Expanded velocity is the exhaust velocity of the rocket when the exit pressure equals the ambient pressure. The expanded velocity increases as the pressure ratio increases and as the enthalpy change per mole is increases. Typical expanded velocity for the combination of methane and oxygen is three thousand two hundred meters per second. Given exhaust molar, exhaust molecular, k, nozzle efficiency, pressure ratio, product enthalpy and reactant enthalpy the expanded velocity can be calculated which is in turn used along with ambient pressure ratio, exit pressure and relative exit to calculate the exhaust velocity.

k = 1.21
temperature change = ( reactant enthalpy - product enthalpy ) * ( 1.0 - 1.0 / k ) / 8,314 J * K / kmol / exhaust molar
expanded change = ( 1.0 - pow( 1.0 / pressure ratio, 1.0 - 1.0 / k ) ) * k / ( k - 1 ) * 8,314 J * K / kmol * temperature change / exhaust molecular
expanded velocity = sqrt( 2.0 * expanded change * nozzle efficiency )

exhaust velocity = expanded velocity + exit pressure * ( 1.0 - ambient pressure ratio ) * relative exit
 
 

This is used in bipropellant rocket, tripropellant rocket, pumped rocket and rocket cost.
 
  Rocket