The normal stress in fish flesh is [45] 



T rr( = -p, + j;^l ( (|M11) 



or 

 so that utilization of equation 11-109 yields: 



'5 [-! 'to 



wp 0f L Po,C, 



T -_P_ % fl i(0 ^l 92P< (H-112) 



Also, 



T = -P (H-113) 



and 



T "a = " P a • (11-114) 



At the air fish-flesh interface the surface tension must be included in the stress equation. For a bubble in 

 water [50], 



2s 

 R 



Pin = Pou, +^ , (H-115) 



where P m and P out are the total pressures inside and outside the bubble and R is the radius of the bubble at any 

 instant. If g represents the small changes in the radius of the bubble and a is the average radius, such that 



R = a + g , (M-116) 



where g<<a, then 



~-f-(1 -g/a) , (11-117) 



R a(1 + g/a) a 

 so that 



P in = Pou. +-f- (1 -g/a) . (11-118) 



Since P in and P out are total pressures, equation 11-1 18 can be linearized utilizing equation 11-10. Thus, the first 

 order equation is 



Pou t1 = Pm+^r- ("-us) 



Due to the harmonic time dependence, 



Ur = »R = - icog . d'-120) 



ot 



Thus 



P , - p. = 2 ' SU :a (11-121) 



The boundary conditions are: 



BC 1 u rw = u rf at r = b, (11-122) 



BC2 x rrw = T rrf at r = b , (II-123) 



17 



