Crocco's theorem

Crocco's theorem is an aerodynamic 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:[1] However, usually this theorem is connected with the name of Italian scientist Luigi Crocco,[2] 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: In the above equations,

is the flow velocity vector,

All quantities considered (entropy, enthalpy, and body force) are specific, in the sense of "per unit mass".