The plunger of a three-cylinder water pump has a diameter of 80 mm and a stroke length of 260 mm. The pressure during the delivery stroke is 800 kPa. Calculate:
a) The power required to drive the pump at 160 r/min if the efficiency of the motor is 80%.
First, calculate the displacement volume of one stroke of the pump:
Displacement volume = π*(diameter/2)^2 * stroke length
Displacement volume = π*(80mm/2)^2 * 260 mm
Displacement volume = 251,327.41 mm^3 = 0.25132741 L
Convert the displacement volume to m^3:
Displacement volume = 0.25132741 L = 0.00025132741 m^3
Since the pump is three-cylinder pump, the total volume displaced in one revolution is:
Total volume displaced = 3 * 0.00025132741 m^3 = 0.00075398223 m^3
Now, calculate the work done in one revolution of the pump:
Work = Pressure * Volume
Work = 800,000 Pa * 0.00075398223 m^3 = 603.18578 J
Since the pump operates at 160 r/min, the power required to drive the pump can be calculated as:
Power = Work done per revolution * Revolutions per minute
Power = 603.18578 J * 160 r/min = 96,510.125 W = 96.51 kW
Since the efficiency of the motor is 80%, the actual power required to drive the pump is:
Actual power = Power required / Efficiency
Actual power = 96.51 kW / 0.80 = 120.64 kW
Therefore, the power required to drive the pump is 120.64 kW.