Q3. (a) A pump has the following characteristics where the usual notation applies:

Q (m3 /s)	0	0.01	0,02	0.03	0.04	0.05	0.06	0.07
Hp (m)	20	19	17	15	13	10	7	2
η (%)	0	35	60	65	65	55	40	25

The pump is to be used to deliver a liquid with density 800 kg/m3 along a 15 km-long, 350 mmdiameter pipeline. The static lift is 12m. Head losses due to friction may be estimated using the Darcy-Weisbach equation with friction factor 0.02 and minor losses amount to 5 times the velocity head in the pipe. Determine the operating discharge and the pump power consumption.

(b) It is proposed to use a second pump in order to increase the discharge. What is the discharge and total pump power consumption if the two pumps are used in series?

C) The critical Thoma cavitation number for the pump in part (a) is 0.32. For a discharge of 0.031 m3 /s, check for the possibility of cavitation if the pump is located 1 km from the pipeline inlet and if the pressure at the pipeline inlet is 151 kN/m2 (Figure Q3). Use a value of 3.1 kN/m2 for the vapour pressure of the fluid, assume no difference in elevation between the inlet and the pump and ignore minor (but not friction) losses between the inlet and the pump.

givens; P_inlet= 151 kN/m²   diameter= 0.35 friction factor= 0.02 discharge= 0.031 m3 /s distance between the inlet and the pump is 1000m

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