefficient. he mass flow rate is onl affected b change in the fluid densit. 4. Recommendations For one to respond to an leak scenario, one has to first establish that a leakage reall eists. his is done b arious leak detecting techniques e.g. the leak-measurement computer LC 60 offers irtuall unlimited possibilities for all kinds of leak measurement tests. he model built requires that the user has prior knowledge of the time the tank has leaked. hus this model will be of use practicall when used together with a leak detecting model which establishes the time the leak commenced. Some of the areas that need further research include: i. A pressuried tank, where the tank is pressuried so that the elocit out from the tank depends mostl on the pressure difference. ii. An application model that establishes that a leakage reall eists and then calculate for the discharge rate. iii. Fluid flow for unstead, compressible fluids ACNOWLEDGEMEN he authors wish to thank NCS for the financial support to carr out this research. REFERENCES [1] American Societ for Nondestructie esting, Columbus, OH - McMaster, R.C. editor, Leak esting olume of ASN Handbook. [] American Societ of Mechanical Engineers (ASME) Measurement of fluid flow using small bore precision orifice meters. ASME MFC- 14M-001. [3] Aallone, E.A., Baumeister,. (eds.) (1997), Marks' Standard Handbook for Mechanical Engineers, 11th ed., McGraw-Hill, Inc. (New York).Aallone, E.A., Baumeister,. (eds.) [4] Binder, R.C. (1973), Fluid Mechanics, Prentice- Hall, Inc. (Englewood Cliffs, NJ). [5] Burgreen, D Deelopment of flow in tank draining.journal of Hdraulics Diision, Proceedings of the American Societ of Ciil Engineers. HY 3, pp [6] Colebrook, C.F. (1938), "urbulent Flow in Pipes", Journal of the Inst. Ciil Eng. [7] Fluid Mechanics, 4th Edition b Frank M. White, McGraw-Hill, [8] Gerhart, P.M, R.J. Gross, and J.I. Hochstein Fundamentals of Fluid Mechanics. Addison-Wesle Publishing Co. ed. [9] H. Lamb, Hdrodnamics, 6th ed. (Cambridge: Cambridge Uni. Press, 1953) [10] ing, Cecil Dr. - American Gas & Chemical Co., Ltd. Bulletin #1005 "Leak esting Large Pressure essels". "Bubble esting Process Specification". [11] Munson, B.R., D.F. Young, and.h. Okiishi(1998). Fundamentals of Fluid Mechanics.John Wile and Sons, Inc. 3ed. [1] Potter, M.C. and D.C. Wiggert.1991.Mechanics of Fluids. Prentice-Hall, Inc. [13] Roberson, J.A. and C.. Crowe.1990.Engineering Fluid Mechanics. Houghton Mifflin Co. [14] White, F.M Fluid Mechanics. McGraw-Hill, Inc. 790

12 [15] 00 LMNO Engineering, Research, and Software, Ltd. Online. ttuniteel.backcolor = Color.AntiqueWhite ttoarea.readonl = rue APPENDIX Program code for calculator application in isual basic Public Class frmcalc ttoarea.et = "Will be calculated" ttoarea.backcolor = Color.AntiqueWhite Priate Sub ComboBo6_SelectedIndeChanged(B al sender As Sstem.Object, Bal e As Sstem.EentArgs) Handles cmborificepe.selectedindechange d ttspout.readonl = rue ttspout.et = "Will be calculated" ttspout.backcolor = Color.AntiqueWhite If cmborificepe.selecteditem = "Rounded" hen ttcoeff.et = "0.98" ElseIf cmborificepe.selecteditem = "Sharp-edged" hen "0.6076" ttcoeff.et = rue ttmassflow.readonl = ttmassflow.et = "Will be calculated" ttmassflow.backcolor = Color.AntiqueWhite ElseIf cmborificepe.selecteditem = "Short-tube" hen ttcoeff.et = "0.8" ElseIf cmborificepe.selecteditem = "Borda" hen "0.5096" End If ttcoeff.et = ttarea.readonl = rue ttarea.et = "Will be calculated" ttarea.backcolor = Color.AntiqueWhite tteel.readonl = rue tteel.et = "Will be calculated" tteel.backcolor = Color.AntiqueWhite ttolflow.readonl = rue ttolflow.et = "Will be calculated" ttolflow.backcolor = Color.AntiqueWhite End Sub 791

13 Priate Sub btncalc_click(bal sender As Sstem.Object, Bal e As Sstem.EentArgs) Handles btncalc.click ttarea.readonl = False ttarea.et = "" ttoarea.readonl = False ttoarea.et = "" tankdiam = al(ttdiam.et) CArea = 3.14 * tankdiam * tankdiam / 4 NCArea = (al(ttlength.et) * al(ttwih.et)) If cmbankpe.selecteditem = "Circular" hen Else ttarea.et = CArea ttspout.readonl = False ttspout.et = "" NCArea End If ttarea.et = False False ttmassflow.readonl = ttmassflow.et = "" tteel.readonl = False tteel.et = "" ttolflow.readonl = ttolflow.et = "" coeff = al(ttcoeff.et) height = (al(ttinleel.et)) ^ 0.5 time = al(ttimeank.et) gr = (( / ) ^ 0.5) gr1 = time * Orarea * coeff / ((al(ttarea.et)) * gr) subt = height - gr1 finalheight = subt * subt Dim Orarea, subt, finalheight, olflowrate, coeff, gr, Eel, gr1, CArea, NCArea, height, mass, time, tankdiam, ordiam As Double ordiam = al(ttodiam.et) ttspout.et = finalheight Eel = coeff * (( * * finalheight) ^ 0.5) tteel.et = Eel Orarea = 3.14 * ordiam * ordiam / 4 ttoarea.et = Orarea 79

14 olflowrate = Orarea * coeff * (( * * finalheight) ^ 0.5) ttolflow.et = olflowrate mass = olflowrate * al(ttfluid.et) ttmassflow.et = mass ttuniteel.et = "m/s" ttunitmass.et = "g/s" ttunitoarea.et = "Square Metres" False Used" False False rue ttdiam.readonl = ttdiam.et = "" Else ttdiam.et = "Not ttwih.et = "" ttlength.et = "" ttlength.readonl = ttwih.readonl = ttdiam.readonl = ttunitspout.et = "Metres" ttunitarea.et = "square Metres" "M^3/s" End Sub ttunitolrate.et = Priate Sub ComboBo1_SelectedIndeChanged(B al sender As Sstem.Object, Bal e As Sstem.EentArgs) Handles cmbankpe.selectedindechanged If cmbankpe.selecteditem = "Circular" hen End Sub End If Priate Sub btnrefresh_click(bal sender As Sstem.Object, Bal e As Sstem.EentArgs) Handles btnrefresh.click ttcoeff.et = "" tteel.et = "" ttfluid.et = "" ttinleel.et = "" rue rue Used" Used" ttlength.readonl = ttwih.readonl = ttwih.et = "Not ttlength.et = "Not ttmassflow.et = "" ttoarea.et = "" ttodiam.et = "" ttspout.et = "" ttarea.et = "" ttdiam.et = "" 793

15 ttimeank.et = "" ttlength.et = "" ttwih.et = "" ttuniteel.et = "" ttunitmass.et = "" ttunitoarea.et = "" ttunitspout.et = "" ttunitarea.et = "" ttunitolrate.et = "" ttolflow.et = "" cmborificepe.selecteditem = "" "" End Sub cmbankpe.selecteditem = Priate Sub frmcalc_load(bal sender As Sstem.Object, Bal e As Sstem.EentArgs) Handles MBase.Load End Sub End Class 794