GATE 2025 AE – Question 48
In a low-speed airplane, a venturimeter with 1.3:1 area ratio is used for airspeed measurement. The airplane's maximum speed at sea level is 90 m/s. If the density of air at sea level is 1.225 kg/m$^3$, the maximum pressure difference between the inlet and the throat of the venturimeter is ________ kPa (rounded off to two decimal places).
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Correct answer: 3.40 to 3.44
Explanation
The inlet is the larger area, with the flow speed $V_1 = 90$ m/s. By continuity the throat speed is $V_2 = 1.3 \times 90 = 117$ m/s. Bernoulli's equation for incompressible flow gives $\Delta p = \frac{1}{2}\rho(V_2^2 - V_1^2) = 0.5 \times 1.225 \times (13689 - 8100) = 3423$ Pa = 3.42 kPa.