Question

Which of these is the correct relation for the entropy across a shock for all the streamlines?

(a) ∇s = 0

(b) ∇ × s = 0

(c) (∇s) × s = 0

(d) (∇ × s).s = 0

The question was posed to me by my school principal while I was bunking the class.

This interesting question is from Quantitative Formulation topic in chapter Linearized and Conical Flows of Aerodynamics

Answer 1

The correct option is (a) ∇s = 0

For explanation: The shock wave in the conical flow is assumed to be straight resulting in same increase in the entropy for all streamlines passing through the shock (∇s = 0). This property implies that the conical flow is irrotational as per Crocco’s equation.