Mechanical and Materials Engineering Homework Solutions
Problem
#4096

Fluid mechanics

Consider the steady flow of a Casson Fluid through a rigid circular pipe of radius R, driven by a pressure gradient ...Show that the VOLUME flow rate is given by...Please see attachment.

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Problem3-2b.doc
. What equation and Boundary conditions govern this motion?

Show that the Volume flow rate is given by:



________________________________________________________________

BACKGROUND INFO:

Variables:

radius of pipe (r=a)

radius

Governing Equation:



Boundary Conditions:

u(a) = 0

may be 0 in the core.

Therefore,



radius of “no shear” region

rc depends on (y (which is only a function of fluid composition and (P.

=0 (Plug flow)

full equation applies





Boundary Conditions:

@ U=0, r=a


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