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chapter 3 - PROBLEMS 199 Problems 6.1 Compute the net...

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Unformatted text preview: PROBLEMS 199 Problems 6.1 Compute the net pressure force exerted by the surroundings on the channel shown. The control volume (indicated by the dashed contour) lies entirely outside of the channel. where the pressure is atmospheric (p = pa) everywhere except at the inlets. Assume pressure is constant on all channel cross sections. Problem 6.1 6.2 Compute the net pressure force exerted by the surroundings on the pipe shown. The control volume (indicated by the dashed contour) lies entirely outside of the pipe. where the pressure is equal to its atmospheric value, pa, everywhere except at the inlet where it is p.. Assume pressure is constant on all pipe cross sections. Problem 6.2 6.3 For flow in a channel of height H, the pressure decreases linearly from 1); to p2 over a distance L. For the control volume indicated by the dashed lines, determine the pressure force per unit width (out of the page) on the control volume on each of the four faces. What is the net pressure force? Problem 6.3 6.4 Determine the net pressure force exerted by the surroundings on the duct section shown. The duct width (out of the page) is 4H. The control volume (indicated by the dashed contour) lies entirely outside of the duct, where the pressure is atmospheric (p = pa) everywhere except on duct cross sections. Assume pressure is constant on all duct cross sections. F: E n + Mu l> "B 13 T5 . Problems 6.4, 6.5 6.5 For the duct section shown, you can assume the velocity is constant on all cross sections and that the flow is incompressible. Also, the duct width (out of the page) is 3H . At the inlet and outlets, determine n, (ucn), ff pu(u- n)dA and ff pv(u-n)dA. 2m CHAPTER 6. CONT ROL-VOLUME METHOD PROBLEMS D 6.6 The velocity vector at the outlet from a tank is u = U[l c0843 —.l sin¢]. The l“ m'm 5.13 The figu area is A and the flow is incompressible. Using each of the two control volumes shown, for the flow of velocl' part of the control-volume surface passing through the jet. determine n. (II-n). ff pu(u- n)dA and flow with vel ff pu(u~ n)dA. velocity at Se MIC!!! 6.6 6.7 The pipe cross-sectional area and velocity at the inlet and the outlet are the same and equal to A and U . respectively for incompressible flow into a 180° bend. Assume the velocity is constant on all cross sections. At the inlet and outlet. determine n, (u . n), and ff pu(u - n)dA. Problem V U’ A 6.14 The figl L. ' ' ' ' flow of veloc 3 Ur A flow with ve “W; is W Problem 6.7 ‘ as The figure depicts an inclined channel whose width (out of the page) is 4h. The velocity is constant 5315 A cylil' throughout the control volume. Using the control volume indicated by the dashed lines, compute the drama. 1%] area. A, outer unit normal, it, normal velocity, u - n, and volume flux. u - ml, at tlw inlet and the outlet. and 3 m“ m the veruct Problem 6.8 6.9 The velocity is constant throughout the pipe segment shown, which has one face slanted to the horizontal at an angle a. Compute the area, A. outer unit normal, It. normal velocity. u- n, and volume » , - flux, u-uA, at the inlet and the outlet. HINT: The area of an ellipse with sentimajor axis a and W semiminor axis b is 1rab. , u 6.16 A cylin U L diameter fisl . , _ I and a vertica problem” ‘ . “mum” 6.10 Using Gauss' Theorem (Appendix D. section 044), verify that in computing the mment on'a 6'17 F“ the control volume due to the pressure, p can be replaced by (p - 11.), i.e., that . _ value of the firx (p-p.)ndS=flrxpndS s " ' s 6.11 Water at 68° F flows Steadily with a mass flow rate rh = 1.714 slug/sec through the nozzle shown. WhataretheaveragevelocitiesU anduifthediametersared=3inandD=9in7 I W a J- T Problem W 6.11, 6.12 . , . . . _ . ' 6.18 For the 6.12 Water at 10°C flows steadily With a mass flow rate m = 31.4 kglsec through the nozzle shown. level is charl What are the average velocities U and u if the diameters are d :5 cm and D: 20 cm? answer for d p PROBLEMS 201 6.13 The figure illustrates a jet pump. At Section 1, a high-speed jet of fluid is injected into a uniform flow of velocity U1 in a duct of area A. The fluid mixes and, at Section 2, returns to nominally uniform flow with velocity U2. If the jet velocity is Uj = 15U1 and the jet area is 11,- = {5.4, what is the velocity at Section 2? Assume the flow is steady and incompressible with density p. Problem 6.13, 6.14 6.14 The figure illustrates a jet pump. At Section I, a high-speed jet of fluid is injected into a uniform flow of velocity U1 in a duct of area A. The fluid mixes and, at Section 2, returns to nominally uniform flow with velocity U2 = %U1. If the jet area is Aj = 315-11, what is the jet velocity, Uj? Assume the flow is steady and incompressible with density p. 6.15 A cylindrical tank of diameter D is supplied with an incompressible fluid of density p by a pipe of diameter 715D and velocity U. Fluid leaves the tank through another horizontal pipe of diameter 715D and a vertical pipe of diameter §D. If the velocity in the horizontal pipe is Uh = ;‘;U and the velocity in the vertical pipe is Uu = %U, at what rate, dh/dt, is the level changing in the tank? 6.16 A cylindrical tank of diameter D is supplied with an incompressible fluid of density p by a pipe of diameter fiD and velocity U. Fluid leaves the tank through another horizontal pipe of diameter fiD and a vertical pipe of diameter 5D. If the water level does not change with time and the velocity in the horizontal pipe is Uh = g-U, what is the velocity in the vertical pipe, Uu? ' 6.17 For the cylindrical tank with attached cylindrical pipes shown, the constant 3 is 1. Determine the value of the constant a for which the water level in the tank is constant. mm 6.17, 6.18 6.18 For the cylindrical tank with attached cylindrical pipes shown, compute the rate at which the water level is changing for a = % and fl = %. Indicate whether the tank is filling or emptying. Express your answer for dh/dt as a function of U . d and D. ammo Jm cl; m ammgmé WW waa with“ ...zm(g$& Low/No. k m , ,.,<_._ , ._ .fhfi/f .. [11991.113 mac cit/1nd“)? _. b? T074 HWZJL J L) >iddzU +_ ‘6 d U -o _.__. :7 ALB; 1043. u .om4kmmwb) (it 25 4-971)..) ,. H , 7 “CE )ob‘? : K‘“,%QHQHQ€< .QQ‘DkMS . W Pa + 3A? M_m_ ________________ __ ___ » ”WM _ "060‘ _. m __ N a - ELM“; fie c.v has. onokamginégw MCLSS (QWMakm ‘ _ V/‘« . _C.V‘. - OS _. . - . . / ,__. ,_ a; A ) AI. _ _flg£gflyz (3A is {4M «3qu fiOrM‘g Loc know Wad V.m_&gi” be (M Ma» .._.. ______ 37;: : U3]: ‘ (17 : it)”m...___,_.m_,.W._m_____.._.______ ~_ VfiL: ‘U 9 . L31)? 0 i “I..- / A ———_~—-———-Ave—m _ ~ ~~~—~—«—~—7~ ...
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