1296 
where V signifies the change in the material velocity across 
the shock-front (the sign of -U corresponds to that of (1-€ )). 
It is to be noted that 
T=T-V 
and fer 
In addition, it is of theoretical interest to consider 
the so-called hydraulic jump 6) 
in the case of water flowing 
in an open, shallow channel. This phenomenon is somewhat 
analogous to the propagation of a plane shock-wave in water. 
The height h of the incompressible water corresponds to 
the density of a compressible fluid; the "sound velocity" is 
equal to yeh - Hence there is an analogous "adiabatic 
equation", viz., 
17/2 
apn 
Thus y has effectively the value 2, which can be immediately 
substituted in the above equations. 
Table 1 7) gives F as a function of M for y = 2.00 
and 7.15 (in this case p/P, also). 
The same formulae hold for normalization n with respect 
to either region provided that iF is defined as D/P, In either 
case y is the density-ratio os » O is the snock-velocity 
relative to the fluid in the normalized region, 7 is the 
shock-velocity relative to the region not normalized, vis 
the increase in material velocity across the shock relative 
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