Page 254 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

JWCL344_ch06_194-229.qxd 8/2/10 9:51 PM Page 214

214 Chapter 6 Water Distribution Systems: Components, Design, and Operation

3. Equivalent line AD. Assume H 8.4 ft (2.56 m).
(a) Line ABD, 4,000 ft, 12 in.; s 8.4 4.00 2.1; Q 1.00 MGD (3.785 MLD).
(b) Line ACD, 4,360 ft, 8 in.; s 8.4 4.36 1.92; Q 0.33 MGD (1.25 MLD).
(c) Total Q 1 0.33 1.33 MGD (5.03 MLD).
(d) Equivalent length of 14-in. (350 mm) pipe: Q 1.33, s 1.68, 1,000 8.4 1.68
5,000 ft (1,524 m).
(e) Result: 5,000 ft of 14-in. (1,524 m of 350-mm) pipe.
Necessary calculations are as follows:
1. Because line ABD consists of two pipes in series, the losses of head created by a given
flow of water are additive. Find, therefore, from the Hazen-Williams diagram (Chapter 5
and/or Appendix 14) the frictional resistance s for some reasonable flow (1 MGD) or (3.78
MLD) (a) in pipe AB and (b) in pipe BD. Multiply these resistances by the length of pipe
to obtain the loss of head H. Add the two losses to find the total loss H 8.4 ft (2.56 m).
Line ABD, therefore, must carry 1 MGD (3.78 MLD) with a total loss of head of 8.4 ft
(2.56 m). Any pipe that will do this is an equivalent pipe. Because a 12-in. (300-mm) pipe
has a resistance s of 2.1% when it carries 1 MGD (3.78 MLD) of water, a 12-in. (300-mm)
pipe, to be an equivalent pipe, must be 1,000 8.4 2.1 400 ft (122 m) long.
2. Proceed in the same general way with line ACD to find a length of 4,360 ft (1,329 m) for
the equivalent 8-in. (200-mm) pipe.
3. Because ABD and ACD together constitute two lines in parallel, the flows through them at
a given loss of head are additive. If some convenient loss is assumed, such as the loss al-
ready calculated for one of the lines, the missing companion flow can be found from the
Hazen-Williams diagram. Assuming a loss of 8.4 ft (2.56 m), which is associated with a
flow through ABD of 1 MGD (3.78 MLD), it is only necessary to find from the diagram
that the quantity of water that will flow through the equivalent pipe ACD, when the loss of
head is 8.4 ft or 2.56 m (or s 8.4 4.36 1.92‰), amounts to 0.33 MGD (1.25 MGD).
Add this quantity to the flow through line ABD (1.0 MGD) or 3.78 MLD to obtain 1.33
MGD (5.03 MLD). Line AD, therefore, must carry 1.33 MGD (5.03 MLD) with a loss of
head of 8.4 ft (2.56 m). If the equivalent pipe is assumed to be 14 in. (350 mm) in diame-
ter, it will discharge 1.33 MGD (5.03 MLD) with a frictional resistance s 1.68‰, and its
length must be 1,000 8.4 1.68 5,000 ft (1,524 m). Thence, the network can be replaced
by a single 14-in. (350-mm) pipe 5,000 ft (1,524 m) long.

No matter what the original assumptions for quantity, diameter, and loss of head, the cal-
culated equivalent pipe will perform hydraulically in the same way as the network it replaces.
Different in principle is the operational replacement of every pipe in a given network
by equivalent pipes with identical diameters and capacity coefficients, but variable length.
The purpose, in this instance, is to simplify subsequent calculations. For the Hazen-
Williams relationship using the US Customary Units: Q (gpd), d (in.), H (ft), L (ft), C and s
(dimensionless), for example,

s
Q 405 Cd 2.63 0.54
s
s 0.54 Q 405 Cd 2.63 0.54
s Q 1.85 (405) 1.85 C 1.85 4.87 (6.5)
d
H L Q 1.85 (405) 1.85 C 1.85 4.87
d
d
L (405) 1.85 C 1.85 4.87 H Q 1.85
L L (l00 C) 1.85 (d d) 4.87
e
e