to a service reservoir situation at an elevation of 200 m above ground level. There are
three booster pumps connected in parallel, each having a reliability of 0.9, but only
two are operated at any one time, at the design flow.
Determine
(a) the reliability of the booster pumps
(b) the reliability of the system
(c) the change in the reliability, if a second pump is installed in the well, to feed the
booster pumps.
(d) Subsequently, a ground reservoir is constructed, to receive water from the well.
The booster pumps are then fed from the ground reservoir. How does this
arrangement affect the reliability of water supply?
Solution
Figure 9.8 shows the initial arrangement.
The booster pumps X, Y and Z are connected in parallel, but only two are
operated at one time. The calculation of pump reliability therefore needs to assume
any two pumps in parallel, say X and Y (Fig. 9.9).
Unreliability of any of the pumps X, Y or Z ¼ 1 – 0.9 ¼ 0.1
Combined unreliability ¼ F SYST = 0.1 Â 0.1 = 0.01
The reliability of pumps X and Y, in parallel is then given by the expression
Town
Service Reservoir
Submersible
Pumps A (B)
Ground
Reservoir
Booster
Pumps X, Y, Z
100 m
200 m
The ground reservoir has been inserted in this diagram, for part (d).
For parts (a), (b), and (c), assume it does not exist, the pump A
feeding directly to the booster pumps X, Y or Z.
Fig. 9.8 Pump arrangement from well to service reservoir
Pump A, R = 0.9
Pump X, R = 0.9
Pump Y, R = 0.9
Pump Z, R = 0.9
Fig. 9.9 Schematic drawing for pump arrangement
9.7 Measures of Reliability
275