Variable Torque Pumps
There are several types of pumps. The most common pump is the end-suction centrifugal pump illustrated below. There are variations of the centrifugal pump. Turbine and propeller pumps are examples. This section deals with variable torque loads. The faster a centrifugal pump turns the more fluid it pumps and the more torque it requires. It should be noted that not all pumps are variable torque. Reciprocating, positive displacement pumps are constant torque.
Horsepower
Calculating horsepower for a pump application is an involved process that requires someone with a thorough knowledge of the application and pumps. The following information is for illustration only. There are three related horsepower calculations involved in pump applications: liquid, mechanical and electrical
Hydraulic Head
Hydraulic head is the difference in hydraulic pressure between two points, which actually includes elevation, pressure and velocity. An increase in pump speed would cause increases in pressure and velocity which increases the hydraulic head
Liquid Horsepower
Liquid horsepower is the hydraulic power transferred to the pumped liquid. The following formula can be used to calculate liquid energy.
Liquid Energy in ft-lb = Total Head x (Gallons x Weight)
Water weighs 8.34 pounds per gallon. If 50 gallons of water per minute were required to be moved through 100 feet of head the energy required would be 41,700 ft I lb/minutes.
100 feet x (50 gallons x 8.34) = 41,700 ft-lb/minute
If the pumps speed were increased so that 100 gallons of water were being pumped through 100 feet of head the energy would be 83,400 ft lb/minute. Twice the energy would be required. The hydraulic head would, in actuality, also increase.
100 feet x (100 gallons x 8.34) = 83,400 ft-lb/minute
The common method of expression is horsepower. One horsepower is equal to 33,000 ft-lb/minute.
Therefore, 41,700 ft-lb/minute is 1.26 HP and 83,400 ft-lb/minute is 2.53 HP.
Mechanical Horsepower
Mechanical horsepower is the horsepower input to the pump and is equal to the liquid horsepower divided by the pump’s efficiency. If the liquid horsepower is 2.53 and the pump is 75% efficient the brake horsepower is 3.4 HP.
Electrical Horsepower
Electrical horsepower is the horsepower required to run the motor driving the pump and is equal to the mechanical horsepower divided by the motor’s efficiency. If the motor is 90% efficient the electrical horsepower is 3.78 HP. It can be seen that with an increase of pump speed there is a corresponding increase in electrical horsepower
Torque, HP, and Speed
The speed on a pump is increased by increasing the AC drive frequency (F) to the motor. Torque (T) is affected by flux (Φ) and working current (IW). The drive will maintain appropriate flux by adjusting the voltage and frequency ratio dependent on speed. During acceleration, working current will increase causing a corresponding increase in torque. In this application, torque increases in proportion to the speed squared. This is due to the increase in hydraulic head as the pump works harder to pump more fluid. Horsepower increases in proportion to the speed cubed due to an increase of torque and speed. The pump cannot be operated above the rated frequency of the motor
(60 Hz) because the drive will no longer be able to provide constant flux. As a result, the motor will be unable to supply rated torque. The load’s torque requirements increase while the motor’s ability to supply torque decreases
Fans
This same principle applies to fan applications. The horsepower of a fan is determined by dividing the product of air flow (in cubic feet per minute) and pressure by the product of the constant 6356 and fan efficiency. Increasing the speed of the fan increases air flow and pressure, requiring the motor to work harder (IW increases). Torque and horsepower increase
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