Table 1 — Physical Properties 



Air Sea Water Fish Flesh 



c, cm/sec 3.3 x 10 4 1.50 x 10 5 1.55 x 10 5 



p , gm/cm 2 1.3 x 10 3 (at 1 atm) 1.026 1.050 



1.3 x 10- 1 (at 100 atm) 



Y 1.40 1.01 1.01 



c P'^rc 0.24 0.93 0.89 



K '^TiiU 5.5x10- 1.34x10- 1.32x10- 



r| s> poise 1.8 x 10-4 1.4 x 10 2 



£, poise 1 to 10 4 



Preliminary analysis of the new model indicated that considerable simplification resulted, with virtually 

 no loss of accuracy, if several approximations were made concerning the physical properties. The first 

 approximations were that y w = y, = 1 . Secondly, since K^a K t »K a , it was assumed that any heat generated 

 in the air is rapidly conducted away, so that the temperature in fish flesh and water is constant. Thirdly, 



since n.sf> >r ls w >>r lsa. ^ was assumed that n. Sw = Hs a = °- 



One further assumption which greatly simplifies the problem is made in this model. As discussed in 

 Chapter I, only the fundamental, or zeroth mode of oscillation will be considered. 



Formulation of Equations 



The first step in the determination of the resonant frequency and acoustic cross section of the new 

 model is the determination of the proper wave equations in water, fish flesh, and air. The wave equations 

 are determined from the basic equations of motion as given by Hunt [45], generally following the method 

 discussed by Epstein and Carhart [46]. The basic equations are the continuity equation, 



-|£ + V • (pfj) = ; (II-2) 



the equation of conservation of momentum, 



p 4r = - P(u • V)u - VP + ^V(V-u) - risV x (VxG) ; (II-3) 



o t 



the equation of conservation of energy, 



pc v ( -|I- + u • VT) + P(Cp p "° v) V ■ + V • q cp v = ; (II-4) 



and the equation of state, 



P = p(P,T) ; (H-5) 



where p is density, t is time, u is a velocity vector, P is pressure, c„ is specific heat at constant volume, T is 

 absolute temperature, (3 is the coefficient of thermal expansion, "q is a heat conduction flux vector, 



q = -kVT , (H-6) 



and cp v is a viscous dissipation function. 



