8.14 Discrete Solution (Step by Step Method)
347
Solution
As stated in the problem, α = 2 and γ = 0.5 for all cases. Therefore:
Condition
Variable
Unit
Bertard and
Bodelle
(1962)
Continuous model
Step by step
model
Solver
Table
Short
Long
Very well
executed
θ: 0.000005 Number of
segments
(n)
–
–
–
–
4
16
Fan
pressure
(P v )
Pa
5889.0
5891.9
5995.9
5861.2 5857.7
Fan airflow
rate (Q v )
m 3 s −1 7.55
7.56
7.56
7.51
7.5
Fan power
(η = 1)
kW
44
45
45
44
44
Well
executed
θ: 0.00001 Fan
pressure
(P v )
Pa
5921.6
5927.2
5991.9
5866.0 5858.8
Fan airflow
rate (Q v )
m 3 s −1 7.61
7.61
7.62
7.51
7.5
Fan power
(η = 1)
kW
45
45
46
44
44
Poor
θ: 0.0001
Fan
pressure
(P v )
Pa
6508.3
6611.9
6757.1
5952.7 5879.9
Fan airflow
rate (Q v )
m 3 s −1 8.59
8.68
8.71
7.63
7.53
Fan power
(η = 1)
kW
56
57
59
45
44
Very poor θ: 0.001
Fan
pressure
(P v )
Pa
12,375.6
19,835.8 21,236.7 6925.6 6096.9
Fan airflow
rate (Q v )
m 3 s −1 18.36
23.23
24.01
8.89
7.83
Fan power
(η = 1)
kW
227
461
510
62
48
The different calculation methods offer similar solutions for very well executed,
well executed and even poor installations, however, they provide very different results
for very poor installations. This can be explained bearing in mind that moderate
leakage was assumed in the derivation of all formulae used in these methods.