n. s( V 2 A + iup 0f A = , (|| . 37) 



( : __i"L\ V 2 P + J^p = o , (H-38) 



V p 0t C f 2 / C f 2 



and 



V 2 P + -^P = . (11-39) 



The coefficient of thermal expansion, B, is defined as 



e — iH-iH 1 ' (IM0) 



so that, in air, equation 11-14 is 



Pi. =J T^- PoaPaT, . (II-4D 



"a 



In addition, equations 11-1 1 through 11-13 for air are, after substitution for u: 



3P ^ - Po a V 2 = , (||-42) 



at 



Poa-^CV x A) = p 0a ^y(VQ) - VP, , ( "" 43) 



and 



P0aCv a y^-Poa ~ fi ~ V 2 Q - K^T, = . (||-44) 



Taking the curl of equation II-43 and utilizing equation II-28 indicates that 



V x A = , (H-45) 



so that 



VPl " Po a ^f(VQ) = . (|| . 46) 



Then, substitution of equation 11-41 into II-42 yields: 



™ = M^-^\ ■ HMD 



Hence, taking the divergence of equation II-46 and substitution of equation II-47 yields: 



V2p '- p ^[p^-- p - T '] "°- (IM8) 



In addition, substitution of equation II-47 into II-44 yields: 



DP 9Tl - Va ( C Pa ~ Cva) 9 P 1 _ K U 2 T =0 C 1 " 49 ) 



Introduction of the harmonic time dependence into equations II-48 and II-49 yields, after eliminating the 

 numerical subscripts: 



V 2 P + ^f-P - co 2 p 0a B a T = (II-50) 



11 



