251 
Sec. 20 -o- 
The Hugoniot conditions must be satisfied at the dotted lines and 
equality of pressure and velocity mintained at the interface. The fluid in 
contact with the piston must have the velocity w of the piston. These con- 
ditions are just sufficient in number to specify all the free variables, 
20. Calculation of the Velocity of the Shock Wave 
Produced by an Explosion 
a. Basic principles. When the detonation wave travelling down a stick 
of explosive reaches the end, reflection occurs and two new waves are pro- 
duced. One is the shock wave in the air at the end of the stick; the other 
is a rarefaction wave moving backward through the burnt gases. The boundary 
between the burnt gases and the outer air will also move forward, though not 
as fast as the shock wave in air. 
The problem is treated most simply if the forward-moving rarefaction 
wave which inevitably follows the detonation wave (see Sec. 18) is ignored; 
i.e. the case of a semi-infinite stick is treated. The effect of this rare- 
faction may be added later. 
Fig. 20-1 
The situation is then as shown in Fig. 20-1. It is assumed that 
across the boundary between the explosive and the air the pressures mst 
remain equal and also the mass velocities. If the properties of the 
explosive are known, Po, Vo, W and D can be calculated as shown in Part II. 
The values of Ps, Ve and Us across the reflected rarefaction wave are 
calculated as seen below if one of them is mown, That is, Py, say, is a 
known function of Pos Voy and U;. Likewise fom the theory of shock 
waves already given, Py V3 and Uz back of the shock wave are connected 
so that P; is a lmown function of Uz, Py, and Vj. It is then meraly neses- 
sary to combine these two equations connecting Ps with Us to solve for both 
B, and Uz, and therefore D , etc. 
