c$)$ Find out the reduced Navier Stokes equation $($i$.$e$.$ Prandlt boundary layer equation$)$ indicating the approximation that you can consider for the boundary layer.

d$)$ Write down the boundary conditions that can be applied for the same.

e$)$ Write down the mathematical relation between the flow velocities and stream functions.

f$)$ Proof that, $\frac{de{l}^{2}u}{del{y}^2}=\frac{U_{}^2}{vx}\frac{d^{3}f}{d{}^3},$ where $u=x$ directional velocity, $U_{}=$ free stream velocity, $v=$ kinematic viscosity, $=\frac{y}{\sqrt[\phantom{2}]{v\frac{x}{U_{}}}}$;$f=\frac{}{\sqrt[\phantom{2}]{U_{}vx}}$; $[$Stepwise derivation starting from the basic relation between velocity and stream function need to be done$].$

g$)$ How the boundary conditions of 'part $d\text{'}$ is going to be modified in terms of $$ and $f()$