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sums of the  matrix are the mean age of air in the corresponding rooms:

h

i¼

j ¼1



ð1:38Þ

This relation enables the measurement of the room mean age of air to be made,

even in rooms where there are several outlets or several ways for the air to leave

the room.

Equations for volume ﬂow rates

All equations above are based on mass balance, and hence include mass airﬂow

rates and mass concentrations. However, for practical reasons, volume ﬂow

rates and volume concentrations are of common use. Therefore, the basic

equations should be adapted as shown below.

The mass of the tracer k in the zone i is:

¼ 



1  C

ﬃ 

¼ 

ð1:39Þ

since C

 1.

The tracer density is deﬁned by 

¼ m

where the volume, V

,is

deﬁned at atmospheric pressure, p. Using the perfect gas law for tracer k:

¼ RT

ð1:40Þ

where R is the molar gas constant, R ¼ 8313.96 [J/(K  kmole)], M

the molar

mass of the tracer, k, and T

is the absolute temperature of zone i. The density

of tracer k in zone i can be computed:



ð1:41Þ

This is also valid for the density of air, by simply omitting the suﬃx k and using

the average molecular weight (M ﬃ 29 g/mole) of the air.

Introducing this in Equations 1.23 and 1.26 gives the set of balance equa-

tions to be used when handling volumes instead of masses. Equation 1.30

becomes:

j ¼0

ðc

 c

ð1  

Þð1:42Þ

where:

T is the absolute te mperature of zone i or j, or of tracer k, depending on the

subscript;

is the volume concentration of tracer k in zone i;

is the volume injection rate of tracer k in zone i;

is the volume ﬂow rate from zone j to zone i.

Airﬂow Rates in Buildings 11

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