Example                                                                         TET401: Material Engineering & Thermofluid
An oil pump is drawing 35kW of electric power while pumping oil with  = 860kg/m3 at rate of
   0.1m3/s as shown in Figure 1. The inlet and outlet diameters are 8cm and 12cm respectively. If the
   pressure rise of oil in the pump is measured to be 400kPa and the motor efficiency is 90%,
   determine the mechanical efficiency of the pump. Take the kinetic energy correction factor to be
   1.05.
                                                                     Figure 1
   Solution
   Assumptions:
          (i)     The flow is steady and incompressible.
          (ii)    The elevation difference across the pump is negligible.
          (iii)   All the losses in the pump are accounted for by the pump efficiency and thus hL = 0.
          (iv)    The kinetic energy correction factors are given to be 1 = 2 =  = 1.05.
   The density of oil is given to be  = 860 kg/m3.
   We take points 1 and 2 at the inlet and the exit of the pump, respectively. Noting that z1 = z2, the
   energy equation for the pump reduces to
           P1      V2                  P       V2                                                       P2  P1  (V 22  V12 )
                1 1  z1  hpump, u  2   2 2  z 2  hturbine, e  h L               hpump, u           
           g       2g                 g       2g                                                        g          2g
   where
                  V         V              0.1 m 3 /s
           V1                                              19.9 m/s
                  A1       D12 / 4        (0.08 m) 2 / 4
                  V          V              0.1 m 3 /s
           V2                                              8.84 m/s
                  A2       D22 / 4        (0.12 m) 2 / 4
                                                                          1
Example                                                                           TET401: Material Engineering & Thermofluid
   Substituting, the useful pump head and the corresponding useful pumping power are determined to
   be
                            400,000 N/m 2           1 kg  m/s 2    1.05[ (8.84 m/s) 2  (19.9 m/s) 2 ]
          hpump, u                                                                                     47.4  17.0  30.4 m
                       (860 kg/m 3 )(9.81 m/s 2 )      1N         
                                                                               2(9.81 m/s 2 )
                                                                                       1 kN             1 kW 
          W pump,u  Vghpump, u  (860 kg/m 3 )(0.1m 3 /s)(9.81m/s 2 )(30.4 m)                     
                                                                                                         1 kN  m/s   25.6 kW
                                                                                   1000 kg  m/s
                                                                                                  2
                                                                                                        
          Then the shaft pumping power and the mechanical efficiency of the pump become
           W pump,shaft   motorW electric  (0.90)(35 kW)  31.5 kW
                    W            25.6 kW
           pump   pump, u           0.813  81.3%
                  Wpump, shaft 31.5 kW