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Consider a steady, twodimensional, homenergic, homentropic flow pattern, in the absence of body forces. Suppose that all quantities are independent of the Cartesian coordinate
,
and that the flow velocity,
, is confined to the

plane. Let
.
Equations (14.25), (14.30), and (14.31) reduce to
where
and
are the uniform stagnation pressure and density, respectively. (Note that
and
must be uniform
because the stagnation specific entropy,
, and the stagnation temperature,
, are both uniform.) Equation (15.95) implies that

(15.96) 
where
is the sound speed. Hence, Equations (15.92)(15.94) yield
Summing the previous two equations, and then making use of Equation (15.97), we obtain

(15.100) 
Finally, given that
, Equation (14.58) implies that

(15.101) 
where
is the stagnation sound speed.
Next: SmallPerturbation Theory
Up: TwoDimensional Compressible Inviscid Flow
Previous: Crocco's Theorem
Richard Fitzpatrick
20160331