Question: Continuity equation for axisymmetric flow
(a) Consider an axisymmetric flow field expressed in terms of the cylindrical coordinate system (r, ?, z), where all flow variables are independent of the azimuthal angle ?-for example, the axial flow over a body of revolution. If the velocity components (u, w) correspond to the coordinate directions (r, z), respectively, show that the continuity equation is given by
(b) Show that the continuity equation can be automatically satisfied by a stream function ψ of a form such that
