# Torque in Couette Flow

1. Apr 26, 2007

### eddie_spaghetti

Hi there,

I'm attempting to solve a relatively simple problem on steady state rotational couette flow in a rotational viscometer.

There are two cylinders, one within the other, seperated by a layer of viscous fluid.

The internal cylinder is stationary, the external one is rotating at a given constant angular velocity with a given torque. End effects are ignored.

I have to find the general form of the tangential shear stress in the fluid as a function of the radius, r. I have set-up and simplified the tangential Navier Stokes equation with the given initial conditions and I am attempting to equate it to the tangential linear momentum equation, which simplifies to:

Sum of the forces acting on the control volume = 0.

The only force acting on the control volume is the applied torque. My question is: how do I use the torque which is applied to the outer cylinder?

Is it simply: F*(internal Radius of the outer cylinder) = torque
or F = torque/(internal Radius of the outer cylinder)

Or do I have to do something more such as applying it over the entire surface of the outer cylinder?