448 30 



The diaphragm velocities observed vary from about 4.1 x 10^ Inches 

 per second at a cnarge distance of 5 inches to 0.6U x T 0^ inches per second 

 at a charge distance of 52 inches. On the other hand, the initial velocities 

 of the edge spots were much lower, varying from about 0.6 x T 0^ Inches per 

 second to 0,1 x 10^ inches per second over the same range of charge distance. 



If the actual distance from the charge to a diaphragm spot is mul- 

 tiplied by the observed initial velocity of that spot, a constant is obtained 

 which is Independent of the charge distance. This may be expressed by the 

 relation 



V = — -. — inches per millisecond 

 a 



where v is the velocity of the spot under consideration and d is the distance 

 of the charge from that spot in inches. The dimensions of the numerical co- 

 efficient is inches^ per millisecond. The product of the edge spot veloci- 

 ties v^ by their respective charge distances is also independent of the 

 charge distance. This is expressed by the relation 



v^ = inches per millisecond 



where the subscript E Indicates that the quantities refer specifically to the 

 edge spots. The dimensions of the numerical coefficient is Inches^ per mil- 

 lisecond. The root mean square deviation from the mean of these constants is 

 i 1 .41 inches^ per millisecond for the diaphragm spots and ± 0.50 inches^ per 

 millibecond for the edge spots. 



A theoretical calculation* based on the theory of the behavior of a 

 free plate, developed by Kennard (11), leads to the values 



17.26 inches^ per millisecond 



and 



2,63 inches^ per millisecond 



for the diaphragm constant and the edge constant respectively. The reason 

 for the discrepancy between these values and those obtained from the streak 

 photographs Is not evident. The differences appear to be larger than the 

 experimental error. 



In this calculation, the assumption is made that cavitation occurs as soon as the pressure in the 

 water drops to zero. The incident pressure wave is assumed to be described by the fonnula 



68.5 38.77 .„3 , . ^ 



p = — -J — e X 10 pounds per square inch 



where t is in microseconds and d is in inches. The numerical coefficients in this formula are calcu- 

 lated on a similarity basis from the peak pressure and time constants, measured by Dr. M. Shapiro of 

 the Taylor Model Basin staff, for 27.2 grams of tetryl at 3 feet (12). 



