Crocco's Theorem

where is the specific enthalpy, the stagnation enthalpy, and the flow velocity. (See Section 14.5.) The fluid equation of motion, (14.31), reduces to

(15.86) |

However, according to Equation (A.171),

(15.87) |

where

(15.88) |

Now, Equation (14.29) implies that

(15.89) |

where is the temperature, and the specific entropy. Moreover, Equation (15.85) yields

(15.90) |

Thus, we arrive at

(15.91) |

In most aerodynamic flows, the fluid originates from a common reservoir, which implies that the stagnation enthalpy,
, is
the same on all streamlines. Such flow is termed *homenergic*. It follows from Equation (14.18) that the stagnation temperature,
, is
the same on all streamlines in homenergic flow.
According to Crocco's theorem, an irrotational
(i.e.,
**
**
everywhere) homenergic (i.e.,
everywhere) flow pattern is also homentropic (i.e.,
everywhere). Conversely, a homenergic, homentropic flow pattern is also irrotational (at least, in two dimensions, where
and
**
**
cannot be parallel to one another).