Approximate formulae relating the flow rate at 50 pascals to the measured infiltration rate at various average wind speeds have been given by Liddament . These formulae apply mainly to small buildings, especially dwellings, and after some manipulation may be expressed in terms of the air permeability:
For Z measured at high average wind speeds (> 4 ms 1) AP50 =
For Z measured at typical average wind speeds, AP50 =
For Z measured at low average wind speeds (< 4 ms 1) AP50 =
10VZ 20VZ 30VZ
where Z is the measured infiltration rate in air changes per hour V is the internal volume of the building.
The formula for typical average wind speeds is also given in CIBSE TM23 , which also quotes an adaptation of this formula for larger non-domestic buildings. In terms of air permeability, this is:
where S is the surface area of the walls and roof, excluding the ground floor.
Sherman and Grimsrud  have developed more detailed formulae relating effective (or equivalent) leakage area, ELA, to infiltration rate, with allowances for the conditions which prevail at the time of the infiltration measurement. After some manipulation, these can be adapted to give an expression for the air permeability at 50 pascals:
ATJ Q50 10ELA 10Z
St St,/p Sr(f? x AT + fw x v2),/p where fs is a function to correct for stack effect fw is a function to correct for wind pressure
AT is the internal to external temperature difference during a test measurement v is the measured open site wind speed at a height of 10 metres. The formulae for fs and fw:
-p _ ELAceiling ELAfloor ^ _ ELAceiling ELAfloor
where A, B are terrain parameters C is a shielding parameter H is the height of the building in metres To is the indoor air temperature g is the acceleration due to gravity
ELAceiling and ELAfloor are the equivalent leakage areas of the ceiling and ground floor planes respectively.
In many cases, measurements will be carried out on newly completed unoccupied buildings. If there is no heating or cooling in operation, AT will be close to zero and so the equation for AP50 simplifies to:
ST x f2 x v2yp
The range of values for the coefficients used to calculate fw are:
C 0.11 to 0.34 median 0.25 A 0.47 to 1.30 median 0.85 B 0.10 to 0.35 median 0.20
Taking, as typical, R = 0.2 and H = 15, gives the following range of values for fw:
Minimum fw = 0.05
Maximum fw = 0.47
These formulae can be used to calculate the infiltration rate which is to be expected at average wind speeds for a building which just meets the AP50 = 10m3/h/m2 standard. By inverting the formulae, we have:
For dwellings, ST/V is about 0.8. For larger buildings, both the ratios S/V and ST/V are likely to be 0.6 or less. Thus the infiltration rates at average wind speeds which correspond to the Part L airtightness standard are about 0.4 ach for dwellings and about 0.2 ach for larger buildings. Note that as the size of a building increases, its volume, V, tends to increase in proportion to the cube of a typical linear dimension, whereas the surface areas S and ST increase only in proportion to the square. Hence, for a facade design with a particular air leakage characteristic, the measured infiltration, in air changes per hour, tends to reduce as the building size increases.
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