GATE 2024 AE – Question 59
Consider the following Fanno flow problem: Flow enters a constant area duct at a temperature of 273 K and a Mach number 0.2 and eventually reaches sonic condition (Mach number =1) due to friction. Assume $\gamma$ = 1.4. The static temperature at the location where sonic condition is reached is_____________ K (rounded off to 2 decimal places).
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Correct answer: 228.17 to 230.47
Explanation
Fanno flow is adiabatic, so the stagnation temperature is constant. The static to sonic temperature ratio is $\frac{T}{T^*} = \frac{\gamma + 1}{2 + (\gamma - 1)M^2}$. At $M = 0.2$ this is $\frac{2.4}{2 + 0.4 \times 0.04} = 1.1905$. So $T^* = \frac{273}{1.1905} = 229.32$ K.