Air flowing over a $1-$m$-$long flat plate at a velocity of $7\frac{m}{s}$ has a friction coefficient given as $C_f=0\mathrm{.}664(V\frac{x}{v}{)}^{-0\mathrm{.}5},$ where $x$ is the location along the plate. Determine the wall shear stress and the air velocity gradient on the plate surface at mid$-$length of the plate. Evaluate the air properties at $20C$ and $1$ atm $.$

${}_w=C_f\frac{V^2}{2},(\frac{N}{m^2})$

$=\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{y}}{|}_y|=0,(\frac{N}{m^2})$