Problem $9$

A flat triangular plate is positioned in the $xy$ plane as shown below. Air at $20C$ and $1$atm flows steadily over the plate. The velocity field near the wall is given approximately by$,$

$u(x,y,z)=\frac{2z{U}^{\frac{3}{2}}}{5}\sqrt[\phantom{2}]{\frac{}{x}}-\frac{z^2}{25}\frac{U^2}{x}$

where $U=5\frac{m}{s}.$

Calculate the drag force exerted by the air on the top of the plate.