APPENDIX A 

 PHYSICAL PROPERTIES OF FISH 



Several of the physical properties of fish flesh which must be known for this study have not been 

 accurately measured. In this appendix, the available data will be discussed and, where necessary, 

 appropriate approximations determined. Properties which must be specified include compressional wave 

 velocity (or sound velocity), c,; density, Po,; specific heat at constant pressure, c p( ; ratio of specific heats, y,I 

 thermal conductivity, k ( ; shear viscosity, rj ; and bulk viscosity, r\ a . In addition, the ratio of swimbladder 

 volume to total fish volume and the surface tension, s, at the air-fish flesh interface must be determined. 



Experimental evidence indicates that swimbladder volumes of small mid-water fishes range from about 

 0.5 to 5 percent of the total fish volume [32]. For larger, near surface marine fishes, swimbladder volumes 

 are about 4 to 5 percent of the total fish volume [A1]. For small fish, the ratio of outer radius, b, to inner 

 radius, a, of the fish flesh shell is chosen to be 2.5 <b/a <6, which corresponds to swimbladder percentage 

 volumes of about 6 to 0.5 percent. For large fish, b/a is chosen to be 2.5 <b/a <3.2, which corresponds to 

 swimbladder percentage volumes of about 6 to 3 percent. The fish size range of interest is about 1 cm to 1 m, 

 which roughly corresponds to 0.1 cm < a < 5 cm [32, A2, A3]. 



The acoustic properties of fish flesh have been measured by several researchers [31, A1, A4-A6]. 

 Experimental values of density range from about 1.02 to 1.09 gm/cm 3 , with an average of about 1.05 

 gm/cm 3 . Experimental sound velocities range from about 1 .50 x 1 5 to 1 .60 x 1 5 cm/sec, with an average 

 of 1.55 x 10 5 cm/sec. The average values are used in this report. 



Measurements on the thermal properties of fish flesh are not available. However, data on the thermal 

 conductivity and specific heat at constant pressure of human and dog tissue do exist [A- 7]. These data 

 provide sufficiently close approximations to the required values. Thus, for fish tissue 



and cal 



K, = 1.32 x 10" 3 - 



' cm sec °C 



These values are quite close to those for sea water of 35 parts per thousand salinity, which are [45] 



cal 

 c„„, = 0.93 



""" gm°C 



and 



cal 

 k w = 1.34 x 10 3 



cm sec °C 

 Also for sea water [45], 



Yw « 1.01 . 

 Thus, it will be assumed that, since other thermal properties of flesh and sea water are very similar, 



Y, « 1.01 . 



Both the shear viscosity, r\ sf , and the bulk viscosity, r)b,> are required for the present model. However, for 

 convenience, a viscosity parameter, ^, will be defined as 



5 = 4/3 Tis, + % • (A-1) 



The ratio, nt/Hs. f° r animal tissue is similar to that for water, which is approximately 3 [A8, A9]. Thus, 



E; X4.3n s , 2? 1.4 rib, • (A-2) 



Only one set of data on the viscosity of animal tissue is available. However, other data exist from which 

 tissue viscosity can be determined indirectly. These data are measurements of absorption, complex shear 

 modulus, and cell viscosity of animal tissue. In all cases it will be assumed that the viscosity of all animal 

 flesh is approximately equal. 



The direct measurements of viscosity were performed on mammalian tissue [A10]. n, s ,was determined 

 by four different methods. The results ranged from 100 to 420 poise, with an average value of 175 poise. 

 Thus the values for E, range from 430 to 1800 poise, with an average value of 760 poise. 



37 



