Choked Flow Check Calculator

Formula used

Critical pressure ratio for choking:

P*/P0 = (2/(γ+1))^(γ/(γ−1))

Choked (sonic) mass flow estimate:

ṁ = Cd · A · P0 · √(γ/(R·T0)) · (2/(γ+1))^((γ+1)/(2(γ−1)))

Unchoked (subsonic) mass flow estimate:

ṁ = Cd · A · P0 · √( (2γ/(R·T0(γ−1))) · [ (P2/P0)^(2/γ) − (P2/P0)^((γ+1)/γ) ] )

These relations assume ideal gas, steady flow, and near-isentropic behavior to the minimum area.

How to use this calculator

1. Pick a gas preset, or choose Custom for γ and R.
2. Enter upstream total pressure P0 and downstream pressure P2.
3. Enter stagnation temperature T0 and minimum flow area A.
4. Set Cd if you want to include losses.
5. Submit to see choking status, critical pressure, and mass flow.
6. Use CSV or PDF buttons to export the latest result.

Example data table

Example values are illustrative. Real systems may differ due to heat transfer, non-ideal gas effects, and geometry.

Professional article

1) Why choking matters in gas systems

Choked flow occurs when the minimum-area Mach number reaches one, limiting mass flow even if downstream pressure keeps dropping. This behavior is central to relief valves, pneumatic actuators, and propulsion feed systems because it caps discharge capacity and stabilizes flow.

2) The key number: critical pressure ratio

For an ideal gas under isentropic assumptions, choking begins when the static-to-total pressure ratio falls below (2/(γ+1))^(γ/(γ−1)). For air with γ≈1.40, the critical ratio is about 0.528, meaning P2 must be at or below 52.8% of P0 for choking.

3) What the calculator checks

The calculator converts inputs to consistent SI units, computes the actual pressure ratio P2/P0, and compares it to the critical ratio. It reports a clear choked or unchoked status, the critical downstream pressure P* = P0·(P*/P0), and a mass-flow estimate for design screening.

4) Mass flow in the choked regime

In choked flow, mass flow depends primarily on upstream total conditions and throat area. A common engineering form is ṁ = Cd·A·P0·√(γ/(R·T0))·(2/(γ+1))^((γ+1)/(2(γ−1))). Increasing P0 or A increases ṁ nearly linearly, while higher T0 reduces ṁ through density.

5) Mass flow in the unchoked regime

When P2/P0 is above the critical ratio, the flow remains subsonic and mass flow depends on both pressures. Small changes in P2 can produce noticeable changes in ṁ, so unchoked conditions are more sensitive to backpressure variations in piping, silencers, and receivers.

6) Role of Cd and geometry

The discharge coefficient Cd accounts for vena contracta, friction, and non-ideal expansion. Sharp-edged orifices may use Cd around 0.60–0.90, while well-shaped nozzles can approach 1.0. If you are unsure, start with 0.9 for preliminary checks and refine using vendor or test data.

7) Gas properties and temperature

γ and R vary by gas and, in reality, with temperature. The preset values are representative for ideal-gas calculations. For steam or CO2 at elevated pressures, real-gas effects can shift results. Use measured properties if accuracy is critical, especially near condensation boundaries.

8) Practical workflow and interpretation

A solid workflow is: estimate operating P0 and T0, measure or size the minimum area, select an appropriate Cd, then check choking status. If choked, lowering P2 further will not increase mass flow, so capacity upgrades require higher P0, larger area, or multiple paths. Export CSV or PDF to document assumptions and iterate systematically.

FAQs

1) Is choking the same as “maximum flow”?

For a fixed upstream total pressure, temperature, area, and gas, choking sets the maximum mass flow through the restriction. You can still raise mass flow by increasing P0, increasing area, or reducing T0.

2) Should I enter gauge pressure or absolute pressure?

Use absolute pressure whenever possible. If you only have gauge pressure, convert it by adding local atmospheric pressure before entering values. Mixing gauge and absolute pressures can invalidate the choking check.

3) Why does mass flow stop increasing after choking?

Once the minimum area reaches Mach 1, information cannot travel upstream through the sonic plane. Downstream pressure changes cannot influence upstream conditions, so the mass flow becomes limited by upstream total properties.

4) What is the “critical downstream pressure” P*?

P* is the downstream pressure at which choking just begins for a given P0 and γ. If the actual downstream pressure is at or below P*, the flow is choked; above it, the flow is unchoked.

5) Does this work for liquids or two-phase flow?

No. The equations used are for compressible gas flow under ideal-gas, near-isentropic assumptions. Liquids and two-phase mixtures require different models that account for cavitation, flashing, and slip effects.

6) How do I choose a discharge coefficient Cd?

Cd depends on geometry, Reynolds number, and surface finish. Use vendor data when available. For quick screening, choose 0.9 for a reasonable nozzle, or 0.7–0.85 for a sharp-edged orifice.

7) Why does the calculator estimate Mach number?

Mach provides a sanity check and helps interpret the regime. In choked flow, the minimum-area Mach is about 1. In unchoked flow, the estimated Mach is below 1 and rises as P2 decreases.

Notes and good practice

• Use absolute pressures, not gauge, unless you convert.
• If P2 is below P*, mass flow stops increasing with lower P2.
• For long pipes, check friction and heat transfer separately.
• For two-phase or highly real gases, use specialized models.

Final thought

Accurate choking checks help design safer, quieter flow systems.