GATE 2023 AE – Question 34
Airplane A and Airplane B are cruising at altitudes of 2 km and 4 km, respectively. The free stream density and static pressure at altitude 2 km are 1.01 kg/m3 and 79.50 kPa, respectively, and at altitude 4 km, they are 0.82 kg/m3 and 61.70 kPa, respectively. The differential pressure reading from the pitot-static tubes is 3 kPa for both the airplanes. Assuming incompressible flow, the ratio of cruise speeds of Airplane A to Airplane B is ______. (round off to two decimal places)
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Correct answer: 0.89 to 0.91
Explanation
**Pitot-static tube (incompressible).** The differential pressure between the stagnation and static ports is the dynamic pressure:
$$\Delta p=\tfrac12\rho V^2\;\Rightarrow\;V=\sqrt{\frac{2\,\Delta p}{\rho}} .$$
Both planes read the same $\Delta p=3$ kPa, so
$$\frac{V_A}{V_B}=\sqrt{\frac{\rho_B}{\rho_A}}=\sqrt{\frac{0.82}{1.01}}=\sqrt{0.8119}=0.901\approx\mathbf{0.90}.$$
(The static pressures are not needed for this ratio.)