Calculator Inputs
Use the orifice model for leaks to atmosphere. Use the pipe model for a line segment feeding a leak where losses dominate.
Example Data Table
Sample scenarios for quick validation and training.
| Scenario | Model | P1 (bar g) | T (°C) | Area (mm²) | Z | Room (m³) |
|---|---|---|---|---|---|---|
| Small flange seep | Orifice | 2.0 | 20 | 5 | 1.00 | 80 |
| Gasket blowout | Orifice | 6.0 | 25 | 80 | 0.95 | 150 |
| Long branch to leak | Pipe | 4.0 | 15 | — | 1.00 | 120 |
For the pipe row, enter diameter, length, f, K, and density.
Formula Used
Pressures
Upstream absolute: P1 = P_g + P_atm
Downstream absolute: P2 = P_atm
Gas properties
Rspec = 8314 / M
Density estimate: ρ ≈ P1 / (Z · Rspec · T)
Orifice model
Critical ratio: (P2/P1)crit = (2/(γ+1))^(γ/(γ−1))
Choked: ṁ = Cd · A · P1 · √( γ/(Z·R·T) · (2/(γ+1))^((γ+1)/(γ−1)) )
Non-choked uses the standard isentropic nozzle expression.
Pipe loss model (screening)
Ktotal = f · (L/D) + Kminor
Q ≈ Cd · A · √( 2·ΔP / (ρ·Ktotal) ), and ṁ = ρ·Q
Time-to-target screening
t ≈ (Ctarget · Vroom) / Q
These equations are simplified for planning and screening.
How to Use This Calculator
- Select a model that fits your leak scenario.
- Enter upstream pressure, ambient pressure, and temperature.
- Set Cd and leak area, or pipe data if needed.
- Adjust gas properties: Z, molecular weight, and γ.
- Optional: enter room volume and target concentration.
- Click Calculate to view rates and screening time.
- Download CSV or PDF for documentation and review.
If your gas differs, replace the property values accordingly.
Professional Guidance
1) Why leak-rate estimates matter on sites
Gas releases can escalate from nuisance odor to serious incident within minutes. A quantified leak rate helps teams select isolation priorities, set exclusion zones, and size temporary ventilation. As a screening benchmark, a sustained release above 10 m³/h often warrants rapid control actions and continuous monitoring.
2) Typical input ranges and practical field data
Construction and maintenance work frequently encounters lines from 0.5 to 10 bar(g). Small defects may be only 1–10 mm², while gasket failures can exceed 50–200 mm². Discharge coefficients commonly fall between 0.60 and 0.80 for sharp-edged gaps. Temperature shifts from 0–40°C materially change density and flow.
For methane-like gases, molecular weight is about 16 kg/kmol and γ near 1.30. For air, molecular weight is about 28.97 kg/kmol and γ near 1.40. Z is often 0.90–1.00 depending on conditions.
3) Understanding choked versus non-choked behavior
When downstream-to-upstream pressure ratio drops below the critical ratio, flow becomes choked and the leak jet reaches sonic conditions at the opening. In that regime, increasing upstream pressure increases mass flow, while further lowering downstream pressure does not. This calculator flags that assumption to support safer planning.
4) Transport losses and line-fed leak scenarios
For a branch line feeding a leak, friction and fittings can limit delivery. The loss-based model combines Darcy friction (f·L/D) and minor losses (K). Long, small-diameter branches can reduce flow significantly compared with a free orifice at the same upstream pressure.
5) Interpreting the mixing-time screening output
The time-to-target estimate assumes perfect mixing in an enclosed volume, which is conservative for well-mixed rooms and non-conservative for stratified spaces. For example, a 5 m³/h leak into a 100 m³ room reaches 0.1% by volume in about 1.2 minutes. Always validate with ventilation and gas detection placement.
Use site-specific factors, detector readings, and qualified judgement for final decisions.
FAQs
1) Which model should I choose?
Use the orifice model for a hole, gap, or flange leak to atmosphere. Use the pipe model when a long branch line and fittings limit the flow feeding the leak.
2) What leak area should I enter?
Estimate the effective opening area. A 2 mm diameter round hole is about 3.14 mm². A 10 mm by 1 mm slit is about 10 mm². Use conservative values when uncertain.
3) What does “choked flow” mean here?
Choked flow occurs when pressure drop is high enough that the leak reaches sonic conditions at the opening. Mass flow then depends mainly on upstream pressure and gas properties, not on further downstream reductions.
4) How do I set gas properties for a different gas?
Enter the correct molecular weight and γ from a trusted reference or supplier sheet. If you have compressibility data, adjust Z. Recalculate and compare outputs for sensitivity.
5) Why is the pipe model called a screening estimate?
It uses a loss-based incompressible approximation to represent friction and fittings. Real gas flow may be compressible and transient. Treat results as planning guidance, not a certified design value.
6) How should I use the time-to-target result?
It assumes perfect mixing in the room. Use it to gauge how quickly conditions could worsen and to plan detection, ventilation, and evacuation. Do not use it as a dispersion model.
7) What should I document in the exported report?
Record the scenario, pressures, temperature, assumed area, Cd, gas properties, and any safety assumptions. Attach detector readings, ventilation status, and the action taken for traceability.