Crocco's theorem


In aerodynamics, Crocco's theorem relates the flow velocity, vorticity, and stagnation pressure of a potential flow. This 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, 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:
  1. Stagnation pressure:
  2. Entropy :
  3. Momentum:
In the above equations, is the flow velocity vector, is the vorticity, is the specific volume, is the stagnation pressure, is temperature, is specific entropy, is specific enthalpy, is specific body force, and is the direction normal to the streamlines. All quantities considered are specific, in the sense of "per unit mass".