1152 
534 
TABLE I. Reported detonation energies of TNT. 
AH 
cal./g’ Source 
840 Bericht tiber die Arbeitstagung Unterwasserspreng- 
wesen, Veranstaltet von der Amtsgruppe Mar 
Rust/FEP im OKM am 28/29 Oktober 1943 im 
Harnackhaus im Berlin (experimental) 
880 G. I. Taylor, The Vertical Motion of a Spherical 
Bubble and the Pressure Surrounding It, TMB 
510, August 1943 
950 G. D. Clift and B. T. Federoff, A Manual for 
Explosives Laboratories (Lefax, Inc., Phila- 
delphia, 1942). This value seems to have been 
obtained from Soukharevsky and Pershakoff, 
__ Explosives, Moscow, 1932 
1060 Private communication from S. R. Brinkley to W. 
D. Kennedy (theoretical) 
because of the fact that the calculated energy 
flux is near a minimum with respect to a base 
line shift. In this case an error of 10 lb./in.? in 
the base line would cause less than 2 percent 
error in the energy, while it would cause a very 
large error in the impulse. 
VII. PARTITION OF ENERGY IN AN 
UNDERWATER EXPLOSION 
23. Energy of Detonation 
At the present time there seems to be a lack 
of precise knowledge concerning the quantity 
of energy released in the detonation of various 
explosives. A wide range of values is quoted in 
the literature, and it is not always possible to 
ascertain the original source of the data. A sum- 
mary of such results is given in Table I. Detona- 
tion energy is defined as the enthalpy change, 
AH, in calories per gram, with final products 
reduced to standard conditions. 
In the theory of the gas bubble oscillation’ it 
is customary to use as a zero energy reference 
the state of infinite adiabatic expansion of the 
product gases. Since it is our purpose to include 
bubble phenomena in the discussion of energy 
partition, it will be more convenient to adopt 
this reference rather than the standard state 
usually used for AH. The order of magnitude of 
the internal energy of the products at standard 
conditions (relative to infinite adiabatic expan- 
sion) is 100 cal./g, and this quantity should be 
added to the values given in Table I. 
For purposes of further discussion, we shall 
arbitrarily adopt the value of 950 cal./g as the 
Ay. \Br YAIRIO N'S) JAIN) Di!) D)-) (Reo YE NINGIGE: 
TABLE II. Energy partition at time of first bubble maximum 
(W=charge weight in lb.; R=distance in ft.). 
Acoustic energy flowing past R= W1/0.352 275 cal./g 
Energy dissipated at the shock front during 
propagation up to R= W1/0.352 (calculated 
in Section 13) 
Unaccounted for 95 
Total energy associated with emission of shock 
wave (1050—480) 570 
Potential energy stored in water at first bubble 
maximum as calculated from measured 
maximum bubble radius 
Internal energy of gaseous products (referred 
to infinite adiabatic expansion: (480 — 385) 95 
385 
_ 1050 
detonation energy of TNT, giving 1050 cal./g as 
the approximate detonation energy relative to 
infinite adiabatic expansion of the products. The 
uncertainty in this figure is at least of the order 
of +10 percent. 
24. The Shock Wave 
It is known that the total energy associated 
with the gas bubble at its first maximum is 
approximately 480 cal./g.? Of this quantity, 385 
cal./g are stored as potential energy because of 
the formation of the cavity in the water, while 
the remainder is in the form of internal energy 
of the gaseous products (referred to an infinite 
adiabatic expansion). The value of the potential 
energy stored in the water is based on the experi- 
mental maximum radius as given by Eq. (36). 
The net energy lost by the bubble up to the 
time of the first maximum is therefore 1050 
minus 480, or about 570 cal./g. 
The partition of this energy has been dis- 
cussed in previous chapters and is summarized 
in Table II. 
The unaccounted term should comprise losses 
resulting from turbulence, viscosity, conduction, 
etc. It should be noted that the magnitude of 
TABLE III. Successive periods of bubble oscillation (TNT 
charges in free water)* at a depth of 500 ft. 
T1/Wi=23.2 millisec./lb.t 
T2/Wi= 16.7 
T;/Wi=13.5 
* See reference 2. 
