A potential flow has a velocity potential reads as

$=x^2-y^2+2xy$

What is the associated streamfunction for this flow?

All flow must satisfy the mass conservation, which is also referred to as the continuity

equation. Under Cartesian coordinates, it reads

$\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}+\frac{\text{d}\text{e}\text{l}\text{v}}{\text{d}\text{e}\text{l}\text{y}}=0$

Under cylindrical coordinates, it reads

$\frac{\text{d}\text{e}\text{l}(r{u}_r)}{\text{d}\text{e}\text{l}\text{r}}+\frac{del{u}_{}}{\text{d}\text{e}\text{l}}=0$

Prove that, the uniform flow, sink$/$source$,$ doublet, and free vortex all satisfy the mass

conservation.