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sci.rocket-nozzle-exit-Mach Calculator
Calculates rocket nozzle throat area, exit Mach number, and thrust from combustion chamber conditions using isentropic nozzle flow equations. Optimum expansion occurs when exit pressure equals ambient pressure — over-expanded nozzles (Pe < Pa) suffer efficiency loss and flow separation at high altitude.
Inputs
P0 Kpa
Force per unit area (Pa). Atmospheric pressure at sea level: 101,325 Pa. Check whether gauge or absolute pressure is required.
Pe Kpa
Force per unit area (Pa). Atmospheric pressure at sea level: 101,325 Pa. Check whether gauge or absolute pressure is required.
Gamma
Energy to raise 1 kg of material by 1°C (J/kg·K). Water: 4,186 J/kg·K. Metals are typically 100–900 J/kg·K.
T0 K
Thermal state of the substance. Check whether the formula needs Celsius, Fahrenheit, or Kelvin (K = °C + 273.15).
Results
exit Mach number Me
Speed relative to the speed of sound. Below 1: subsonic. Equal to 1: sonic. Above 1: supersonic. Above 5: hypersonic. At Mach 1, aerodynamic drag increases dramatically.
exit velocity Ve (m/s)
Reference formula or conversion factor shown for context.
exit temperature Te (K)
The value at the specified point or condition.
thrust coefficient Cf estimate
Forward propulsive force generated by the engine or motor. Net thrust = gross thrust minus inlet momentum drag.
isentropic: P₀/Pe = (1 + (γ−1)/2·Me²)^(γ/(γ−1))
Sample size or count used in the calculation.
expansion ratio A_e/A_t
The proportional relationship between two quantities.