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GATE 2020 AE – Question 48

Aerodynamics · Basic fluid mechanics: kinematics, conservation laws, dimensional analysis, incompressibility and Newtonian fluids · 2 marks · Numerical answer

Uniform low-speed flow U₀ passes an airfoil of chord c. Far downstream, velocity is 0.995U₀ over a width c and U₀ elsewhere, as drawn. Static pressure is equal at sections A and B. Find drag coefficient to 3 decimals.

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Correct answer: 0.009 to 0.011

Explanation

The wake momentum deficit per unit span is $D\prime=\rho\int u(U_0-u)dy=\rho(0.995U_0)(0.005U_0)c$. Divide by $\tfrac12\rho U_0^2c$ to get $C_D=2(0.995)(0.005)=0.00995$, which rounds to 0.010. Equal section pressures remove an additional pressure-force term.

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