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GATE 2024 AE – Question 24

Aerodynamics · Airfoils and wings: coefficients, Kutta-Joukowski theorem, thin airfoil theory, finite wing theory, critical and drag divergence Mach numbers · 1 mark · Multiple choice

Consider steady, incompressible, inviscid flow past two airfoils shown in the figure. The coefficient of pressure at the trailing edge of the airfoil with finite angle, shown in figure (I), is $C_{P_I}$ while that at the trailing edge of the airfoil with cusp, shown in figure (II), is $C_{P_{II}}$. Which one of the following options is TRUE?

Two airfoils in a stream $U$. (I) has a trailing edge with a finite wedge angle. (II) has a cusped trailing edge.
  1. $C_{P_I} < 1$, $C_{P_{II}} < 1$
  2. $C_{P_I} = 1$, $C_{P_{II}} = 1$
  3. $C_{P_I} = 1$, $C_{P_{II}} < 1$
  4. $C_{P_I} < 1$, $C_{P_{II}} = 1$

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Show answer and explanation

Correct answer: (C) $C_{P_I} = 1$, $C_{P_{II}} < 1$

Explanation

At a trailing edge with a finite angle the Kutta condition requires the velocity to be zero (a stagnation point), so $C_p = 1 - \left(\frac{V}{U}\right)^2 = 1$. At a cusped trailing edge the flow from the two surfaces leaves in the same direction with a finite and equal speed, so $C_p < 1$.