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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 = 0The 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»

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.



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