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Couette Flow Velocity Distribution

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Using the log law, determine the velocity distribution for Couette flow between parallel plates a distance h apart, with U = the velocity of the top plate.

Prove that the centerline velocity is:
(Re/(4*f))^.5=(1/kappa)*ln((.5)*(Re*f)^.5)+B
Re=Uh/nu
f=Tau_wall*h/(mu*U)

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The expert examines Couette Flow velocity distribution for log laws.

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Problem:

Using the log law, determine the velocity distribution for Couette flow between parallel plates a distance h apart, with U = the velocity of the top plate.

Prove that the centerline velocity is:
(Re/(4*f))^.5=(1/kappa)*ln((.5)*(Re*f)^.5)+B
Re=Uh/nu
f=Tau_wall*h/(mu*U)

Solutions:

The logarithmic law of velocity profile in turbulent flows is a good approximation of the full velocity field, excepting a small area near the wall, where a laminar sublayer needs to be considered.
Observing a symmetry of the velocity profile about the centerline (as shown in the figure below), the ...

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