Consider a two$-$dimensional, incompressible flow over an airfoil in the $x-y$ plane.

The velocity components in this flow are given by:

$u=\frac{Cy}{(x^2-y^2)}$

$v=\frac{Cx}{(x^2-y^2)}$

where $C$ is a constant.

For this velocity, perform the following:

Prove that this flow is physically possible.

Derive the equation for the streamlines of the flow.

Using a computational tool such as MATLAB or Python, plot the stream$-$

lines to visualize the flow pattern. Also, indicate arrows showing the flow

direction in each quadrant.

If $C=0\mathrm{.}25,$ calculate the velocity vector and magnitude for the fluid at

point $(x,y)=(4,1).$