In fluid mechanics, the steady two-dimensional flow of a fluid can be described in terms of a function y(x, y) called the stream function. Let u(x, y) and v(x, y) denote the velocity components of the fluid in each of the coordinate directions at the point (x, y). They are related to the stream function (x, y) by მს მს U = and V = ду Әх '
(a) For the stream function y(x, y) = ln √√(x − a)² + (y − b)², find the velocity components u(x, y) and v(x, y).
(b) Consider a fluid flow in a domain D (a subset of R2) which is described by a stream function (x, y). The first and second derivatives of are continuous at all points in D. Show that this flow satisfies the continuity equation ди Əv + = = 0. əx dy
