Question 5.17: For a two-dimensional incompressible flow, the x-component o......

Given that:            u = 2xy

Hence,                \frac{\partial u}{\partial x}=2 y

For a two-dimensional, incompressible flow the continuity equation can be written in differential form as

\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}=0

or                            2 y+\frac{\partial v}{\partial y}=0

or                            \frac{\partial v}{\partial y}=-2 y

or                              v = — y² + f (x)

where f(x) is a constant of integration.