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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(un)dA. 2m CHAPTER 6. CONT ROLVOLUME 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 controlvolume surface passing through the jet. determine n. (IIn). ff pu(u n)dA and ﬂow with vel
ff pu(u~ n)dA. velocity at Se
MIC!!! 6.6
6.7 The pipe crosssectional 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, uuA, 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 (pp.)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 highspeed 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 highspeed 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 = 31511, 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 = gU, 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 ..
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(it 25 4971)..) ,. H , 7 “CE )ob‘? : K‘“,%QHQHQ€< .QQ‘DkMS .
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_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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 Spring '08
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