Consider a steady potential flow that is characterized by the velocity potential  Then  satisfies
where , the sound speed is expressed as a function of the velocity magnitude  For a polytropic gas, we can write
where  is the specific heat ratio,  is the stagnation sound speed (i.e., the sound speed in a gas at rest) and  is the stagnation enthalpy. Let  be the characteristic velocity scale and  is the characteristic value of the sound speed, then the function  is of the form
where  is the relevant Mach number. 
For small Mach numbers, we can introduce the series
Substituting this governing equation and collecting terms of different orders of  leads to a set of equations. These are
and so on. Note that  is independent of  with which the latter quantity appears in the problem for .