Question

Q2. 50 marks Water at 20°C is pumped at 5.7 m3 min-1 from the lower to the upper reservoir, as in Fig. 2. The free surface of the upper reservoir is at height Z2 = 46 m, and of the lower reservoir at 21 = 15 m. The pipe diameter before and after the pump is D= 15 cm. Pipe friction losses are approximated by h = 27v2/(29), where V is the average velocity in the pipe. The gravitational acceleration is g = 9.81 m s-?, and, at 20°C, the mass density of water is p=998 kg m-3. (a) Choose appropriate reference fluid states, and write the energy equation for water flow between them. [15 marks] (b) Compute the pump head hpump. [24 marks] (c) Compute the power Pp (in watts) that the pump delivers to the flow. [8 marks] (d) If the pump is 75 per cent efficient, what power (in watts) is needed to drive it? [3 marks] 22 = 46m 21 = 15m D = 15cm Pump Figure 2: Pumping water from the lower to the upper reservoir

Answer 1

Solutions Q = 5-7 m/min = 5:7 m2 D- 15 cm = 0.15m 60 Set = 27 V2 2 28 22= 46m, Z= 15m { = P = 1 atm , g = 9.81m/secz h at T-20c , P=998 Kgfm Q=AV=400 V V-40 TD² **0.15) #1 4= 5.376 m/sec Aphrey 4* 5.7 60 marzec # At 20°c water is the ligheidl form of we can apply Behruli's eqfuation Mechanical Energy Balance Equation) between Beint © £ @ 0 Pg + Zith pump /29 +2+ hy 1 20 # Case-In 1=1 (100 % efficerey), # Cs-19 =0.75 (75% flang) After simplification ® from Zythromb = Z the 46m +27*/5-376}mt/54 249.817/sect 1.5m+ 1* Kruges

hpump (46+39.773)m – 15 m Answer th pump = 70.773 m Affroy Pp = Pg h pump *2 Pp = 998 Kg *9.81m),* 70.773m*. m3 bec? 60 Sec Shoewel Pp = 65825 Watt) Alpex n = 0.75 Po Pop 65825 Watt 0.75 = 87766-67 Watt Affool

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