Question

Steady, incompressible, inviscid flow past two airfoils is shown. The pressure coefficient at the trailing edge of (I) with a finite included angle is \(C_{pI}\); for (II) with a cusp (zero included angle) it is \(C_{pII}\). Which statement is TRUE?

• A. \(C_{pI}<1,\; C_{pII}<1\)
• B. \(C_{pI}=1,\; C_{pII}=1\)
• C. \(C_{pI}=1,\; C_{pII}<1\)
• D. \(C_{pI}<1,\; C_{pII}=1\)

Hint:

Remember: finite-angle TE → stagnation at TE (\(C_p=1\)); cusped TE → finite nonzero exit speed (\(C_p<1\)).

Answer 1

The Correct Option is C

Step 1: Kutta condition at the trailing edge.
For inviscid flow, the Kutta condition enforces a finite velocity at the TE and the flow leaves smoothly.

Step 2: Finite-angle TE (case I).
At a wedge with finite included angle, the only finite-velocity potential-flow solution at the vertex is zero velocity (stagnation) at the TE. Therefore \(V_{\mathrm{TE}}=0 \Rightarrow C_{pI}=1\) (stagnation pressure coefficient).

Step 3: Cusped TE (case II).
At a cusped TE (zero included angle), the Kutta condition yields a finite, nonzero velocity as the upper and lower surface velocities meet smoothly. Hence \(V_{\mathrm{TE}} > 0 \Rightarrow C_{pII}<1\).

\(\boxed{C_{pI}=1,\quad C_{pII}<1}\)