Approximations to non-equilibrium performance

The overall method described above can be quite complex when many reactions are considered and consequently can be quite time consuming with respect to machines and thus at times quite expensive to calculate. 

A complex reacting mixture with which one must deal in propulsive devices may have ten to fifteen reactions to be considered. However, it is known that a reacting 

to repeat, when the selected three-body reaction freezes, one can, for impulse purposes, consider the system frozen. Now it is possible to find the point at which the system freezes in the same manner Bray used for the less complicated supersonic tunnel problems. 

Bray obtained his approximate condition for dissociation-recombination reactions merely by estimating the sizes of the various terms in the rate equation. Essentially he writes the rate equation  

1) When the flow is near equilibrium, as at the beginning of the nozzle expansion r -F r B 

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