Question $6$: $(25$ pts$/$a$)\backslash (15\backslash$mathrm$\{$pts$\},\backslash$mathrm$\{$b$\})-10\backslash$mathrm$\{$pts$\})\backslash )$

A source is located at distance $\backslash ($ l $\backslash )$ from the origin. A sink is located at distance $-1$ from the origin of the Cartesian system of coordinates. Assuming that the velocity field is incompressible and irrotational and source and sink have the same strength magnitude $\backslash (\backslash$boldsymbol$\{\backslash$Lambda$\}\backslash ),$ find:

a$)$ The velocity potential and stream function for this flow; velocity field; velocity at the origin;

b$)$ Using Bernoulli equation find the pressure distribution at the wall located at the origin of the Cartesian system of coordinates, assuming you know an ambient pressure and density.

Hint: Use the Cartesian system of coordinates and formulas for the source discrete flow at the arbitrary point.