Thrust⚠ unverified
Physics / Fluids · Compute the thrust produced by a rocket or jet nozzle
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| mass_flow_rate | massflowrate | kg/s | 1.0 | Propellant mass flow rate |
| exhaust_velocity | exhaustvelocity | m/s | 1.0 | Exhaust velocity at the nozzle exit |
| pressure_diff | pressurediff | Pa | 1.0 | Difference between exit and ambient pressure |
| exit_area | exitarea | m**2 | 1.0 | Nozzle exit area |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | F | N | Total thrust, in newtons (N) |
The science & history
Understanding the Parameters
- $\dot{m}$, $v_e$ — momentum rate out the nozzle; higher mass flow or exit speed → more thrust.
-
$p_e - p_a$ — underexpanded ($p_e > p_a$) adds pressure thrust; overexpanded can subtract. Perfectly expanded: $p_e = p_a$, pressure term vanishes.
-
$A_e$ — multiplies the pressure difference.
- $F$ — axial force on the vehicle (ideal 1-D control volume).
Derivation (Approaching a Proof)
Steady control-volume momentum balance on the engine: net force on the CV equals momentum flux out minus in (inlet terms omitted in the pure rocket form) plus pressure forces on the exit plane. With ambient pressure acting on the exterior, the standard result is
$$F = \dot{m} v_e + (p_e - p_a) A_e.$$
Related mass flow: Mass Flow Rate. Related fluid force scales: Drag, Lift.
History
The rocket equation and nozzle thrust formula are classical propulsion results (Godard, Oberth, and standard gas-dynamics texts); they size every chemical rocket nozzle.
Related Concepts: Mass Flow Rate, Continuity, Speed Of Sound, Mach Number, Drag
Notes: Registry calculator thrust (unverified). Ideal 1-D exit model; inlet momentum for air-
breathing engines needs extra terms.