What does Crocco's theorem establish?

Correct Answer : Option (C) :   Gradient of entropy and vorticity

Explanation : According to the Crocco’s theorem, there is a relationship established between vorticity, gradient of enthalpy and gradient of entropy.

V × (∇ × V) = ∇h0 – T∇s

Where, ∇ × V is the vorticity

∇h0 is gradient of total enthalpy

T∇s is gradient of entropy

Correct Answer : Option (B) :   False

Explanation : Across a stationary shock wave, the change in enthalpy is zero therefore ∇s = 0. But for a curved shockwave, the enthalpy does not remain constant making ∇s ≠ 0. This results in V × (∇ × V) ≠ 0 according to the Crocco’s theorem. Therefore the vorticity behind a curved shock wave is not zero and the flow behind the curved shock wave is rotational.

Correct Answer : Option (A) :   True

Explanation : A fluid while passing through a curved shock wave, experiences a strong entropy change due to the presence of shock wave. This leads to a rotational fluid causing vorticity behind the shock wave and the gradient in entropy change is non zero.