Free · Physics models
Steady Rocket Thrust with Exit Pressure
Estimate steady thrust from exhaust momentum flow and the nozzle exit pressure force.
- Formula & worked example
- Private in your browser
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
mass loss rate = 10.000000 kg; thrust = 21.000000 kN.
F = ṁ ve + Ae(pe−pa); ṁ = expelled mass / elapsed seconds.
Worked example
Enter these known values and leave the other values blank.
- Effective velocity
- 2000 m/s
- Flow area at nozzle
- 0.01 m²
- Mass lost
- 20 kg
- Time
- 2 sec
- Ambient pressure
- 100 kPa
- Pressure at nozzle
- 200 kPa
- Mass flow per second
- 10 kg /s per second
- Thrust
- 21 kN
Assumptions and limitations
- Estimate steady thrust from exhaust momentum flow and the nozzle exit pressure force.
- Mass-flow selector choices mean the chosen mass per second; the retained mass unit label is accompanied by “per second”. Expelled mass and time determine this flow independently.
- Exit and ambient pressures are absolute. Exhaust velocity is relative to the rocket; the momentum-only velocity is used here, rather than a velocity that already includes the pressure correction.
- The captured physical range requires positive pressure, so exact vacuum pressure is excluded. This is steady one-dimensional arithmetic, not an engine or nozzle performance simulation.
- Inputs and inverse outputs share the displayed unit selectors. Clear a known field to solve for it, and lock quantities that must remain fixed. Singular inverses may have no finite result.
Common questions
Why is there a pressure term?
Pressure different from ambient exerts an additional force across the nozzle exit area.
Does this predict acceleration?
No. Vehicle mass, gravity and other forces are needed to convert thrust to acceleration.
References
Estimate steady thrust from exhaust momentum flow and the nozzle exit pressure force. Mass-flow selector choices mean the chosen mass per second; the retained mass unit label is accompanied by “per second”. Expelled mass and time determine this flow independently. Exit and ambient pressures are absolute. Exhaust velocity is relative to the rocket; the momentum-only velocity is used here, rather than a velocity that already includes the pressure correction. The captured physical range requires positive pressure, so exact vacuum pressure is excluded. This is steady one-dimensional arithmetic, not an engine or nozzle performance simulation.