Help solving the Rayleigh Problem in fluid dynamics please

In summary, the conversation discusses the Rayleigh problem and the relationship between shear stress and velocity in a plate that is moved in a certain way. The equations for shear stress and velocity are provided, but the poster is unsure of how to solve the problem. They are seeking help and suggestions for solving the problem.
  • #1
UFeng
27
0

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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  • #2
did you solve the problem?
 
  • #3
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.
 

Related to Help solving the Rayleigh Problem in fluid dynamics please

1. What is the Rayleigh Problem in fluid dynamics?

The Rayleigh Problem is a classic problem in fluid dynamics that involves the study of a viscous fluid flowing between two parallel plates. It is used to model the behavior of fluid flow in various engineering applications.

2. What are the main equations used to solve the Rayleigh Problem?

The Navier-Stokes equations, which describe the motion of viscous fluids, are the main equations used to solve the Rayleigh Problem. These equations take into account factors such as viscosity, pressure, and velocity to determine the behavior of the fluid.

3. How is the Rayleigh Problem solved?

The Rayleigh Problem is typically solved using numerical methods, such as finite difference or finite element methods. These methods involve discretizing the problem domain into smaller elements and using mathematical algorithms to solve for the flow variables at each point.

4. What are some common challenges when solving the Rayleigh Problem?

One of the main challenges when solving the Rayleigh Problem is the nonlinearity of the Navier-Stokes equations. This can make it difficult to find an analytical solution, and numerical methods may require a significant amount of computational power and time. Additionally, boundary conditions and initial conditions must be carefully chosen to accurately model the physical system.

5. What are some real-world applications of the Rayleigh Problem?

The Rayleigh Problem has applications in various engineering fields, such as fluid mechanics, aerodynamics, and heat transfer. It can be used to model the behavior of fluids in pipes, channels, and other flow systems. It is also relevant in the design of turbines, pumps, and other industrial equipment that involve fluid flow.

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