Formula & Calculator
Choked (Sonic) Mass Flow Rate
Mass flow rate through a nozzle throat when the flow is choked (locally sonic), independent of downstream pressure.
Interpretation
Choked mass flow rate: ṁ = (p_c·A_t / √T_c) · √(γ/R)·(2/(γ+1))^((γ+1)/(2(γ−1))). It is the maximum mass flow through a nozzle at sonic condition (throat). Example: p_c=5 MPa, A_t=0.002 m², T_c=3000 K, γ=1.3, R=300 → ṁ ≈ 50 kg/s.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| mdot | Mass flow rate | kg/s |
| p_c | Chamber pressure | Pa |
| A_t | Throat area | m2 |
| T_c | Chamber temperature | K |
| γ | Ratio of specific heats | |
| R | Specific gas constant | J/(kg*K) |
What it means
When the flow reaches sonic speed at the throat, the mass flow rate is choked and cannot increase further for a given upstream condition. This formula gives the mass flow rate through a nozzle under choked conditions. It is derived from the continuity equation and isentropic relations. This is crucial for rocket and jet engine performance: the mass flow determines thrust. Understanding choked flow is essential for propulsion system design and for analysing nozzle operation.
Worked example
Choked Mass Flow – Two Examples
Real‑World| Parameter | Value |
|---|---|
| p_c | 7×10⁶ Pa |
| A_t | 0.05 m² |
| T_c | 3500 K |
| γ | 1.2 |
| R | 350 |
| Parameter | Value |
|---|---|
| p_c | 1×10⁷ |
| A_t | 0.06 |
| T_c | 3300 |
| γ | 1.22 |
| R | 400 |
Common mistakes
- Choked (sonic) mass flow rate: ṁ = (p_c·A_t / √T_c) · √(γ/R) · (2/(γ+1))^((γ+1)/(2(γ−1))).
- p_c: Chamber pressure (Pa).
- A_t: Throat area (m²).
- T_c: Chamber temperature (K).
- Valid when flow is sonic at throat (M=1).
- Mass flow is maximum for given p_c and T_c.
Applications
Choked (sonic) mass flow rate, ṁ = (p_c·A_t/√(T_c))·√(γ/R)·(2/(γ+1))^((γ+1)/(2(γ−1))), gives the maximum mass flow through a nozzle throat when the flow is sonic. It is used to size rocket engine throats, to compute chamber pressure, and to design turbopumps. Engineers use this to ensure that the throat area is adequate for the required mass flow, and to set operating conditions. By applying the choked flow equation, aerospace engineers can design stable, predictable rocket engines.
- Rocket engine throat sizing and design
- Chamber pressure and propellant flow rate determination
- Turbopump and feed system design
- Flow rate measurement and control in engine testing
- Nozzle design and performance analysis
Frequently Asked Questions
It gives the mass flow rate through a nozzle throat when the flow is choked (locally sonic), which is independent of downstream pressure.
pc = chamber pressure (Pa)
At = throat area (m²)
Tc = chamber temperature (K)
γ = specific heat ratio
R = specific gas constant (J/kg·K)
It determines the maximum mass flow through the nozzle, which sets the thrust capability of the engine.
- Assuming mass flow depends on exit conditions once choked; choked flow depends only on upstream (chamber) conditions.
- Using the wrong value of γ for combustion gases.
- Forgetting to use absolute temperature (Kelvin).
pc = 10 MPa, At = 0.01 m², Tc = 3500 K, γ=1.2, R=300. ṁ = (10e6×0.01/√3500) × √(1.2/300) × (2/2.2)^((2.2)/(0.4)) = (100000/59.16) × √0.004 × (0.909)^5.5. Compute stepwise: 100000/59.16=1690; √0.004=0.0632; 0.909^5.5≈0.584. ṁ = 1690×0.0632×0.584 ≈ 62.4 kg/s.
ṁ is directly proportional to pc. Doubling chamber pressure doubles the mass flow.
ṁ is directly proportional to At. A larger throat allows more flow.
Higher Tc reduces ṁ (since ṁ ∝ 1/√Tc).
The flow remains choked; the mass flow is still determined by the upstream conditions.
It is used to size the throat and to predict the engine’s propellant consumption.