The method of characteristics for one-dimensional, unsteady flows

Let us next consider one-dimensional, unsteady flows with velocity v in the X direction. In this case, equations (46), (48), (49), and (54) reduce to 

Equations (88), (89), and (91) constitute a useful set of governing conservation equations for characteristic analyses of one-dimensional, unsteady flows. 

Similarly, along the Mach lines, which are defined by Ax = (i %)At, equation (91) assumes the total-differential form 

One-dimensional, unsteady sound propagation in a binary, reacting ideal-gas mixture for the reaction B 

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