text: Assume a fluid enters an internally contracting nozzle at cross-section 0, and passes through a throat of smaller area at cross-section 4. A normal shock is assumed to start at the beginning of the nozzle contraction, and this point in the nozzle is referred to as cross-section 2. Due to conservation of mass within the nozzle, the mass flow rate at each cross section must be equal:
  For an ideal compressible gas, the mass flow rate at each cross-section can be written as,
  where  is the cross-section area at the specified point,  is the Isentropic expansion factor of the gas,  is the Mach number of the flow at the specified cross-section,  is the ideal gas constant,  is the stagnation pressure, and  is the stagnation temperature.
  Setting the mass flow rates equal at the inlet and throat, and recognizing that the total temperature, ratio of specific heats, and gas constant are constant, the conservation of mass simplifies to,
  Solving for A/A,
  Three assumptions will be made: the flow from behind the normal shock in the inlet is isentropic, or p = p , the flow at the throat (point 4) is sonic such that  M = 1, and the pressures between the various point are related through normal shock relations, resulting in the following relation between inlet and throat pressures,
  And since M = 1, shock relations at the throat simplify to,
  Substituting for  and  in the area ratio expression gives,
  This can also be written as,