Worked Example 13.1
The gravity flow between an impounding reservoir and a service reservoir
is to be augmented by 25% owing to immediate future demand. Gravity
flow data are as follows: head available100 m; pipeline length1000 m;
pipe diameter250 mm; pipe roughness0.15 mm. A pump with an oper-
ating speed of 1450 rev min^1 will be used to boost the flow in the existing
main.
- What type of pump would you recommend?
- Assuming the pump manometric efficiency to be 70% and the elec-
trical motor efficiency to be 90%, calculate the continuous power
consumption in kW.
- Where on the pipeline would you install the pump?
Solution
GRAVITY FLOW
As given above, L1000 m, D0.25 m, k0.15 mm, and H100 m.
Combining the Darcy–Weisbach and Colebrook–White formulae (Feath-
erstone and Nalluri, 1995) gives
V 2(2gDSf)1/2log[k/3.7D2.51v/D(2gDSf)1/2] (i)
whereSfis the friction gradient.
The first iteration with Sf100/10000.1 gives V5.256 m s^1.
Therefore minor losses, hm1.5V^2 /2g2.11 m. Hence the new friction
gradient,Sf(100.00 2.11)/10000.0979.
A better estimate of V(from equation (i)) is 5.2 m s^1 , giving Q
255 l s^1. The boosted flow is 1.25 255 319 l s^1.
Equation (i) gives (by iteration) the corresponding head loss
SfL153 m. Hence the total head needed to give 319 l s^1
153 1.5V^2 /2g156.23 m. Therefore the increase in the head needed for
568 PUMPING STATIONS
Table 13.3 Sludge flow head losses
Moisture content Factor F (equation (13.24))
of sludge (%)
100 1.00
98 1.25
96 1.75
94 2.75
92 4.75
90 7.00
