Answered: Recall that the transverse velocity for…

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Mechanical Engineering

Recall that the transverse velocity for Poiseuille flow is Др -p² + C1 4µL In r + c2 , u(r) = 0

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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Question

Please solve

Recall that the transverse velocity for Poiseuille flow is
Др
p² + cj In r + c2,
4µL
и(г) —
0 <r < R,
where Ap/L is the (constant) pressure gradient, µ is the dynamic viscosity, and L is the length of the tube. Since the solution can't blow
up at r = 0, c = 0, and c2 is determined by the no-slip condition u(R) = 0. Integrating the resulting solution over the cross-section of
the tube gives the flux
AR* Ap
Qo
8µ L
1
Now imagine that the tube has a central catheter so that -R <r < R. Use the solution for u above and apply no-slip conditions at
3
1
R and r = R to compute the flux Q for the catheterized tube.
3
r =
Qo

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