Discharge (l s^1 ) 000204060
Head (m) 100 90 66 38The discharge is 64 l s^1 at a total head of 31.5 m. Hence the head per
pump is 31.5/215.75 m. The corresponding efficiency is 35%.
Therefore the total power consumption in series operation is
2 9.810.06415.75/0.3556.5 kW.Two pumps in parallel deliver 73 l s^1 (Qin series) to a head of 36 m
(Hin series) with a power consumption of 37.36 kW (power in series).
Hence a parallel system is the best option to provide the increased flow.
Worked Example 13.3
Water from an abstraction well in a confined aquifer is pumped to the
ground level by a submersible borehole pump; an in-line booster pump
delivers the water to a reservoir, with the level 20 m above ground level at
the well site. The system’s pipework has the following characteristics:
System characteristics:
discharge (l s^1 ) 2030405060
head losses (m) 01.38 03.14 05.54 08.56 12.21
Pump discharge (l s 1) 0010203040
Borehole pump head (m) 10.0 09.6 08.7 07.4 05.6
Booster pump head (m) 22.0 21.5 20.4 19.0 17.4
Aquifer and well data are as follows: the coefficient of permeability of the
aquifer,K50 m per day; the aquifer thickness, b20 m; the radius of the
well,rw0.15 m.
A pumping test suggested that the drawdown was 3 m when the
abstraction rate was 30 l s^1. The water table is 2 m below ground level. The
drawdown is as follows:
zw(Q/2πKb)ln(R 0 /rw) (ii)whereQis the abstraction rate in m^3 per day, and R 0 is the radius of influ-
ence of the well, which may be assumed to be linearly related to the
abstraction rate.
Determine the maximum discharge which the combined pumps
would deliver to the reservoir.