# Fluid mechanics :sample question

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Consider the steady flow of a Casson Fluid through a rigid circular pipe of radius R, driven by a pressure gradient . What equation and Boundary conditions govern this motion?

Show that the Volume flow rate is given by:

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BACKGROUND INFO:

Variables:

radius of pipe (r=a)

radius

Governing Equation:

Boundary Conditions:

u(a) = 0

For Casson Flow, 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.

For =0 (Plug flow)

full equation applies

Boundary Conditions:

@ U=0, r=a

Q=

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#### Solution Summary

The solution completes the problems through equations.

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