4. Consider fully developed laminar flow in the annular space formed by two concentric cylinders with a pressure gradient, ap/ox, and the inner cylinder stationary. Let r = Rand r = kR. Assuming that the velocity profile is given by u= R² op 4μ &x - () + = ² 1-k² R In(1/k) a) Obtain an expression for the location of the maximum velocity as a function of k. b) Compare the limiting case, k→ 0,with the corresponding expression for flow in a circula pipe. c) Determine the volume flow rate. d) Find an expression for the average velocity. e) Compare the limiting cases for the volume flow rate and average velocity, k→0, with th corresponding expression for flow in a circular pine.
4. Consider fully developed laminar flow in the annular space formed by two concentric cylinders with a pressure gradient, ap/ox, and the inner cylinder stationary. Let r = Rand r = kR. Assuming that the velocity profile is given by u= R² op 4μ &x - () + = ² 1-k² R In(1/k) a) Obtain an expression for the location of the maximum velocity as a function of k. b) Compare the limiting case, k→ 0,with the corresponding expression for flow in a circula pipe. c) Determine the volume flow rate. d) Find an expression for the average velocity. e) Compare the limiting cases for the volume flow rate and average velocity, k→0, with th corresponding expression for flow in a circular pine.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:4. Consider fully developed laminar flow in the annular space formed by two concentric
cylinders with a pressure gradient, op/ax, and the inner cylinder stationary. Let r = Rand
r = kR. Assuming that the velocity profile is given by
u:
[¹-( 7 )² +
+(ma
1
R
R² ap
4μ &x
1-k²
In-
In(1/k) R
a) Obtain an expression for the location of the maximum velocity as a function of k.
b) Compare the limiting case, k→ 0,with the corresponding expression for flow in a circular
pipe.
c) Determine the volume flow rate.
d) Find an expression for the average velocity.
e) Compare the limiting cases for the volume flow rate and average velocity, k →0, with the
corresponding expression for flow in a circular pipe.
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