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, vz = 0 and at x = 0, vz = vz, 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, vz = v0 and at r = kR, vz = 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.
(c) Work the following problems using the vorticity equation: 2B.6, 2B.7, 3B.1, 3B.10, 3B.16.
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