text: The expansion fan consists of an infinite number of expansion waves or Mach lines. The first Mach line is at an angle  with respect to the flow direction, and the last Mach line is at an angle  with respect to final flow direction. Since the flow turns in small angles and the changes across each expansion wave are small, the whole process is isentropic. This simplifies the calculations of the flow properties significantly. Since the flow is isentropic, the stagnation properties like stagnation pressure (), stagnation temperature () and stagnation density () remain constant. The final static properties are a function of the final flow Mach number () and can be related to the initial flow conditions as follows, where  is the heat capacity ratio of the gas (1.4 for air):
  The Mach number after the turn () is related to the initial Mach number () and the turn angle () by,
  where,  is the Prandtl–Meyer function. This function determines the angle through which a sonic flow (M = 1) must turn to reach a particular Mach number (M). Mathematically,
  By convention, 
  Thus, given the initial Mach number (), one can calculate  and using the turn angle find . From the value of  one can obtain the final Mach number () and the other flow properties. The velocity field in the expansion fan, expressed in polar coordinates  are given by
   is the specific enthalpy and  is the stagnation specific enthalpy.