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86 Advanced Mine Ventilation

Figure 6.4 Characteristics of an axial flow fan.

6.4 Fan Laws

A detailed discussion of fan laws is available in literature [1], hence only a summary
discussion will be provided here.
Assuming the density of air is constant, fan performance is controlled by only two
variables: speed (n) and fan diameter, D. The efficiency is usually a constant.
Table 6.1 summarizes the impact of variation in (n) and D; on quantity, Q; head, H;
and power, P.
The changes in pressure and power are directly proportional to air density, but the
quantity is not impacted.
An example:
A fan running at 500 rpm produces a head of 1 W.G. (water gauge), with 40,000
00
CFM and a horsepower of 7.00 and an efficiency of 0.9.
Calculate the new Q, H and horsepower if (a) the speed is changed to 1000 rpm or
(b) the diameter is doubled, keeping tip speed constant.

1. From Table 6.1; speed is doubled to 1000 rpm.
Q 2 ¼ ; hence, Q 2 ¼ 80,000 CFM
n 2
a.
Q 1 n 1
2
H 2 n 2
¼ 2 ; hence, H 2 ¼ 4 in.
b. n
H 1
1
n 2 3
H:P: 2 ¼ð Þ ; hence, new H.P 2 . ¼ 56 H. P.
c.
H:P: 1 n 1
Note that efficiency, h, does not change.
2. If tip speed, PDn, stays constant and D 2 ¼ 2D 1
D 2 2
Q 2 ¼ ð Þ ;Q 2 ¼ 160,000 CFM
a.
Q 1 D 1
b. H 2 ¼ H 1 ¼ 1 in.
¼ð Þ ; hence H.P. 2 ¼ 28 H.P.
H:P: 2 D 2 2
c.
H:P: 1 D 1