Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 1, Problem 1.58P
The laminar pipe flow example of Prob. 1.12 can be used to design a capillary viscometer [29]. If Q is the volume flow rate, L is the pipe length, and ?p is the pressure drop from entrance to exit, the theory of Chap. 6 yields a formula for viscosity:
Pipe end effects are neglected [29]. Suppose our capillary has r0 — 2 mm and L — 25 cm. The following flow rate and pressure drop data are obtained for a certain fluid:
| Q, m3/h | 0.36 | 0.72 | 1.08 | 1.44 | 1.80 |
| ?p, kPa | 159 | 318 | 477 | 1274 | 1851 |
What is the viscosity of the fluid? Note: Only the first three points give the proper viscosity. What is peculiar about the last two points, which were measured accurately?
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The laminar pipe flow example of"
design a capillary viscometer|. If Q is the volume flow
rate, L is the pipe length, and Ap is the pressure drop from
entrance to exit, the theory of Chap. 6 yields a formula for
viscosity:
can be used to
8LQ
Pipe end effects are neglected [29]. Suppose our capillary
has r, = 2 mm andL = 25 cm. The following flow rate and
pressure drop data are obtained for a certain fluid:
Q. m'h
0.72
0.36
1.08
1.44
1.80
Ap, kPa
159
318
477
1274
1851
What is the viscosity of the fluid? Note: Only the first three
points give the proper viscosity. What is peculiar about the
last two points, which were measured accurately?
Q4: Use dimensional analysis to show that in a problem involving shallow water
waves (Figure 1), both the Froude number (Fr
T) and the Reynolds number
%3|
Vgh
(Re =
pch
are relevant dimensionless parameters Fr = f (Re). The wave speed c of
waves on the surface of a liquid is a function of depth h, gravitational acceleration
g, fluid density p, and fluid viscosity u.
P.u
Figure 1
The differential equation for small-amplitude vibrations
y(r, f) of a simple beam is given by
a*y
+ E = 0
ax
pA
where p = beam material density
A = cross-sectional area
I= area moment of inertia
E = Young's modulus
Use only the quantities p, E, and A to nondimensionalize y, x,
and t, and rewrite the differential equation in dimensionless
form. Do any parameters remain? Could they be removed
by further manipulation of the variables?
Chapter 1 Solutions
Fluid Mechanics
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