Rheometers use steady flow in the annular gap between long coaxial cylinders, one of which is rotated at a constant angular velocity, to measure the viscosity of fluids, especially those with low viscosity.

4. Rheometers use steady flow in the annular gap between long coaxial cylinders, one of which is rotated at a constant angular velocity, to measure the viscosity of fluids, especially those with low viscosity. In a Couette on a rheometer the inner cylinder is rotated at a constant angular velocity . The thickness of the fluid filled gap is R and the inner radius of the outer cylinder is R and the outer radius of the inner cylinder is (1)R. You can assume circular symmetry and neglect edge effects from the top and bottom. (a) Define the dependence of the velocity on each dimension. (b) Derive the velocity field. (c) Define the change in the dynamic pressure in all three dimensions. (d) Find the torque if the fluid is in a narrow gap