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flow with M = 3 comes straight on in the x-direction towards the wedge. We know theta from our geometry of the wedge. From this we can calculate the normal component of our free stream Mach number.
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\LARGELarge \begin{equation}\nonumber M_{1N} = M_1sin(\beta) \end{equation} \\ |
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Now we can relate the normal Mach numbers to each other through the normal shock relations
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\LARGELarge \begin{equation}\nonumber M_{2N}^2 = M_{1N}^2(\frac{(\gamma -1)M_{1N}+2}{2\gamma M_{1N}-(\gamma -1)}) \end{equation} \\ \\ \begin{equation}\nonumber M_2 =\frac{M_{2N}}{sin(\beta-\theta)} \end{equation} \\ \\ \begin{equation}\nonumber \frac{p2}{p1} = \frac{2\gamma M_{1N}^2 - (\gamma - 1)}{\gamma + 1} \end{equation} \\ \\ \begin{equation}\nonumber \frac{T_2}{T_1} = \frac{(2\gamma M_{1N}^2 - (\gamma - 1))((\gamma -1)M_{1N}^2 +2)}{(\gamma +1)^2 M_{1N}^2} \end{equation} \\ |
From the equations above it is quite easy to relate upstream quantities.
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