Sharp JX-9400 Informations techniques Page 25

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Constant concentration
Using an electronic mass flow controller monitored by the tracer gas analyser,
the concentration of tracer gas can be maintained constant by varying the
injection rate in an appropriate way. In this case, the time derivative of the
concentration is zero and Equation 1.4 becomes very simple:
I þ Q
io
ðC
i
C
o
Þ¼0 ð1:15Þ
hence:
Q
io
¼
I
ðC
i
C
o
Þ
¼
I
C
ð1:16Þ
This method provides an unbiased estimate of the airflow rate, even when it
varies with time.
Pulse injection
The method can also be used with the tracer injected as a short pulse at time t
0
.
The injected mass M will result in a tracer gas concentration at sampling loca-
tion that varies with time, starting from background concentration C
0
, growing
and then decaying back to background concentration. Let C(t) be the tracer
concentration above background.The total mass of tracer gas passing at the
sampling location is then:
M ¼
ð
1
t
0
CðtÞ QðtÞdt ð1:17Þ
An app roximation to infinite time can be good enough when the experiment
(and the integral) is stopped at time t
f
, when the concentration is close
enough to background.
Since both functions C(t) and Q(t) are positive and continuously derivable,
we can apply the integral mean value theorem (Axley and Persily, 1988), that is:
M ¼ QðÞ
ð
t
f
t
0
Cð tÞdt with t
0
<<t
f
ð1:18Þ
This means that there exists a time during the experiment, when the airflow
rate Q has a value satisfying the above equation. The knowledge of the injected
mass M and measurements of the integral of the concentration down wind can
then provide a value of Q.
The integral of the concentration can be calculated from the mass of
tracer m sampled downwind from the injection port by pumping the air at
known rate Q
s;i
through a tube. The sa mpled mass is related to concentration
by:
m ¼
ð
1
0
CðtÞQ
s
ðtÞdt ð1:19Þ
4 Ventilation and Airflow in Buildings
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