$(40$ points$)$ You are to design a quonset hut to serve as a temporary shelter. The hut can be considered to be a close semi$-$cylinder, whose radius is $R,$ mounted on tie$-$down blocks, as shown in the figure below. Assume that the flow is inviscid and that the flow field over the top of the hut is identical to the flow over a cylinder for $0.$ The wind speed is $U_{}$ and the static free$-$stream properties $({}_{},p_{})$ are those of standard sea$-$level conditions. HINT: start with elementary flow results of flow over a cylinder and only consider half the portion of the cylinder.

$($a$)(10$ points$)$ What is the pressure distribution $($in terms of $C_p)$ on the outer $($upper$)$ surface and on the lower surface of the cylinder? Provide the answer as a function of the relevant variables stated in the problem.

$($b$)(20$ points$)$ What is the coefficient of lift for this semi$-$cylinder? Recall that lift$/$drag can be computed by integrating the pressure distribution around a surface.

$($c$)(10$ points$)$ What is the coefficient of drag? Explain your findings with respect to expectations in a real condition $($i$.$e$.$ if viscosity is included$).$

$(40$ points$)$ You are to design a quonset hut to serve as a temporary shelter. The hut can be considered to be a close semi$-$cylinder, whose radius is $R,$ mounted on tie$-$down blocks, as shown in the figure below. Assume that the flow is inviscid and that the flow field over the top of the hut is identical to the flow over a cylinder for $0.$ The wind speed is $U_{}$ and the static free$-$stream properties $({}_{},p_{})$ are those of standard sea$-$level conditions. HINT: start with elementary flow results of flow over a cylinder and only consider half the portion of the cylinder.

$($a$)(10$ points$)$ What is the pressure distribution $($in terms of $C_p)$ on the outer $($upper$)$ surface and on the lower surface of the cylinder? Provide the answer as a function of the relevant variables stated in the problem.

$($b$)(20$ points$)$ What is the coefficient of lift for this semi$-$cylinder? Recall that lift$/$drag can be computed by integrating the pressure distribution around a surface.

$($c$)(10$ points$)$ What is the coefficient of drag? Explain your findings with respect to expectations in a real condition $($i$.$e$.$ if viscosity is included$).$