Problem 2: Parallel-disk viscometer. A fluid, whose viscosity is to be measured, is placed in the gap of thickness B between the two disks of radius R (figure shown below). One measures the torque T: required to turn the upper disk at an angular velocity 2. Develop the formula for deducing the viscosity from these measurements. Assume creeping flow. Fluid with viscosity and density pis held in place by, surface tension Disk at z = B rotates with angular velocity Disk at z = 0 is fixed Both disks have radius R and R >> B (a) Postulate that for small values of 2 the velocity profiles have the form V = 0, V₂ = 0, Ve=rf(z); and P = P(r,z). Write down the resulting simplified equations of continuity and motion. (b) From the 0-component of the equation of motion, obtain a differential equation for f(z). Solve the equation for f(2) and evaluate the constants of integration. This leads ultimately to the result of velocity distribution Ve(r,z). (c) Show that the desired working equation for deducing the viscosity is µ = 2BT ΠΩΛΕ