Low-pressure air leakage opening

Estimate flow through a known opening with a supplied discharge coefficient at a small pressure difference.

How this calculation works

This tool estimates airflow through one opening whose physical area and discharge coefficient are already known. Enter the opening area, pressure-difference magnitude, upstream air density, discharge coefficient and upstream absolute pressure. The coefficient multiplies the ideal square-root pressure velocity; multiplying that mean opening velocity by area gives flow. Absolute pressure is used to check that the differential is small enough for the implemented incompressible approximation. The coefficient must represent the actual opening rather than being treated as a universal value. This model assumes negligible upstream velocity and does not infer an effective leakage area from a test. Crack-flow exponents, multiple connected leakage paths, wind and stack networks need different analysis. The result cannot certify smoke control, containment, safe entry or code compliance.

Inputs and units

Physical opening area (m²)
Pressure difference magnitude (Pa)
Upstream air density (kg/m³)
Opening discharge coefficient (fraction)
Upstream absolute pressure (kPa)

Method and formula

Q = Cd A sqrt(2 Δp/ρ); mean opening velocity = Q/A. Q is m³/s, A is m², Δp is Pa and ρ is kg/m³.

Worked example

Example inputs

Physical opening area: 0.01 m²
Pressure difference magnitude: 50 Pa
Upstream air density: 1.2 kg/m³
Opening discharge coefficient: 0.65 fraction
Upstream absolute pressure: 101.325 kPa

Calculation steps

Pressure ratio = 50 / (101.325 × 1000) ≈ 0.000493462, below the model limit of 0.02.
Mean opening velocity = 0.65 × √(2 × 50 / 1.2) ≈ 5.933661 m/s.
Leakage flow = 0.01 × 5.9336610396 = 0.0593366104 m³/s ≈ 59.336610 L/s.

Example results

Estimated leakage flow: 59.3366104 L/s
Mean opening velocity: 5.93366104 m/s

Assumptions

One known opening with an applicable supplied discharge coefficient; negligible upstream velocity.
Pressure difference is at most 2% of absolute pressure.

Limitations

Does not infer leakage area or crack-flow exponent and does not model series paths, wind or stack networks.
Not smoke-control, pressure-containment, code-compliance or safe-entry certification.
Preliminary educational check; verify inputs and equipment data before design or operation.

Sources

NIST GCR 01-820: Printed page 61, equation 3.25: pressure drop and orifice discharge coefficient
NASA Glenn: Pitot-static tube: Bernoulli relation between total pressure, static pressure, density and velocity