# Kinetic Theory of Gas question involving viscosity

1. Oct 25, 2008

### rabbit44

1. The problem statement, all variables and given/known data

Two plane disks, each of radius 5 cm, are mounted coaxially with their adjacent surfaces
1 mm apart. They are in a chamber containing Ar gas at S.T.P. (viscosity
2.1×10−5 Nsm−2) and are free to rotate about their common axis. One of them rotates
with an angular velocity of 10 rad s−1. Find the couple which must be applied to
the other to keep it stationary.

2. Relevant equations
I know there's an equation of F/A = viscosity*d<ux>/dz

Where <ux> is the average x-velocity at a given z (z is along the axis).

3. The attempt at a solution

I tried taking ux to be the component of a particle's velocity along the theta direction (perpendicular to the radius of the disc), and replacing it with rw. I then tried to integrate that equation up there wrt z, so that the RHS gives viscosity*r*(w - w0) where w0 is the value given for angular velocity and w is the value at the other disc.

However I am confused as to what F is. I think it's the force exerted on the spinning disc, but if so how do I know what it is? I thought about using Idw0/dt = torque, but w0 is constant. I also thought about centripetal force acting on parts of the disc, but I don't understand how that could be right.

I'm very confused!

Thanks!