Consider a flow in x $-$direction over a flat surface from to $x=L$ in the same direction. The free$-$stream velocity is given as with density $$ and viscosity $.$ An approximate equation for the shear stress distribution inside the boundary layer is given by$,$

$(x,y)=2V_{}(\frac{\sqrt[\phantom{2}]{R{e}_x}}{7\sqrt[\phantom{2}]{x}}-\frac{y\sqrt[\phantom{2}]{R{e}_x}}{25x^2})$

where $R{e}_x$ is the Reynolds number with reference length. Calculate the friction drag coefficient $C_{D,f}$ for the surface.

Hint: $C_{D,f}=\frac{{}_{av}}{q_{}}$ with ${}_{av}=\frac{1}{L}{\displaystyle \underset{0}{\overset{L}{}}}{}_{w}dx$ and $q_{}=\frac{1}{2}{V}_{}^2$

$C_{D,f}=\frac{2}{7}\frac{\sqrt[\phantom{2}]{V_{}^3}}{q_{}}$

$C_{D,f}=\frac{2}{7}\frac{\sqrt[\phantom{2}]{V_{}^3}}{L{q}_{}}$

$C_{D,f}=\frac{4}{7}\frac{\sqrt[\phantom{2}]{V_{}^3}}{q_{}}$

$C_{D,f}=\frac{2}{7}\frac{L\sqrt[\phantom{2}]{V_{}^3}}{q_{}}$