Page 123 - 48Fundamentals of Compressible Fluid Mechanics

5.3. THE MOVING SHOCKS 85

The same can be said for the “downstream” side of the shock. The difference
between the stagnation temperature is in the moving coordinates is

(5.51)

It should be noted that the stagnation temperature (in the stationary coor-
dinates) rises as opposed to the stationary normal shock. The rise of total tem-
perature is due to the fact that new material has entered the c.v. at a very high
velocity, and is “converted” or added into the total temperature.

(5.52)

And according to equation (5.51) leads to

(5.53)

Again, this difference in the moving shock is expected due to fact that moving

material velocity (kinetic energy) converted into internal energy. This difference
can also view are results of unsteady state of the shock.
5.3.1 Shock Result From A Sudden and Complete Stop
The general discussion can be simplified in the extreme case where the shock is
moving from a still medium. This situation arises in many cases in the industry,
for example, a sudden and complete closing of a valve. The sudden closing of the
valve must result in a zero velocity of the gas. This shock is viewed by some as a
reflective shock. This information propagates upstream in which the gas velocity
is converted into temperature. In many such cases the steady state is established
. The equations
is positive values. is zero and
quite rapidly. In such case, the shock velocity “downstream” is
(5.42) to (5.56) can be transformed into simpler equations when
The “upstream” Mach number reads
(5.54)