A fluid of viscosity µ is placed between two horizontal circular disks of the same radius R. The disk at z = 0 is stationary and the disk at z = b rotates with angular velocity ?. Assuming laminar, steady-state, and incompressible flow; vr = vz = 0; v?= r f(z) for the velocity components where z is the vertical direction and P = P(r,z), solve for f(z). Derive the equation for the viscous force and viscous torque in terms of all the variables given in the problem.