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2.9 FAN LAWS.  Fan laws are a set of relationships that predict the changes
in a fan's operating characteristics when its speed is changed.  When the
speed of a fan is increased, the flow (cfm) increases, the static pressure
(sp) produced by the fan (and used up in the system ductwork friction)
increases, and the horsepower (hp) required to drive the fan increases.  The
following formulas predict how much each of these variables will increase:
= cfm1 x (rpm2/rpm1)
= sp2 x (rpm  2/rpm  1)2
= hp1 x (rpm2/rpm  1)3
In other words, the flow (cfm) increases in direct proportion with the
rpm, the static pressure increases with the square of the wpm, and the
horsepower consumed by the fan varies with the cube of the rpm.
Example:  A fan is delivering 4,000 cfm against a static pressure of
1.6 inches water column.  It is driven by a motor that has a 3.5-inch
sheave.  The fan horsepower is 1.4 hp.  If the motor sheave were changed
to 4.5 inches, what would be the new cfm, static pressure, and
Solution:  The diameter of the motor sheave has been increased by a
factor of (4.5/3.5) = 1.29.  Remember when you increase the motor pulley
you increase the flow, static pressure and horsepower requirement.
Therefore, the ratio of the new fan rpm to the old fan rpm is:
(rpm2/rpml) = 1.29
The new cfm being delivered will be:
= (4,000) x (1.29) = 5,160 cfm
The new static pressure will be:
= (1.6) x (1.29)2 =
2.66 inches water column
and the new horsepower will be:
= (1.4) x (1.29)3 = 3.0 hp
The most important facet of the fan laws to the technician is to under-
stand how fast the horsepower draw increases with a relatively small
increase in fan speed.  In the example above, the airflow and fan rpm were
increased by 29 percent, the static pressure was increased by 166 percent
and the horsepower requirement more than doubled to a 214 percent increase.


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