Question

Which of these is Crocco’s theorem?

(a) V × (∇ × V) = ∇h0 – T∇s

(b) V(∇ × V) = ∇h0

(c) (∇ × V) = T∇s

(d) (∇ × V) = ∇h0 + T∇s

The question was asked in an interview for internship.

This intriguing question comes from Crocco’s Theorem topic in section Differential Conservative Equations for Inviscid Flow of Aerodynamics

Answer 1

Correct choice is (a) V × (∇ × V) = ∇h0 – T∇s

Explanation: Crocco’s theorem is formulated for inviscid flow having no external body forces. According to the theorem, the vorticity is equal to the difference between total enthalpy gradient and the gradient of entropy. It is given by:

V × (∇ × V) = ∇h0 – T∇s