$3\mathrm{.}38.$ Consider the flow around the quonset hut shown in Fig. P$3\mathrm{.}38$ to be represented by superimposing a uniform flow and a doublet. Assume steady, incompressible, potential flow. The ground plane is represented by the plane of symmetry and the hut by the upper half of the cylinder. The free$-$stream velocity is $175k\frac{m}{h}$; the radius $R_0$ of the hut is $6$ m $.$ The door is not well sealed, and the static pressure inside the hut is equal to that on the outer surface of the hut, where the door is located.

$($a$)$ If the door to the hut is located at ground level $($i$.$e$.,$ at the stagnation point$),$ what is the net lift acting on the hut? What is the lift coefficient?

$($b$)$ Where should the door be located $($i$.$e$.,$ at what angle ${}_0$ relative to the ground$)$ so that the net force on the hut will vanish?

For both parts of the problem, the opening is very small compared to the radius $R_0.$ Thus, the pressure on the door is essentially constant and equal to the value of the angle ${}_0$ at which the door is located. Assume that the wall is negligibly thin.