NSWC/WOL TR 76-155 



where In is the natural logarithm, Aj^ is the initial at rest bladder 

 radius, and AMIN and AMAX are the smallest and largest radii during 

 the oscillatory response. In the cases studied so far, the first 

 compression has always been AMIN, while AMAX generally occurs during 

 or following the negative phase. We will use the bladder oscillation 

 parameters X, Y, and Z in Sections 3.2 and 3.3 to discuss and correlate 

 the observed injuries to fish specimens on our tests. 



The bladder radius, A. — Tables 3.1.3 and 3.1.4, column 7 — 

 is the radius for a sphere of the same volume as the fishes' bladder 

 at fish depth for a fish which has not acclimated, i.e., for a fish 

 at equilibrium with one atmosphere pressure which is isothermally 

 compressed to hydrostatic pressure at fish depth.* Bladder radius A. 

 for non-acclimated fish is given by 



A. = (A.) A^Oy_x_loA V3 (3.1.6)** 



1 ° V p i / 



where p. is the pressure at fish depth in pascals and (A.) , the 

 radius at one atmosphere pressure, is given by 



(A ± ) /L - 0.033 (Spot) (3.1.7) 



(A.) /L = 0.055 (White Perch) (3.1.8) 



where L is the fork length of the fish. The constants 0.0 33 and 

 0.055 were selected for each species by trial and error so as to 

 optimize the correlation between experimentally observed injuries to 

 the test specimens and the calculated bladder oscillation parameter 

 Z (e.g., Figure 3.2.1). 



*This is how it was done on the explosion tests. It would have been prohibitively 

 expensive to have let the fish acclimate to testing depth, because of the time 

 required. This problem is discussed by Gaspin, Wiley, Peters, 1976. 



** For the calculations of this report the exponent, l/3y, where Y - 1.4 — for 

 adiabatic compression — was inadvertently used. Since the computations reported 

 here should be quite insensitive to this error, they were not redone. 



34 



