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An aeroplane is flying at a height of 14 km where temperature is – 45°C. The speed of the plane is corresponding to M = 2. Find the speed of the plane if R = 287 J/kg K and γ = 1.4. |
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Answer» Temperature (at a height of 14 km), t = – 45°C. T = – 45 + 273 = 228 K Mach number, M = 2 Gas constant, R = 287 J/kg K γ = 1.4 Speed of the plane, V : Sonic velocity, (C) is given by, C = \(\sqrt{γRT}\) (assuming the process to be adiabatic) = \(\sqrt{1.4\times287\times228}\) = 302.67 m/s M = \(\cfrac VC\) 2 = \(\cfrac V{302.67}\) V = 2 × 302.67 = 605.34 m/s = \(\cfrac{605.34\times3600}{1000}\) = 2179.2 km/h |
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