Page 248 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

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6.6 Office Studies of Pipe Networks 209
Although the network in Example 6.3 is simple, it cannot be solved conveniently by
algebraic methods, because it contains two interfering hydraulic constituents: (a) a crossover
(pipe 4) involved in more than one circuit and (b) a series of takeoffs representing water used
along the pipelines, fire flows through hydrants, or supplies through to neighboring circuits.

EXAMPLE 6.3 ANALYSIS OF A WATER NETWORK USING THE RELAXATION METHOD
OF BALANCING HEADS
Balance the network of Fig. 6.12 by the method of balancing heads.

Q 0 Q 1 Q 2 Q 3 Take-off
Inflow
2.0
1.00 1.21 1.24 1.25 0.6
A 1. 2,000´ 12˝ B

Q 3 .75 1,000´ 8˝ Q 3 .65 1,000´ 8˝

Q 2 .76 I Q 2 .64

Q 1 .79 Q 1 .61
3. 2.
Q 0 1.00 Q 0 Q 1 Q 2 Q 3 Q 0 0.40
0.50 0.36 0.36 0.36 C Take-off
4. 2,000´ 8˝ 0.6

Q 3 .39 1,000´ 6˝ Q 3 .41 1,000´ 6˝

Q 2 .40 II Q 2 .40

Q 1 .43 Q 1 .37
6. 5.
Q 0 0.50 Q Q Q Q Q 0 0.30
2
1
3
0
D 0.30 0.23 0.20 0.19 E
Take-off 0.2 7. 2,000´ 6˝ 0.6
Take-off
All flows are in MGD
Figure 6.12 Plan of Network Analyzed by the Method of Balancing Heads (Example 6.3)
Conversion factors: 1 MGD 3.785 MLD; 1 1 ft 0.3048; 1 1 in. 25.4 mm

Solution:
The schedule of calculations (Table 6.4) includes the following:
Columns 1 to 4 identify the position of the pipes in the network and record their length and di-
ameter. There are two circuits and seven pipes. Pipe 4 is shared by both circuits; “a” indicates this in
connection with circuit I; “c” does so with circuit II. This dual pipe function must not be overlooked.
Columns 5 to 9 deal with the assumed flows and the derived flow correction. For purposes of
identification the hydraulic elements Q, s, H, and q are given a subscript zero.