A supersonic wind tunnel is in the design stage. It is to be driven by a large upstream reservoir of compressed air and discharges to atmospheric conditions downstream. The test section has a constant cross$-$sectional area and lies downstream of a throat, which is a converging$-$diverging section that serves to accelerate the flow to supersonic conditions. For the duration of any given experiment, the reservoir can be considered to have constant stagnation conditions that are $T_0=313K$ and $p_0=6{10}^{5}Pa.$ The specific gas constant $R=287Jk{g}^{-1}{K}^{-1}$ and the specific heat ratio is $Y=1\mathrm{.}4.$

The wind tunnel test section is designed to run with a cross$-$sectional area $A($ test section