how to calculate power and volume in the example

Question

The plungers of a 3 cylinder, single acting pump have diameters of 12com each stroke lengths of 50cm each. The pressure during the delivery stroke is 1000kPa. Calculate the power required to drive the pump at 350 rev/min, if the efficiency of the motor is only 90%. Calculate the volume of water delivered per minute if there is a 13% slip

Answer 1

Given

Diameter of the pump D = 12 cm

Stroke length , l_s  =50 cm

Delivered pressure, p = 1000 kPa

Speed of the pump , N = 350 rev/min

Efficiency,η =90%=0.9

Slip percentage = 13%

Volume per cylinder  = (Area) (stroke length)

                             =(π/4)D ²l_s 

                             = (π/4)(12)²(50)

                              = 5652  cm³/ cylinder. 

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Total volume, V =(Volume per cylinder)(Number of cyliders)

                     = (5652)(3)

                      = 16956 cm³

                              = 0.016956 m³

Calculate the volume flow rate by using the following formula:

                    Q =VN

                       = (0.016956)(350)

                       =5.9346 m³ /min

Consider the 13% slip :

Q (at 13% slip) = (5.9346)(1-0.13)

                     = 5.163 m³ /min

                     =  0.08605  m³ /sec            

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Calculate the power of the motor:

P = (p)(Q )/η

   =(1000)(0.08605)/0.9

   =95.61 kW

Therefore, the power of the motor is 95.61 kW