Mechanical and Materials Engineering Homework Solutions
Problem
#4075

velocity

Consider the steady flow of a Casson Fluid through a rigid circular pipe of radius a, driven by a pressure gradient, show velocity is given by... Please see attachment

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Problem3-2a.doc
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a) Show that the velocity is given by:



Then rewrite this solution in a form that separates the dimensionless
groups.



____________________________________________________________

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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