Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 1, Problem 1.12P
For low-speed (laminar) steady flow through a circular pipe, as shown in Fig. P1.12, the velocity u varies with radius and takes the form
where µ is the fluid viscosity and Δp is the pressure drop from entrance to exit. What are the dimensions of the constant B?
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The pressure drop (Ap) test is carried out using a pipe configuration as illustrated below:
Manometer 1
Manometer 2
straight pipe
D= 2R R= radius in pipe
The pipe data and the flowing fluid are as follows: Pipe: D = 1 cm; L= 100 cm.
Fluid: Water, with density (A) = 1000 kg/m"; absolute viscosity (u) = 0.001 kg/im.s);
Experimental data is shown as shown in the following table:
Task:
Ja. Plot the graph of the pressure as a function of the average velocity (V.v).
b. Based on the equation for laminar flow in the pipe as follows:
Ap = 32VuL,
Vavg (m/s) Ap (Pa)
0,001
0,002
0,005
0,01
0,02
0,04
0,06
0,08
0,1
0,12
0,15
0,30
0,62
1,61
3,10
6,10
12,10
20,10
26,00
32,50
38,90
47,20
D
Compare the experimental results in the table with the results of
calculations using the above equation. Leave a comment.
Note: Ap = p1-p2.
c. The coefficient of friction (f) in the pipe is formulated as follows:
f- 2DAD
PL(V.)
plot (plot) this distribution of fas a function of the Reynolds number (Re). Re is…
Viscosity can be measured by flow through a thin-bore or
capillary tube if the flow rate is low. For length L, (small)
diameter D« L, pressure drop Ap, and (low) volume flow
rate Q, the formula for viscosity is u = D'Ap/(CLQ), where
C is a constant.
(a) Verify that C is dimensionless. The following data are
for water flowing through a 2-mm-diameter tube which
is 1 meter long. The pressure drop is held constant at
Ap = 5 kPa.
T, °C
10.0
40.0
70.0
Q, L/min
0.091
0.179
0.292
(b) Using proper SI units, determine an average value of C
by accounting for the variation with temperature of the
viscosity of water.
The velocity distribution in a 0.02 m
diameter horizontal pipe conveying carbon
tetrachloride (specific gravity = 1.59,
absolute viscosity = 9.6 x 10-6 Pa sec) is
given by the parabolic equation:
v(r)=0.01(0.12- r?), where v(r) is the velocity
in (m/s) at a distance r in (m) from the pipe
center. What is discharge?
O a.
3.13 x-8 m3/s
O b. None of the mentioned
O c. 1.047 x 108 m3/sec
O d. 4.97 x 109 m3/sec
Chapter 1 Solutions
Fluid Mechanics
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