1
Homework Set #4:
Due date: 10/12/10, by 12:00 pm
Problem # 1:
A Newtonian fluid fills a long cylindrical tube of radius R held vertically as shown.
The tube
wall is moving upward with velocity V < 0 (V is less than zero if the tube is moving up and z is
defined pointing downward as shown below).
Meanwhile, pressure and gravity push the fluid in
the downward direction (i.e., in the positive z direction).
Newtonian fluid
inside tube
R
z
cylinder wall moves
upward with velocity V
a) You are not asked here (in part (a)) to solve for the velocity u
z
.
If you were to do so, you
would notice how similar this problem is to BSL Example 3.61, and you could use much
of that derivation unchanged in this case.
What is the last equation in BSL Example 3.61
that applies directly to this problem?
In other words, what is the last equation in BSL
Example 3.61 that one could apply directly to this problem without changing anything?
Write your answer on your answer sheet, not here, in the form "a) Equation # 3.6____."
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 Spring '11
 Q.P.NGUYEN
 Fluid Dynamics, BSL Example, long cylindrical tube

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