Consider a steady, two-dimensional flow field in the xy-plane whose x-component of velocity is given by

where a, b, and c are constants with appropriate dimensions. Of what form does the y-component of velocity need to be in order for the flow field to be incompressible? In other words, generate an expression for ν as a function of x, y, and the constants of the given equation such that the flow is incompressible.

u = a + b(x c)