Hydraulics Math Problem and Solution || Reciprocating Pump Chapter

 Hydraulics Math Problem and Solution || Reciprocating Pump Chapter ||

 Problem :  A single acting reciprocating pump has a bore of 500 mm and a stroke of 500 respectively. The pump delivers 0.11 m³/s of water against a head of 100 m. The head loss due to friction in suction and delivery pipes are 2 m and14 m respectively. The velocity of water in the pipe is 1.5 m/s. If the pump efficiency is 92% and the slip is 5%, calculate the speed of the pump and the power required to drive the pump.

Question

Solution: 

Given data, 

          Bore, D = 500 mm = 0.5 m 

          Stroke, L = 500 mm = 0.5 m

          Actual Discharge, Qac = 0.11 m³/s

          Head, H = 100 m 

          Friction head loss in suction pipe, H(fs) = 2 m 

          Friction head loss in delivery pipe, H(fd) = 14 m 

          Velocity, v = 1.5 m/s

           Pump Effiency η = 92%

          Slip, S = 5%

          To Find, 

                    (i) Speed of the pump, N = ?

                    (ii) Power of the pump, P = ?

We know, Slip = {Q(th) - Q(ac) } / Q(th)

                 ⇨ 0.05 = {Q(th) - 0.11] / Q(th) 

                ∴ Q(th) = 0.116 m³/s

Again, Q(th) = LAN / 60

             ⇨ 0.116 X  60 = 0.5 X π /4 X (0.5)^2 X N

              ∴ N = 70.89 r p m (Answer) 

Total Head , H(t) = H + H(fs) + H(fd) + v^2 / 2g

                           = 100 + 2 + 14 + (1.5)^2 / 2 x 9081

                           = 116.11 m

Power, P = {Q(th) γ H(t)} / η 

              = (0.116 x 9.81 x 116.11) / 0.92

              = 143.62 KW (Answer)