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Belt driven fans are common in heating, ventilation and cooling systems.

The length of the belt can be calculated as
lb = ((df + dm) 1.5708 ) + (2 lfm) (1)
where
lb = length of belt (mm, inches)
df = pulley diameter fan (mm, inches)
dm = pulley diameter motor (mm, inches)
lfm = center to center distance of fan and motor pulleys (mm, inches)
The velocity at which a belt travels may be expressed as
v = π dm nm / 12 (2)
where
v = velocity of belt (ft/min)
nm = velocity motor (rpm)
The relationship between the speed of the motor, the fan and their disc diameters can be expressed as
df nf = dm nm (3)
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