Which of the following statements regarding supersonic flow past a sharp right circular cone at zero angle of attack governed by the Taylor-Maccoll equation are **CORRECT**?

(A) The attached shock wave is conical and concentric with the cone surface

(B) Unlike planar wedge flow where flow properties are completely uniform behind the oblique shock, conical flow exhibits continuous isentropic compression between the shock wave and the cone surface

(C) The static pressure continuously increases along rays from the conical shock wave down to the cone surface

(D) The deflection angle of streamlines behind the conical shock is constant all the way to the cone surface

Answer Key:

Verified in official key

### 1. Strategy & Theoretical Principles 1. **3D Relief Effect:** Flow past a 3D cone has an extra dimension for fluid to expand sideways compared to a 2D planar wedge. This 3D relief effect causes significant physical differences: - In 2D wedge flow, the flow properties ($p, T, M$) behind the straight oblique shock are strictly constant and uniform. - In 3D conical flow, the shock wave is conical. Between the conical shock wave and the solid cone body, streamlines are curved towards the cone surface. - In this region between shock and cone, the flow undergoes **continuous isentropic compression**: static pressure $p$ and temperature $T$ continuously *increase*, while Mach number $M$ *decreases* along rays from the shock to the surface. 2. **Streamline Deflection:** Streamlines continuously curve as they approach the cone; the flow deflection angle is NOT constant (it gradually increases to match the cone semi-vertex angle at the surface). ### 2. Statement Evaluation - **Statements A, B, C:** **CORRECT.** - **Statement D:** **INCORRECT.** Streamlines are curved, so flow deflection angle varies from shock to surface. ### 3. Exam Trap & Standard Reference - **Trap Alert:** Remember the fundamental difference between wedge flow (uniform properties) and Taylor-Maccoll cone flow (continuous compression between shock and cone). - **Standard Reference:** Anderson, J.D., *Modern Compressible Flow*, Chapter 10 (Conical Flow).

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