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GATE 2025 AE – Question 49

Aerodynamics · Compressible flows: isentropic flow, normal and oblique shocks, Prandtl-Meyer flow, nozzles and diffusers · 2 marks · Numerical answer

A supersonic stream of an ideal gas at Mach number $M_1 = 5$ is turned by a ramp, as shown in the figure. The ramp angle is $20^o$. The pressure ratio is $\frac{p_2}{p_1} = 7.125$ and the specific heat ratio is $\gamma = 1.4$. The pressure coefficient on the ramp surface is _______ (rounded off to two decimal places).

A Mach 5 stream along a flat wall meeting a 20 degree ramp, with an oblique shock from the corner. Region 1 is upstream of the shock and region 2 is between the shock and the ramp.

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Correct answer: 0.34 to 0.36

Explanation

The pressure coefficient is $C_p = \frac{p_2 - p_1}{\frac{1}{2}\rho_1V_1^2} = \frac{\frac{p_2}{p_1} - 1}{\frac{\gamma}{2}M_1^2}$, because $\rho V^2 = \gamma p M^2$. So $C_p = \frac{6.125}{0.7 \times 25} = 0.35$.