Aircraft Propulsion·momentum-equation-control-volume

Momentum Equation Control Volume

Given a control volume with fluid flowing in at inlet and out at outlet, calculate the net force exerted by the fluid on the control volume using the momentum equation. Inputs include mass flow rate, inlet and outlet velocities, inlet and outlet gage pressures, inlet and outlet cross-sectional areas, weight of contents, and weight of fluid in the control volume. Sum all momentum and pressure contributions to find the total force.

✓ All 2 test cases pass.

Inputs

Mass flow rate

Mass flow rate in kg/s

Inlet velocity

Velocity at inlet in m/s

Outlet velocity

Velocity at outlet in m/s

Inlet gage pressure

Gage pressure at inlet in Pa

Outlet gage pressure

Gage pressure at outlet in Pa

Inlet cross-sectional area

Cross-sectional area at inlet in m²

Outlet cross-sectional area

Cross-sectional area at outlet in m²

Weight of control volume contents

Weight of solid contents in N

Weight of fluid in control volume

Weight of fluid held in control volume in N

Test cases

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#	Inputs	Expected	Got	Status
1	{"mass_flow_rate":0.599,"velocity_inlet":2.98,"velocity_outlet":30.6,"pressure_inlet":464000,"pressure_outlet":0,"area_inlet":0.0002011,"area_outlet":0.00001963,"weight_contents":0.981,"weight_fluid":0.0278}	77.8	77.8	✓
2	{"mass_flow_rate":1,"velocity_inlet":5,"velocity_outlet":10,"pressure_inlet":100000,"pressure_outlet":0,"area_inlet":0.001,"area_outlet":0.0005,"weight_contents":1,"weight_fluid":0.05}	95.05	96	✓

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Endpoint

POST/api/calculators/aircraft-propulsion/momentum-equation-control-volume/compute

Inputs (9)

mass_flow_ratenumberdefault 0.599
velocity_inletnumberdefault 2.98
velocity_outletnumberdefault 30.6
pressure_inletnumberdefault 464000
pressure_outletnumberdefault 0
area_inletnumberdefault 0.0002011
area_outletnumberdefault 0.00001963
weight_contentsnumberdefault 0.981
weight_fluidnumberdefault 0.0278

Example

curl -sX POST http://localhost:3001/api/calculators/aircraft-propulsion/momentum-equation-control-volume/compute \
  -H "Content-Type: application/json" \
  -d '{"inputs":{"mass_flow_rate":0.599,"velocity_inlet":2.98,"velocity_outlet":30.6,"pressure_inlet":464000,"pressure_outlet":0,"area_inlet":0.0002011,"area_outlet":0.00001963,"weight_contents":0.981,"weight_fluid":0.0278}}'

Try it live

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Request body

Response

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Source: Pattern from: Momentum Eq.pdf. Reproduces a standard momentum-equation-control-volume computation; problem text paraphrased.

AI disclosure: Calculator code generated by anthropic/claude-haiku-4-5-20251001; verified by 2 test cases.