Acoustics of a Nonhomogeneous Moving Medium Page: 22 of 202
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14 NACA TM 1399
From the law of the conservation of energy,
t+ div N = 0 (1.53)
This equation is one of the fundamental equations of hydrodynamics,
that is, equation (1.4) for the case of an ideal fluid (t =X = 7 = 0).
For an ideal gas PE = p/(y - 1) (equation (1.38)); hence
N - ' + 1 (1.52')
2 7 -
For acoustics the initial medium is considered motionless (v = 0)
The energy of the sound e2 = U2 - P0 E and the flow of sonic energy
N2 is obtained with an accuracy up to the order of magnitude A2. Terms
of the order of A3 rejected,
i + div N2 = 0 (1.53)
where2
P0 xl + n2
2 7 - 1Y70PO
N2 = 7 - 1
7(1 2) + -
7y -1Inasmuch as
p = p + ( d)o
" + ) + O dp2
0 dp /52+
1 "PO + cO(s1 2) + 2 (y- 1)c0i pO + l + ... '"
Pg + CO 2(1.55)
(cp = (dp/dp) = 7 o/PO is the square of the adiabatic velocity) and
l = c251, equation (1.54) may be rewritten in the form (1.54')2 2 -
2 zcp
N2 = -11-
7 -]2 c
2 '0 0# 71 1
2 -+ 1
+ 7- 1-)
-44(1.54)
(1.54')
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Blokhintsev, D. I. Acoustics of a Nonhomogeneous Moving Medium, report, February 1956; (https://digital.library.unt.edu/ark:/67531/metadc65701/m1/22/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.