Page 175 - Water Engineering Hydraulics, Distribution and Treatment

EXAMPLE 5.48 DETERMINATION OF THE MOST ECONOMICAL DISTRIBUTION OF HEADS FOR THREE
CONDUIT SECTIONS
Given the costs and losses of head shown in Fig. 5.21 for three sections of a conduit, find the most economical distribution of the
available head H = 60 ft (18.3 m) between the three sections.
Solution:
By trial, the three heads h , h ,and h that satisfy the constraint h + h + h = H are as follows:
3
2
1
2
3
ft
h = 13.5
4.1
1
1
c = 2.1 × 10
h = 19.0
5.8
2
2
h = 27.5 m 1 c = 2.0 × 10 4 4 4 5.3 Capacity and Size of Conduits 153
c = 2.2 × 10
8.4
3
3
H = 60.0 18.3 C = 6.3 × 10 4
EXAMPLE 5.49 UPGRADING CAPACITY AND SIZE OF PIPES
A gravity water supply system consists of a water pipe (C = 100) 150 mm in diameter and 3,000 m long that joins two reservoirs
that have a difference of water surface elevation of 13 m.
Expecting a higher water demand in the near future, the flow needs to be increased between the reservoirs to three times what
would be produced by the present system. Two alternatives are being investigated for tripling the flow: either place a pump on the
existing line or install an additional parallel line between the two reservoirs.
1. If a pump is placed, compute the required water head for the added pump.
2. If an additional line is installed, calculate the required size of the added pipe.
Solution:
First let us determine the existing flow in the 150 mm pipe:
2
2
P ∕ + Z + (v ) ∕2g = P ∕ + Z + (v ) ∕2g + h .
B
B
f
B
A
A
A
0 + (Z − Z ) + 0 = 0 + h .
B
f
A
h = 13 m.
f
s = h ∕L = 13∕3,000 = 4.3 .
f
3
The nomogram (C = 100) of Fig. 5.17 for D = 150 mm and s = 4.3 will give Q = 0.010 m ∕s.
1. The required water head for the added pump:
3
Future flow Q = 3Q = 3 × 0.010 = 0.030 m ∕s.
2
3
The nomogram (C = 100) of Fig. 5.17 for D = 150 mm and Q = 0.030 m ∕s will give s = 30%.
2
h = sL = 30%× 3,000 = 90 m.
f
2
2
P ∕ + Z + (v ) ∕2g + h = P ∕ + Z + (v ) ∕2g + h .
P
B
A
f
A
B
B
A
0 + (Z − Z ) + 0 + h = 0 + 0 + h .
f
B
A
P
13 + h = 90.
P
h = 90 − 13 = 77 m.
P
The required water head for the pump = 77 m.
2. The required size of the added pipe:
3
Q pipe 2 = 0.030 − 0.010 = 0.020 m ∕s.
3
The nomogram (C = 100) of Fig. 5.17 for Q pipe 2 = 0.020 m ∕sand s = 4.3% will give D = 200 mm.
The required size of the added pipe is 200 mm.