(Solved): Designing a Supersonic Wind Tunnel 1. We need to design a supersonic wind tunnel reproducing at M=2 ...

Designing a Supersonic Wind Tunnel 1. We need to design a supersonic wind tunnel reproducing at $M=2.8$ free-stream flow. The cross section of the test section area is $A_{\text{test }}=1{\mathrm{m}}^2$. The air in the reservoir is at ambient temperature $T_0=280K$. (a) Determine the nozzle throat cross section $A_{t,1}$. (b) Determine the total pressure in the reservoir $p_0$ and the mass flow $\dot{m}$ through the nozzle in the hypothesis that the nozzle discharges the air directly in the ambient $(p_{amb}=1atm$, $T_{amb}=280\mathrm{K})$ at supersonic conditions and without any shock. (c) A supersonic diffuser is placed behind the test section. Now the flow is decelerated through a normal shock wave at $M_{\text{shock }}=2.8$. Determine the diffuser throat minimum cross section $A_{t,2}$, the minimum total pressure $p_0$ in the reservoir and the mass flow through the wind tunnel.