Assignment $1$: Consider boundary layer flow over a flat plate. The governing equations can be solved by replacing the nonlinear inertia terms $(vec(V)gradvec(V))$ by $U\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}$ where $U$ is the free stream velocity. Solve the governing equation using similarity principle to obtain the velocity field in the following form.

$\frac{u}{U}=$erf$(y\sqrt[\phantom{2}]{\frac{U}{4x}})$

Also obtain expressions for the boundary layer thickness and skin friction coefficient in terms of local Reynolds number.

In the above expression, erf stands for error function and is given by erf $(x)={\displaystyle \underset{0}{\overset{x}{}}}\frac{2}{\sqrt[\phantom{2}]{}}{e}^{-t^2}dt$