What Is the De Laval Nozzle Isentropic Supersonic Expansion Calculator?
A de Laval nozzle is a hourglass-shaped tube used to accelerate hot pressurized gas into an energetic supersonic exhaust jet.
How Does the De Laval Nozzle Isentropic Supersonic Expansion Calculator Work?
Iteratively solves the non-linear supersonic branch of the area-Mach relation.
Computes static temperature Te using isentropic temperature ratio.
Computes static exit pressure Pe using isentropic pressure ratio.
De Laval Nozzle Isentropic Supersonic Expansion Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
(Ae/A*)² = (1/Me²) · [ (2/(γ+1)) · (1 + ((γ-1)/2)·Me²) ]^((γ+1)/(γ-1))
1D isentropic area-Mach equation solved for the supersonic exit flow branch.
How to Use the De Laval Nozzle Isentropic Supersonic Expansion Calculator
- Enter chamber pressure P₀ and flame temperature T₀.
- Input gas specific heat ratio γ and nozzle area expansion ratio Ae/A*.
Step-by-Step Example Calculation
Rocket Engine Sea-Level Bell Nozzle
Input Values:
chamberPressure:50
chamberTemperature:3000
gamma:1.2
areaRatio:10
Worked Steps: 50 bar chamber expanding through 10:1 area ratio nozzle.
Understanding Your Result
Primary output indicates supersonic exit Mach number.
Summary displays static exit pressure and temperature.
Factors That Affect the Result
- Area ratio (higher Ae/A* produces higher Mach and lower exit pressure).
- Ambient atmospheric pressure (governs over-expanded vs under-expanded flow).
When Should You Use This Calculator?
- Rocket engine nozzle design, wind tunnel supersonic test sections, and steam turbines.
Assumptions & Limitations
- Assumes steady, 1D, inviscid, isentropic ideal gas flow with frozen chemistry.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard compressible fluid dynamics formulation.