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On the Canonical Form of the Equations of Steady Motion of a Perfect Gas

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2 Author(s)
Munk, Max M. ; Naval Ordnance Laboratory, Washington, D. C. ; Prim, Robert C.

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The equations for general steady motion of a perfect gas are expressed in terms of a reduced number of basic dependent variables. Neither constant entropy nor constant flow energy is assumed throughout the flow, but only along individual streamlines. The basic dependent variables used are the ``reduced velocity'' vector

wv/
 2γ 
 γ-1 
 p 
 ρ 
+v2
 1 
 2 
and the logarithm of the pressure, lnp. The resulting form of the dynamic equation is
(w·grad)w+
 γ-1 
 2γ 
(1-w2) grad lnp=0,
and that of the continuity equation is div[(1-w2)1/γ-1w]=0, representing four equations in four unknowns. The fundamental characteristic and shock relations are also expressed in terms of these reduced variables.

Published in:

Journal of Applied Physics  (Volume:19 ,  Issue: 10 )