Flow Changes in Gases in which Mass and Impulse are Conserved

Summary

This note discusses changes in the state of a gas flowing in a duct of constant area. In the past, changes, such as normal shock waves, combustion and other phenomena, which are defined by the equations of energy, conservation of momentum and mass flow, have each been treated on their merits. In this note a method is developed whereby all phenomena governed by these three equations can be solved by a single general method. The method rests on the derivation of a parameter which is unaltered in value by the change, in all cases where the total temperature is constant. A shock wave is an example of such a discontinuity. In problems of heat addition or extraction, the parameter changes its value only because of the change in total temperature. The change in total temperature may be calculated from the known quantity of heat added or extracted.

The parameters derived are useful in showing how problems of this type should be attacked analytically. With oblique waves it is easy to derive a relation between the normal velocities before and after the wave, and it is probable that this relationship has not been published before.