293 
p, Is the pressure (10? kgm./sqacm. © 6.35 tons/square inch) behind tne Incident shock wave; 
Pr Is the Instantaneous reflected pressure, and p, is the stagnation pressure. 
The thickness of the shock waves } . 
The Admiralty records of the pressure pulses of underwater explosions (e.9-. “ood, *#ature 
of the pressure Impulse produced by the detonation of explosives under water. An investigation by 
the plezo electric cathode-ray oscillograph method", hereafter called Report "B*) all show a finite 
time of rise T of the pressure to Its peak value; the observed values of 7 range from 50 to 100 
microseconds, Even when correction is made for the finite dimensions of the gauges, It still appears 
that T measures a real effect, whose exact nature Is uncertain. 
If the time of rise is 50 microseconds, the peak pressure lags by about 7 cm, behind the 
leading edge. We have estimated the thickness of shock waves In water of Intensity less than 
1000 atmospheres, to see If T may be partly attributed to the thickness of the shock wave. 
The calculations are only rough, and follow those of Taylor and MacColl for shock waves in 
air. (Durand - Aerodynamic Theory, Vol. 3, pe218). 
Tne equation of energy Is 
2 2 
LN ei see) oe ae = m4 2 
f Fe dG: Ox ae 
dx 3 Ox x x 
The equation of continutiy Is 
puerto 
The equation of state may be taken as 
v= v, (1+a6-B p) 
The adiabatic may be taken as 
(p+ op)” = Cp 
where Po and cn are functions of 0, and Y Is constant, 
Solving the equations in a similar way to that devised by Taylor and MacColl, it Is found 
that BOs of the Change of velocity on the two sides of the shock wave occurs within the thickness T 
Ts a.u0F (u, = u,) 
ERS GB) tas 
The numerical valpes of the parameters are 
a= .00036, B= .0256 x10, j= .01006, k= .00138, y= .138, so that 
T = xf(u, - u,) 
where x = .001 If p = 1000 kym./sqecm. and x = .0106 if p = 4000 kgmd/ sq.cm. 
THUS ooece 
