GATE 2025 AE – Question 50
A perfect gas flows through a frictionless constant-area duct with heat addition. The inlet conditions are as follows: pressure 100 kPa, density 1 kg/m$^3$, and velocity 100 m/s. At a particular downstream location, the gas velocity is 200 m/s. The static pressure at the downstream location is ______ kPa (answer in integer).
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Correct answer: 90
Explanation
This is Rayleigh flow. Continuity gives $\rho_2 = \rho_1\frac{V_1}{V_2} = 0.5$ kg/m$^3$. The momentum equation for a constant-area frictionless duct is $p_1 + \rho_1V_1^2 = p_2 + \rho_2V_2^2$, so $p_2 = 100000 + 10000 - 0.5 \times 40000 = 90000$ Pa = 90 kPa.