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Kinetic Theory of Gas question involving viscosity

  1. Oct 25, 2008 #1
    1. The problem statement, all variables and given/known data
    PLEASE help! I really should be able to do this but am so stuck:

    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!

  2. jcsd
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