Deriving a second equation for the Mach number at station

1 Deriving a second equation for the Mach number at station 2  

We begin by recalling the general energy equation for frictionally resisted flow developed in Section 4.2 and repeated below  

Also the energy loss due to friction may be found from equation (4.20) in terms of the increment of pipe-length, dx  

Substituting from equations (6.8), (6.9) and (6.10) into equation (4.15) gives the energy equation as  

First we make use of the following thermodynamic relationships for a near-ideal gas, as discussed in Chapter 3, Section 3.3  

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