fluid_mechanics

450 Chapter 8 ■ Viscous Flow in Pipes
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 and FlowLab problems
can also be accessed on this web site.
Section 8.1 General Characteristics of Pipe Flow (Also
see Lab Problem 8.130.)
8.1 Obtain a photograph/image of a piping system that would
likely contain “pipe flow” and not “open channel flow.” Print this
photo and write a brief paragraph that describes the situation involved.
8.2 Water flows through a 50-ft pipe with a 0.5-in. diameter at
5 gal/min. What fraction of this pipe can be considered an entrance
region?
8.3 Rainwater runoff from a parking lot flows through a 3-ft-diameter
pipe, completely filling it. Whether flow in a pipe is laminar or
turbulent depends on the value of the Reynolds number. (See Video
V8.2.) Would you expect the flow to be laminar or turbulent? Support
your answer with appropriate calculations.
8.4 Blue and yellow streams of paint at 60 °F (each with a density
of 1.6 slugsft 3 and a viscosity 1000 times greater than water) enter
a pipe with an average velocity of 4 fts as shown in Fig. P8.4.
Would you expect the paint to exit the pipe as green paint or separate
streams of blue and yellow paint? Explain. Repeat the problem
if the paint were “thinned” so that it is only 10 times more viscous
than water. Assume the density remains the same.
Splitter
Yellow
Blue
F I G U R E P8.4
2 in.
25 ft
Green?
8.5 Air at 200 °F flows at standard atmospheric pressure in a pipe
at a rate of 0.08 lb/s. Determine the minimum diameter allowed if
the flow is to be laminar.
8.6 To cool a given room it is necessary to supply 4 ft 3 /s of air
through an 8-in.-diameter pipe. Approximately how long is the entrance
length in this pipe?
8.7 A long small-diameter tube is to be used as a viscometer by
measuring the flowrate through the tube as a function of the pressure
drop along the tube. The calibration constant, K Q¢p, is
calculated by assuming the flow is laminar. For tubes of diameter
0.5, 1.0, and 2.0 mm, determine the maximum flowrate allowed
(in cm 3 /s) if the fluid is (a) 20 °C water, or (b) standard air.
8.8 Carbon dioxide at 20 °C and a pressure of 550 kPa (abs) flows
in a pipe at a rate of 0.04 Ns. Determine the maximum diameter allowed
if the flow is to be turbulent.
8.9 The pressure distribution measured along a straight, horizontal
portion of a 50-mm-diameter pipe attached to a tank is shown in the
table below. Approximately how long is the entrance length? In the
fully developed portion of the flow, what is the value of the wall
shear stress?
x (m) (0.01 m) p (mm H 2 O) (5 mm)
0 (tank exit) 520
0.5 427
1.0 351
1.5 288
2.0 236
2.5 188
3.0 145
3.5 109
4.0 73
4.5 36
5.0 (pipe exit) 0
8.10 (See Fluids in the News article titled “Nanoscale flows,” Section
8.1.1.) (a) Water flows in a tube that has a diameter of
D 0.1 m. Determine the Reynolds number if the average velocity
is 10 diameters per second. (b) Repeat the calculations if the
tube is a nanoscale tube with a diameter of D 100 nm.
Section 8.2 Fully Developed Laminar Flow
8.11 Obtain a photograph/image of a piping system that contains
both entrance region flow and fully developed flow. Print this
photo and write a brief paragraph that describes the situation involved.
8.12 For fully developed laminar pipe flow in a circular pipe, the
velocity profile is given by u(r) 2 (1 r 2 R 2 ) in m/s, where R
is the inner radius of the pipe. Assuming that the pipe diameter is
4 cm, find the maximum and average velocities in the pipe as well
as the volume flow rate.
8.13 The wall shear stress in a fully developed flow portion of a
12-in.-diameter pipe carrying water is 1.85 lbft 2 . Determine the
pressure gradient, 0p0x, where x is in the flow direction, if the
pipe is (a) horizontal, (b) vertical with flow up, or (c) vertical with
flow down.
8.14 The pressure drop needed to force water through a horizontal
1-in.-diameter pipe is 0.60 psi for every 12-ft length of pipe. Determine
the shear stress on the pipe wall. Determine the shear stress
at distances 0.3 and 0.5 in. away from the pipe wall.