# What is the relationship between pressure and leakage air flow rate?

**The relationship between the air flow rate (Q) and the pressure difference (ΔP) is often modeled by a power low:**

**Q = C P ^{n}**

**The air flows from the higher to the lower pressure.**

**For air to flow through the building envelope there must be:**

**An open pathway (leakage)****A pressure difference at the pathway**

**For the same pathway, a higher pressure difference results in more air flow.**

Whether found by extrapolation, interpolation or direct measurement, the principle metric used to quantify air tightness is the air leakage flow rate, the air flow through the envelope at a specific reference pressure. The most common reference pressures are 50 Pa and 4 Pa, but 1 Pa, 10 Pa, 25 Pa, and 75 Pa are used as well. The air flow is often denoted with the reference pressure as a subscript (e.g. Q_{50} or Q_{25}) [1].

Regardless of the flow regime the air leakage flow rate Q can be calculated from the pressure difference ΔP using the power law description:

Q = C P^{n}

where C is the flow coefficient and n is the pressure exponent. The fluid flow regime ranges from fully laminar (n=1) to a fully turbulent flow (n=0.5) so 0.5 <= n <=1. The pressure exponent is normally found in the vicinity of 0.65 [2].

The power law is broadly accepted in air tightness measurement standards.

An alternative is the so-called quadratic form that

P=AQ+BQ^{2}

based on a combination of the pressure flow relationships for laminar flow (Q=K_{1}P) and turbulent flow (Q=K_{2}P^{1/2})

Walker et al. [3] compared both formulations and concluded that, based on theoretical considerations and field and laboratory measurements, the power law is valid for low pressure (<100 Pa) building envelope leakage. More on this can be found in Sherman and Rengie [1].

**References**

*[1] Sherman, M., & Chan, R. (2004). "Building airtightness: Research and practice". James & James. Lawrence Berkeley National Laboratory. LBNL Report #: LBNL-53356. Retrieved from https://escholarship.org/uc/item/5jb277km*

*[2] Orme M., Liddament M., Wilson A., "AIVC TN 44: Numerical Data for Air Infiltration and Natural Ventilation Calculations (replaced by Guide GU05)", AIVC, 1994*

*[3] Iain S. Walker, David J. Wilson Max H. Sherman, "A comparison of the power law to quadratic formulations for air infiltration calculations" Energy and Buildings, Volume 27, Issue 3, June 1998*