278 
Gye 
TABLE 3, 
a Tick ito ce ee 
Once again the units for Vand f(0) are metres per second, 
SECTION III. SHOCK WAVES IN WATER, 
The theory of Hugoniot and others on shock waves in air may be modified to apply to 
water, There is no need to consider anything but plane waves because the Shock wave is of 
negligible thickness, ana the shack wave equaticns only 2xcfess conservation thecrems for various 
properties from the. fluid on one side to the other, 
Let the shock wave velocity be U, the mass velocity, pressure, temperature and specific 
volume on the high pressure side de u, 0, T and v respectively, and the Corresponding variables 
on the low pressure side by 0, Por Urs and vhs respectively. 
The conservation of mass gives 
(U =u) vo = uv, (11) 
and the conservation of momentum 
Wu = (p- p) Vor ( 12) 
where the units cf velocity are cm/sec. and of pressure are dynesfem?, 
Write U = xu, and take tne unit of velocity as metres/sec., and of pressure as 
3 kgm/em?, Then the equivalent forms of (11) and (12) are 
10 
U = xu = 313 /(xp) 
x 
n 
vol (v. - v} 
Clearly, we need one further equation to determine x before it is possible to find all 
variables in terms of 0. 
The usual arjument of the piston in the cylinder shows that the increase in internal 
energy per unit mass of fluid in oassing from the low pressure side to the high pressure side Is 
p(y, Sy) oe igs Using (11) an3 (12) we obtain the usual Hugoniot equation 
ANE = ee (oet ip5),(Voc— iv) (13) 
In order to put this equation in a form from which v may be found, we proceed as follows, 
Evaluate the work done in an adiabatic expansion from the initial state p,v to the state Por 
wnere Vv, is the volume corresponding to the pressure Py on the adiabatic containing p,v. Supply 
heat at constant pressure until the volume has increased to v. Then by the first law of 
thermodynamics 
Qe 
tt 
° 
a 
=a 
1 
oc 
a 
< 
' 
aS) 
< 
' 
< 
T v 
+ (p + py) (v, - ¥) 
Substituting esses 
