A flow is passing over a \({20^ \circ }\) half-angle wedge having a upstream Mach number, pressure and temperature of \(2.8,\,1\,atm\,\) and \(310\,K\). Find the wave angle and downstream Mach number, pressure and temperature.
A flow is passing over a \({20^ \circ }\) half-angle wedge having a upstream Mach number, pressure and temperature of \(2.8,\,1\,atm\,\) and \(310\,K\). Find the wave angle and downstream Mach number, pressure and temperature.
Wave angle can be found from \(\theta -\beta -M\) diagram. For deflection angle \(\theta =20^{\circ}\) and Mach number, \(M_{1}=2.8\) , wave angle \(\beta =39.5^{\circ}\).
Therefore, normal component of upstream Mach number,
\[M_{n1}=M_{1}Sin\beta = 2.8Sin\left ( 39.5^{\circ} \right )=1.78\]
From normal shock properties table, for \(M_{n1}=1.78\),
\(\frac{p_{2}}{p_{1}}=3.530,\frac{T_{2}}{T_{1}}=1.517,M_{n2}=0.6210\)
Therefore, Downstream pressure, \[ p_{2}=\left ( \frac{p_{2}}{p_{1}} \right )p_{1}=\left ( 3.530 \right )\left ( 1\,atm \right )=3.53\,atm\]
Downstream temperature, \[T_{2}=\left ( \frac{T_{2}}{T_{1}} \right )T_{1}=\left ( 1.517 \right )310=470.27\,K\]
Downstream Mach number, \[ M_{2}=\frac{M_{n2}}{sin\left ( \beta -\theta \right )}=\frac{0.6210}{Sin\left ( 39.5-20 \right )}=1.86\]
