Answered: Pipe wall Fluid: p, u -D- R \P2 X2 X1…

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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Consider steady, incompressible, laminar flow of a Newtonian fluid in an infinitely long round pipe of diameter D or radius R = D/2. We ignore the effects of gravity. A constant pressure gradient ∂P/∂x is applied in the x-direction, where x₁ and x₂ are two arbitrary locations along the x-axis, and P₁ and P₂ are the pressures at those two locations. Note that we adopt a modified cylindrical coordinate system here with x instead of z for the axial component, namely, (r, ?, x) and (u_r, u_?, u). Derive an expression for the velocity field inside the pipe and estimate the viscous shear force per unit surface area acting on the pipe wall.

Pipe wall
Fluid: p, u
-D-
R
\P2
X2
X1
ӘР Р.- Р,
дх х— X]

P, - P,
X2 - X1
дР
Applied pressure gradient:
constant
%D
дх

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