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                                          Chapter 8
                                                   Pumping, Storage, and Dual Water Systems
                                                                                          In theSIormetricsystem:
                                    8.2.1 Power Requirements and Efficiencies
                                    of Pumps
                                                                                                              3
                                                                                                 3
                                                                                       MP = (Q,m ∕s)(1,000 kg∕m )(H,m)(kW∕101.97 m-kg∕s)
                                    Work can be expressed as lifting a weight a certain vertical
                                                                                       MP = 9.8066(Q)(H)
                                                                                                                                 (8.7b)
                                    distance. It is usually defined in terms of ft-lb of work. Power
                                    is work per unit of time. These statements are expressed
                                                                                                           3
                                                                                       where Q = water flow, m /s; H = head or lift, m; and MP =
                                    mathematically by the following relationships:
                                                                                       power in metric unit, kW. Here 1 kW = 101.97 m-kg/s =
                                                                                       1,000 W; 1 W = 0.102 m-kg/s = 1 J/s; and 1 hp = 0.746 kW =
                                                                                (8.5)
                                                      Work = WH
                                                                                       550 ft-lb/s.
                                                     Power = Work∕t
                                                                                (8.6)
                                                                                          The total power input can be determined using the fol-
                                                                                       lowing equation:
                                    where
                                                                                        INHP = input power in US customary unit = (V)(A)∕746
                                       Work = work, ft-lb (m-kg)
                                                                                                                                  (8.8a)
                                       W = weight, lb (kg)
                                                                                       INMP = input power in metric unit = 0.001(V)(A)
                                       H = height, ft (m)
                                                                                                                                 (8.8b)
                                       Power = power, ft-lb/s (m-kg/s)
                                       t = time, s                                     where V = voltage, V; and A = current, amp.
                                                                                          The wire-to-water efficiency is the efficiency of the total
                                        If the water flow from a pump is converted to weight  power input to produce water horsepower:
                                    of water and multiplied by the vertical distance it is lifted,
                                                                                           E ww  = (E pump )(E motor )(E )         (8.9)
                                                                                                               o
                                    the amount of work or power done can be represented by the
                                    following equation:                                    E ww  = water horsepower∕input horsepower  (8.10)
                                        Power = Work∕t = WH∕t                          where
                                           HP = (Q, gpm)(8.34 lb∕gal)(H,ft)(min ∕60 s)
                                                                                         E ww  = wire-to-water efficiency
                                                × (horsepower∕550 ft-lb∕s)
                                                                                         E pump  = efficiency of the pump
                                           HP = (Q)(H)∕3,957                   (8.7a)    E motor  = efficiency of the motor driving the pump
                                    where Q = water flow, gpm; H = head or lift, ft; and HP =  E = efficiency of any other parts in the entire motor-
                                                                                          o
                                    power in US customary unit, hp.                        pump-wiring system
                                      EXAMPLE 8.2 DETERMINATION OF PUMP POWER
                                      Determine the water horsepower, break horsepower, and motor horsepower for a pump operating under the following conditions:
                                                             3
                                      water flow of 620 gpm (0.039 m ∕s = 39 L∕s) is to be pumped against a total head of 135 ft (41.15 m); the pump efficiency is 80%;
                                      and the motor driving the pump has an efficiency of 90%.
                                      Solution 1 (US Customary System):
                                                              WHP = water horsepower in US customary unit = (Q)(H)∕3,957
                                                                  = (620) (135)∕3,957 = 21.2 hp                                 (8.11)
                                                                                                                              (= 8.7a)
                                                               BHP = break horsepower in US customary unit = WHP∕E pump
                                                                   = 21.2∕0.80 = 26.5 hp                                        (8.12)
                                                              MHP = motor horsepower in US customary unit = BHP∕E motor
                                                                   = 26.5∕0.90 = 29.4 hp                                        (8.13)
                                      where Q = water flow, gpm; and H = head or lift, ft.
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