$6\mathrm{.}25$ An air$-$supported structure is used to enclose a set of tennis courts. It is a semi$-$cylinder structure with a diameter of $50$ ft and a length of $50$ ft $.$ The blowers used to inflate the structure can maintain the air pressure inside the structure at $0\mathrm{.}75$ in $.$ of water above ambient pressure. At design conditions, the wind blows at $35$ mph perpendicular to the axis of the semi$-$cylindrical shape. The resulting pressure distribution is expressed as

$\frac{p-p_{}}{\frac{1}{2}{V}_{}^2}=1-4si{n}^2$

Where the angle $$ is measured from the ground on the upwind side of the structure, $p$ is the pressure at the surface, $p_{}$ the atmospheric pressure, and $V_{}$ the wind speed. Determine the net vertical force exerted on the structure.