An exercise room has six weight-lifting machines that have no motors and seven treadmills, each equipped with a 2.5-hp (shaft output) motor. The motors operate at an average load factor of 0.7, at which their efficiency is 0.77. During peak evening hours, all 13 pieces of exercising equipment are used continuously, and there are also two people doing light exercises while waiting in line for one piece of the equipment. Assuming the average rate of heat dissipation from people in an exercise room is 740 W, determine the rate of heat gain of the exercise room from people and the equipment at peak load conditions.

Question

Engineering

Levi Daugherty

2 June, 11:24

An exercise room has six weight-lifting machines that have no motors and seven treadmills, each equipped with a 2.5-hp (shaft output) motor. The motors operate at an average load factor of 0.7, at which their efficiency is 0.77. During peak evening hours, all 13 pieces of exercising equipment are used continuously, and there are also two people doing light exercises while waiting in line for one piece of the equipment. Assuming the average rate of heat dissipation from people in an exercise room is 740 W, determine the rate of heat gain of the exercise room from people and the equipment at peak load conditions.

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Case Ryan · Answer 1

25.4 kW

Explanation:

There are 15 people doing exercises, each will dissipate 740 W of heat, so they will disspiate a total of p = 15*740 = 11100 W = 11.1 kW

There are 7 treadmills, each has a 2.5 hp motor (1.86 kW) running at a load factor of 0.7 with an efficiency of 0.77. So their total power would be p = 7*1.86*0.77/0.7 = 14.3 kW

So the total heat dissipated would be 11.1 + 14.3 = 25.4 kW.