Help solving the Rayleigh Problem in fluid dynamics please

AI Thread Summary
The discussion revolves around solving the Rayleigh problem in fluid dynamics, specifically with a time-dependent plate velocity, V(t). Participants are asked to show that the shear stress, defined as tau = du/dy multiplied by absolute viscosity, follows the same diffusion equation as velocity. The problem also requires determining the velocity profile and surface velocity when the plate generates a constant surface shear stress. One user expresses uncertainty about how to begin the problem and seeks assistance. The thread concludes with a suggestion to start a new thread for similar questions, as the original poster is unlikely to respond.
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Homework Statement


Consider the Rayleigh problem, but allow the plate velocity to be a function of time, V(t). By differentiation show that the shear stress, tau = du/dy*absolute viscosity, obeys the same diffusion equation that the velocity does. Suppose that the plate is moved in such a way as to produce a constant surface shear stress. What are the velocity profile and the surface velocity for this motion.


Homework Equations


I'm not sure that these are actually relavant but here is what I assume:

Shear Stress = - Absolute Viscosity*V0 / SQRT(PI *kinematic viscosity*t)

density*dv/dt = absolute viscosity*d^2v/dy^2 => simplified momentum eqn.




The Attempt at a Solution


I'm not sure how to even get started on this problem. Any suggestions or help would be appreciated. Thanks
 
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did you solve the problem?
 
dianaku said:
did you solve the problem?
Welcome to the PF. :smile:

Their last post here was in 2009, so they are not likely to respond to you now. If you have a similar question, go ahead and start a new thread here in the Homework Help, Intro Physics forum and show as much of your work as you can. You should get good help that way.
 

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