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# 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:

________________________________________________________________
BACKGROUND INFO:

Variables:
radius of pipe (r=a)

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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