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corresponding to the nominal time constant. The air exchange eﬃciency in

this very theoretical case is 100 per cent. At 99 per cent air exchange eﬃ-

ciency, there is already some spreading of the ages around an average still

equal to the nominal time constant. When probability density function

spreads out and the probability function smoothens, the mean age at exhau st

remains the same, but there are more young air particles and more aged ones.

In addition, the most probable age (the time of the maximum of the curve) is

reduced. At 66 per cent air change eﬃciency, this most probable age is

already half the nominal time constant. At 50 per cent eﬃciency or complete

mixing, the probability density of the age of the air at exhaust is an exponen-

tial: there are more young particles than old ones reaching the exhaust. With

this distribution, the most probable age is zero, but the mean age is still

equal to the nominal time constant. The last curve, with 25 per cent eﬃ-

ciency, represents a situation with a shortcut.

Figure 3.3 shows the corresponding probability curves for the age of the

air at exhaust, still with one hour as nominal time constant. This function

shows the percentage of particles at exhaust that are older tha n the value

given on the ordinate. At 100 per cent eﬃciency, all particles are exactly one

hour (one time constant) old. When the eﬃciency decreases, the function

progressively changes to become an exponential at 50 per cent eﬃciency or

complete mixing. When the eﬃcie ncy decreases, there are less and less young

particles and more and more old ones at exhaust. At 25 per cent eﬃciency,

which is very poor, 10 per cent of the volume of the air at exhaust is older

than three time constants!

Measurement method

The air entering the room is marked with a gas (the tracer gas), and the

concentration of that tracer gas is monitored at the location of interest. This

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.5 1 1.5 2 2.5 3

(τ)

25%

50%

66%

80%

90%

99%

100%

Figure 3.3 Typical probability curves for the age of the air

Note: These theoretical curves are for illustration. Some of them, in particular at very

high eﬃciency, are not likely to be found in practice.

42 Ventilation and Airﬂow in Buildings

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