A belt drive on a motor driven fan has a drive sheave of 3 inch pitch diameter on the motor. The sheave of the fan shaft has a pitch diameter of 5 inch. When the motor speed is 1720 rpm, what is the fan speed?

A belt drive on a motor driven fan has a drive sheave of 3 inch pitch diameter on the motor. The sheave of the fan shaft has a pitch diameter of 5 inch. When the motor speed is 1720 rpm, what is the fan speed?

• A. 103.2 rpm
• B. 1032 rpm
• C. 1200 rpm
• D. 10320 rpm

Answer: (B)

The speed of a belt-driven pulley system is determined by an inverse relationship between pulley diameters and rotational speed because the belt covers the same linear distance per unit time on both pulleys. With the motor drive pulley having a pitch diameter of 3 inches and the fan pulley having a pitch diameter of 5 inches, the fan speed is reduced in proportion to the ratio of the diameters: N_fan = N_motor × (D_motor / D_fan) = 1720 × (3 / 5) = 1032 rpm. So the fan turns at 1032 rpm. The other numbers would come from using the wrong ratio or dimensions, which is why they don’t fit this setup.

The speed of a belt-driven pulley system is determined by an inverse relationship between pulley diameters and rotational speed because the belt covers the same linear distance per unit time on both pulleys. With the motor drive pulley having a pitch diameter of 3 inches and the fan pulley having a pitch diameter of 5 inches, the fan speed is reduced in proportion to the ratio of the diameters: N_fan = N_motor × (D_motor / D_fan) = 1720 × (3 / 5) = 1032 rpm. So the fan turns at 1032 rpm. The other numbers would come from using the wrong ratio or dimensions, which is why they don’t fit this setup.