Nozzles
Calculate critical pressure ratios and mass flow through sonic nozzles based on gas properties and inlet conditions.
Critical Pressure Ratio for Nozzles
The maximum gas flow through a nozzle is determined by critical pressure. Critical flow nozzles are also called sonic chokes.
The ratio between critical pressure and initial pressure is:
pc / p1 = (2 / (n + 1))^(n / (n - 1))
Where:
- pc = critical pressure (Pa)
- p1 = inlet pressure (Pa)
- n = polytropic constant (index of isentropic expansion)
Common Gas Values for n:
- Steam (wet region): n = 1.135
- Steam (superheated): n = 1.30
- Air: n = 1.4
- Methane: n = 1.31
- Helium: n = 1.667
Mass Flow through Sonic Nozzles
The mass flow through a nozzle with sonic flow (where minimum pressure equals critical pressure) is:
mc = Ac × √(n × p1 × ρ1) × (2 / (n + 1))^((n + 1) / 2(n - 1))
Where:
- mc = mass flow at sonic flow (kg/s)
- Ac = nozzle cross-sectional area (m²)
- ρ1 = initial density (kg/m³)
- n = polytropic constant