Crocco's theorem is a fluid dynamics theorem relating the flow velocity, vorticity, and stagnation pressure (or entropy) of a potential flow. Crocco's theorem gives the relation between the thermodynamics and fluid kinematics. The theorem was first enunciated by Alexander Friedmann for the particular case of a perfect gas and published in 1922:
However, usually this theorem is connected with the name of Italian scientist Luigi Crocco, a son of Gaetano Crocco.
Consider an element of fluid in the flow field subjected to translational and rotational motion: because stagnation pressure loss and entropy generation can be viewed as essentially the same thing, there are three popular forms for writing Crocco's theorem:
- Stagnation pressure:
u × ω = v ∇ p 0 - Entropy (the following form holds for plane steady flows):
T d s d n = d h 0 d n + u ω - Momentum:
∂ u ∂ t + ∇ ( u 2 2 + h ) = u × ω + T ∇ s + g ,
In the above equations,