
We have mentioned abo ve the following recirculation rates:
External R
e
¼
_
mm
i
_
mm
o
_
mm
e
¼
_
mm
e
_
mm
a
_
mm
e
ð5:20Þ
Inlet to exhaust R
ie
¼
_
mm
i
_
mm
rs
_
mm
i
¼
_
mm
e
_
mm
re
_
mm
i
ð5:21Þ
Extract to supply R
xs
¼
_
mm
s
_
mm
rs
_
mm
x
¼
_
mm
x
_
mm
re
_
mm
x
ð5:22Þ
The mass flow balance for the whole building is:
_
mm
a
þ
_
mm
exf
¼
_
mm
o
þ
_
mm
inf
ð5:23Þ
Combining this equation with the definition of the exter nal recirculation rate,
we get:
_
mm
e
¼
1
1 R
e
ð
_
mm
o
þ
_
mm
inf
_
mm
exf
Þð5:24Þ
Then, writing the mass flow rate balance at node 1 (see Figure 5.8), we get:
_
mm
i
¼
_
mm
o
þ R
e
_
mm
e
¼
_
mm
o
þ R
e
ð
_
mm
inf
_
mm
exf
Þ
1 R
e
ð5:25Þ
The mass balance at node 2 gives:
_
mm
rs
¼ð1 R
ie
Þ
_
mm
i
¼
ð1 R
ie
Þ
ð1 R
e
Þ
½
_
mm
o
þ R
e
ð
_
mm
inf
_
mm
enf
Þ ð5:26Þ
From mass balances at nodes 3 and 4:
_
mm
s
¼
_
mm
rs
þ R
xs
_
mm
x
ð5:27Þ
and
_
mm
s
¼
_
mm
x
þ
_
mm
exf
_
mm
inf
ð5:28Þ
we get
_
mm
x
¼
1
1 R
xs
½
_
mm
rs
þ
_
mm
inf
_
mm
exf
¼
_
mm
o
ð1 R
ie
Þþð1 R
e
R
ie
Þð
_
mm
inf
_
mm
exf
Þ
ð1 R
xs
Þð1 R
e
Þ
ð5:29Þ
Mass balance at node 5 gives:
_
mm
re
¼
_
mm
x
ð1 R
xs
Þð5:30Þ
Therefore:
G
¼
_
mm
x
ð1 R
xs
Þ
_
mm
x
þ
_
mm
exf
"
HR
¼
x
re
"
HR
ð5:31Þ
Measurements and Measures Related to Energy Efficiency in Ventilation 91
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