fluid_mechanics

Problems 133
References
1. Riley, W. F., and Sturges, L. D., Engineering Mechanics: Dynamics, 2nd Ed., Wiley, New York, 1996.
2. Tipler, P. A., Physics, Worth, New York, 1982.
3. Panton, R. L., Incompressible Flow, Wiley, New York, 1984.
Review Problems
Go to Appendix G for a set of review problems with answers. Detailed
solutions can be found in Student Solution Manual and Study
Guide for Fundamentals of Fluid Mechanics, by Munson et al.
(© 2009 John Wiley and Sons, Inc.).
Problems
Note: Unless otherwise indicated, use the values of fluid properties
found in the tables on the inside of the front cover. Problems
designated with an 1*2 are intended to be solved with the
aid of a programmable calculator or a computer. Problems designated
with a 1†2 are “open-ended” problems and require critical
thinking in that to work them one must make various
assumptions and provide the necessary data. There is not a
unique answer to these problems.
Answers to the even-numbered problems are listed at the
end of the book. Access to the videos that accompany problems
can be obtained through the book’s web site, www.wiley.com/
college/munson. The lab-type problems can also be accessed on
this web site.
Section 3.2 F ma along a Streamline
3.1 Obtain a photograph/image of a situation which can be analyzed
by use of the Bernoulli equation. Print this photo and write
a brief paragraph that describes the situation involved.
3.2 Air flows steadily along a streamline from point (1) to point (2)
with negligible viscous effects. The following conditions are measured:
At point (1) z 1 2 m and p 1 0 kPa; at point (2) z 2 10
m, p 2 20 N/m 2 , and V 2 0. Determine the velocity at point (1).
3.3 Water flows steadily through the variable area horizontal pipe
shown in Fig. P3.3. The centerline velocity is given by V
1011 x2 î fts, where x is in feet. Viscous effects are neglected.
(a) Determine the pressure gradient, 0p0x, 1as a function of x2
needed to produce this flow. (b) If the pressure at section 112 is
50 psi, determine the pressure at 122 by 1i2 integration of the pressure
gradient obtained in (a), 1ii2 application of the Bernoulli
equation.
front of the object and V 0 is the upstream velocity. (a) Determine
the pressure gradient along this streamline. (b) If the upstream
pressure is p 0 , integrate the pressure gradient to obtain the pressure
p1x2 for x a. (c) Show from the result of part (b) that
the pressure at the stagnation point 1x a2 is p 0 rV 2 0 2, as
expected from the Bernoulli equation.
Dividing
streamline
V x = 0
0
x
p o Stagnation
a
point
F I G U R E P3.5
3.6 What pressure gradient along the streamline, dpds, is required
to accelerate water in a horizontal pipe at a rate of 30 ms 2 ?
3.7 A fluid with a specific weight of 100 lb/ft 3 and negligible viscous
effects flows in the pipe shown in Fig. P3.7. The pressures at
points (1) and (2) are 400 lb/ft 2 and 900 lb/ft 2 , respectively. The
velocities at points (1) and (2) are equal. Is the fluid accelerating
uphill, downhill, or not accelerating? Explain.
Q
V(x)
= 3 ft
(1)
10 ft
(1)
x
F I G U R E P3.3
(2)
30
F I G U R E P3.7
(2)
3.4 Repeat Problem 3.3 if the pipe is vertical with the flow down.
3.5 An incompressible fluid with density r flows steadily past
the object shown in Video V3.7 and Fig. P3.5. The fluid velocity
along the horizontal dividing streamline 1 x a2 is found
to be V V 0 11 ax2, where a is the radius of curvature of the
3.8 What pressure gradient along the streamline, dpds,
is required
to accelerate water upward in a vertical pipe at a rate of 30 fts 2 ?
What is the answer if the flow is downward?
3.9 Consider a compressible fluid for which the pressure and
density are related by pr n C 0 , where n and C 0 are constants. Integrate
the equation of motion along the streamline, Eq. 3.6, to