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there is a priori only one neutral plane at the height z

. The neutral plane is the

generally horizontal plane in the building or part of it where the indoor–

outdoor pressure diﬀerential is zero. Its height depends on the size and position

of the ventilation and leakage openings. It is such that the airﬂows going in and

out of the building are balanced.

The pressure diﬀerence, p, caused by the stack eﬀect at any height, z,ina

given building conﬁguration is then:

pðzÞ¼

ðzÞgdz ð4:21Þ

where ðz Þ is the diﬀerence between the densities of indoor and outdoor air at

height z, and g ¼ 9:81 m/s

is the accele ration due to gravity.

If the temperatures are homogeneous, Equation 4.21 gives:

pðzÞ¼gðz  z

Þð4:22Þ

Using the law of perfect gases to express the air density, we get:

pðzÞ¼







gðz  z

Þð4:23Þ

where:

and T

are the indoor and outdoor air absolute temperatures,

M is the average molar mass of the air, i.e. 0.029 kg/mole,

p is the atmospheric pressure,

R is the constant for perfect gases, i.e. 8.31396 J/mole K.

The leakage of the building is represented by the usual power law:

Q ¼ C p

ð4:24Þ

Assuming that the exponent n is the same for every leak, there are three

unknowns, the leakage coeﬃcients, C

, C

and C

. To estimate these coeﬃcients,

three measurements are performed, where the pressure diﬀerences, the tempera-

tures at various heights in the building and some airﬂows are measured. A ﬁrst

relationship is given by the conservation of mass with a closed envelope. The

two other equations are obtained by mass conservation with a large opening at

the bottom and at the top of the building. In these cases, the airﬂows through

these openings are measured. The relations are as follows:

1 All openings closed – in this case, the neutral plane is somewhere at mid-

height of the building and, by conservation of the mass of air, we have:



pðz

¼ 

pðz

dð

pðz

Þð4:25Þ

where 

, 

and 

are the densities of the air at the ground level, the

remaining ﬂoors and at the top level in order to hav e the proper mass ﬂow.

2 Entrance door open – the airﬂow through the open entrance door (or any

other large opening on the ground level), Q

, is measured, either by

Airtightness 71

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