Mass Flow Rate⚠ unverified
Aerospace / Propulsion · Compute the choked mass flow rate through a nozzle throat
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Pc | Pc | Pa | 1.0 | Chamber pressure |
| At | At | m^2 | 1.0 | Nozzle throat area |
| T0 | T0 | K | 1.0 | Stagnation temperature |
| R | R | — | 1.0 | Specific gas constant, in joules per kilogram-kelvin (J/(kg*K)) |
| gamma | γ | — | 1.0 | Ratio of specific heats of the gas (dimensionless) |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | mdot | kg/s | Choked mass flow rate, in kilograms per second (kg/s). Returns 0.0 when ``T0`` is not positive or ``gamma`` is not greater than 1 |
The science & history
Understanding the Parameters
- $\rho$ — for gases, from equation of state; for liquids, nearly constant.
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$v$ — bulk/average speed; profile factors matter for laminar pipe flow if you use centreline speed by mistake.
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$A$ — geometric area open to flow.
- $\dot{m}$ — conserved in a steady stream tube without sources (Continuity).
Derivation (Approaching a Proof)
In time $dt$, a fluid slab of volume $A\,v\,dt$ crosses the section; its mass is $\rho A v\,dt$. Rate:
$$\dot{m} = \rho v A.$$
Volume flow rate is $Q = v A = \dot{m}/\rho$.
History
Mass continuity is the first conservation law applied in duct and nozzle design; $\dot{m} = \rho v A$ is the working form in propulsion (Thrust) and HVAC sizing.
Related Concepts: Continuity, Thrust, Bernoulli Total Pressure, Drag
Notes: Registry calculator fluids-mass-flow-rate (unverified). Mean one-dimensional form.