Viscous liquid between two circular discs.

[guitar24]

Homework Statement

That is the problem statement. I can't seem to get started on part a.

For part b I can find the velocity profile of the viscous liquid form the equations of motion relating velocity and change in pressure, find the avg velocity, and find the change in pressure from that.

Any hints ??

Thank you!

 

[LawrenceC]

This is a creeping motion fluids problem like something you experience in a bearing. In this case the pressure gradient in the radial direction equals the Laplacian of the radial velocity times the viscosity. You indicate you can solve for the pressure and velocity profiles so you already are aware of the equation involved. If you integrate the pressure over the area of the disk, that should give you the weight that can be supported.

 

[guitar24]

Thank you for your reply.

So there is no way I can find the weight that can be supported without finding the pressure drop and doing part b first?

I was thinking about integrating the stress Tau(rz) over the area of the top plate to find the force of the fluid on the solid. Would this be correct?

 

[LawrenceC]

Below is a good reference regarding this problem.

http://www.syvum.com/cgi/online/serve.cgi/eng/fluid/fluid306.html

 

[guitar24]

Thank you, I understand it a little better now and the velocity profile I got is the same. But that reference still doesn't mention anything about a force acting on the disc. Regarding to what I said earlier, can I integrate Tau(rz) over the area of the disc to find the force on the plate by the liquid?

 

[LawrenceC]

How do you define Tau(rz). Is it shear stress?

 

[guitar24]

Yes but nvm that isn't correct. I am sure I have to integrate the change in pressure + Tau (zz) (normal stress, but this is 0 for any fluid solid interface) over the disc area. I see what you were saying in your initial comment and you were right. Thank you!