336
8 Secondary Ventilation
Calculation Procedure
Assuming that conditions are such that pressure at the duct outlet (gallery face) is P f
= 0 and that the airflow rate, Q f , at the face can be measured, the following procedure
allows us to determine the operating conditions (Q v , P v ) of the fan:
1st Calculation of the integration constant (C 1 ) can be done using Eq. 8.50, relating
the values for pressure and airflow rate at the duct outlet:
P
3
2
f =
r
2θ
Q
3
f + C 1
Therefore:
C 1 =
2θ
r
P
3
2
f − Q
3
f
Since P f = 0, then:
C 1 = −Q
3
f
2nd Calculation of z at duct outlet.
z =
3
1 −
C 1 r
2θ
1
P
1.5
f
Note that, since P f = 0, then z → ∞.
3rd Calculation of the constant C 2 for the conditions at the duct outlet (L = x; P f
= 0 and z → ∞).
First, using Eq. 8.54, we find I(z):
I (z) =
1
3
ln
(z − 1)
2
z 2 + z + 1
−
2
√
3
arctan
2z + 1
√
3
=
Taking the limit z → ∞:
lim
z→∞
1
3
ln
(z − 1)
2
z 2 + z + 1
=
1
3
ln(1) = 0
lim
z→∞
−
2
√
3
arctg
2z + 1
√
3
= −
2
√
3
·
π
2
= −
π
√
3
Then, using Eq. 8.55, knowing that x = L: I(z) = r
2θ
r
2
3 L + C 2
Therefore:
−
π
√
3
= r
2θ
r
2
3
L + C 2