Help solving the Rayleigh Problem in fluid dynamics please

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SUMMARY

The discussion centers on solving the Rayleigh problem in fluid dynamics, specifically with a time-dependent plate velocity, V(t). The shear stress, defined as tau = du/dy multiplied by absolute viscosity, adheres to the same diffusion equation as the velocity. The problem also explores the conditions for achieving a constant surface shear stress and determining the corresponding velocity profile and surface velocity. The relevant equations include the simplified momentum equation and the relationship between shear stress and viscosity.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly the Rayleigh problem.
  • Familiarity with shear stress and its relationship to viscosity.
  • Knowledge of differential equations and diffusion equations.
  • Basic concepts of kinematic viscosity and its role in fluid motion.
NEXT STEPS
  • Study the derivation of the diffusion equation in fluid dynamics.
  • Learn about the relationship between shear stress and velocity profiles in viscous flows.
  • Explore time-dependent boundary conditions in fluid mechanics.
  • Investigate numerical methods for solving differential equations in fluid dynamics.
USEFUL FOR

Students and professionals in fluid dynamics, mechanical engineers, and researchers focusing on viscous flow problems and shear stress analysis.

UFeng
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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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