What Is the Rocket De Laval Nozzle Expansion Ratio Calculator?
A de Laval nozzle accelerates combustion gases to supersonic velocities by contracting to a choked sonic throat before expanding divergent bells.
How Does the Rocket De Laval Nozzle Expansion Ratio Calculator Work?
In supersonic flow, fluid accelerates as cross-sectional area increases due to compressibility dynamics.
Rocket De Laval Nozzle Expansion Ratio Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
rac{A_e}{A_t} = rac{1}{M_e}left[ rac{2}{gamma + 1}left(1 + rac{gamma - 1}{2} M_e^2
ight)
ight]^{ rac{gamma + 1}{2(gamma - 1)}}
One-dimensional isentropic area-Mach relation for supersonic nozzle expansion.
How to Use the Rocket De Laval Nozzle Expansion Ratio Calculator
- Specify design exit Mach number, gas specific heat ratio gamma, and combustion chamber stagnation pressure.
Step-by-Step Example Calculation
Hydrolox Vacuum Rocket Engine
Input Values:
exitMach:3.5
specificHeatRatio:1.22
chamberPressureBar:70
Worked Steps: Area expansion ratio Ae/At = 12.8:1, ideal thrust coefficient CF = 1.74.
Understanding Your Result
Outputs the area expansion ratio Ae/At, static pressure ratio Pe/Pc, and ideal vacuum thrust coefficient CF.
Factors That Affect the Result
- Lower gamma (polyatomic combustion gases) increases required expansion area for equivalent Mach number.
When Should You Use This Calculator?
- Sizing rocket combustion chambers, divergent bell skirts, and high-altitude thrusters.
Assumptions & Limitations
- Assumes 1D isentropic ideal gas flow with frozen or shifting chemical equilibrium without viscous boundary layer displacement.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard 1D isentropic gas dynamics formulation.