A centrifugal fan is being installed in a duct system. When the fan shaft is operated at 1150 rpm, the fan requires brake horsepower of 5,976 W (~8.0 hp). The fan laws may be applied to estimate the change in required fanshaft-power with shaft-speed. A 6-pole induction motor is to be directly coupled to the fan. The motor characteristics are as follows: Synchronous Speed = 1200 rpm Rated Speed = 1150 rpm Rated hp = 7,460 W (10.0 hp)

a. Provide calculations to verify that the operating shaft-speed of the fan and motor will be approximately 1159 rpm when they are coupled. (That is, verify that the power output of the motor and the power input required by the fan are approximately balanced at that shaft speed.)

b. Estimate the electric power consumption of the motor (W) when it drives the fan-shaft at 1159 rpm if it operates with motor-efficiency of 90% at that condition.

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