Solving Hard Viscosity Q Homework: Find Couple on Disk

[bon]

Homework Statement

Two plane disks, each of radius 5cm, are mounted coaxially with their adjacent surfaces 1mm apart. They are in a chamber containing gas at STP (viscostiy of gas = 2.1 x 10^-5 Ns/m^2) and are free to rotate about the common acis. One of them rotates with angular velocity of 10 rad/s. Find the couple which must be exerted to keep the other stationary.

Homework Equations

The Attempt at a Solution

So letting the bottom plate be where r=0, top plate is at r=0.001

then i say du/dr = w + rdw/dr

textbook says that only the second term contributes to viscous shearing stress...Why is this?

so assuming that to be true,

F = pi (0.05)^2 n r dw/dr where n is the viscosity..

we can then integrate...but isn't the integral dr from 0 to 0.001? and don't we have a lnr between those limits..and ln 0 is a problem?

Help Please :S!

 

[bon]

anyone>

 

[bon]

heloooo?

 

[bon]

*bump*

 

[bon]

101 views and no one knows the answer?