🚀 Rocket Nozzle Design (De Laval) Calculator
Size converging-diverging nozzles using isentropic compressible flow relations. Compute throat/exit areas, expansion ratio, thrust, CF, and specific impulse Isp.
🔥 De Laval Nozzle Schematic
📝 Configuration
Key Equations:
A/A* = (1/M)[(2+(γ−1)M²)/(γ+1)](γ+1)/(2(γ−1))
F = ṁVe + (Pe−Pa)Ae
CF = F/(PcAt)
Isp = F/(ṁg₀)
c* = √(γRTc)/γ/√[(2/(γ+1))(γ+1)/(γ−1)]
A/A* = (1/M)[(2+(γ−1)M²)/(γ+1)](γ+1)/(2(γ−1))
F = ṁVe + (Pe−Pa)Ae
CF = F/(PcAt)
Isp = F/(ṁg₀)
c* = √(γRTc)/γ/√[(2/(γ+1))(γ+1)/(γ−1)]
📊 Results
Configure inputs and click Design to view results.
📘 Methodology
Isentropic Relations
The De Laval nozzle accelerates flow from subsonic to supersonic through a converging-diverging geometry. All thermodynamic properties along the nozzle follow from the local Mach number and isentropic relations.
Thrust & Isp
Thrust includes both momentum flux ṁVe and pressure thrust (Pe−Pa)Ae. Specific impulse Isp = F/(ṁg₀) characterizes propellant efficiency. The thrust coefficient CF normalizes thrust by chamber conditions.
Assumptions
- Steady, quasi-1D isentropic flow.
- Calorically perfect gas (constant γ).
- No boundary layer, friction, or heat loss.
- Fully expanded nozzle at design Pe.
- Choked flow at throat (M = 1).