Discussion
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?
(The figure shows a uniform stream U approaching two airfoils: (I) Trailing edge with finite angle, where the upper and lower surfaces meet at an angle; (II) Trailing edge with cusp, where they meet tangentially.)
Answer: C
The correct option is \(C_{P_{I}} = 1,\ C_{P_{II}} \lt 1\).
The Kutta condition requires the flow to leave the trailing edge smoothly. With a finite trailing-edge angle the upper and lower surfaces point in different directions there, so the only way both streams can leave with one velocity is for that velocity to be zero: the trailing edge is a stagnation point and
\[ C_{P} = 1 - \left(\frac{V}{U}\right)^{2} = 1 \]
At a cusped trailing edge the two surfaces are tangent, so the flow can leave with a common, finite, non-zero velocity, and \(C_{P} \lt 1\).
So the airfoils differ: the options giving both the same value, or reversing them, are wrong.
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