Use of the vorticity equation

(a) Work Problem 2B.3 using the y-component of the vorticity equation (Eq. 3D.2-1) and the following boundary conditions: at x = ±B, v_z = 0 and at x = 0, v_z = v_z, _max. Show that this leads to vz = vz, max [1 – (x)/B)²] then obtain the pressure distribution from the z-component of the equation of motion. 

(b) Work Problem 3B.6 (b) using the vorticity equation, with the following boundary conditions: at r = kR, v_z = v₀ and at r = kR, v_z = v₀. In addition an integral condition is needed to state that there is no net flow in the z direction. Find the pressure distribution in the system.