v = mean velocity (m/s) 10.7 -...
TRANSCRIPT
2. The Hazen -Williams formula
It has been used extensively for designing of water- supply systems
V C R SHW h 0 85 0 63 0 54. . .
85.1
87.47.10
HWf C
QD
Lh
85.1
62.7
HWf C
VDLh
V = mean velocity (m/s)Rh = hydraulic radiusS = head loss per unit length of pipe = CHW = Hazen-williams Coefficient
hLf
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Hazen-Williams Coefficient, CHW, for different types of pipe
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Example 2: A 100 m long pipe with D = 20 cm. It is made of riveted steel and carries a discharge of 30 l/s. Determine the head loss in the pipe using Hazen-Williams formula.
Solution:
V C R SHW h 0 85 0 63 0 54. . .
54.063.0 )100/()05.0)(110(85.0 hfV
RH = D/4 = 0.2/4 = 0.05 m
CHW = 110 from previous table
V = Q/A = 2
3
)2.0)(4/14.3()10(30 x
=
hf = 0.68 m
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3. The Manning Formula
V n R Sh1 2 3 1 2/ /
3/16
223.10
DQLnh f
2233.135.6 Vn
DLh f
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Example 3: A horizontal pipe with 10 cm uniform diameter is 200 m long. It is made of uncoated cast iron and is in bad condition. The measured pressure drop is 24.6 m in water column. Determine the discharge using manning formula.
Solution
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4. The Chezy Formula
V C R Sh 1 2 1 2/ / 2
4
CV
DLh f
where C = Chezy coefficient
• It can be shown that this formula, for circular pipes, is equivalent to Darcy’s formula with the value for
[f is Darcy Weisbeich coefficient]
• The following formula has been proposed for the value of C:
[n is the Manning coefficient]
Cg
f
8
C S n
SnRh
23 0 00155 1
1 23 0 00155
.
( . )
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B. Minor lossesIt is due to the change of the velocity of the flowing fluid in the magnitude or in direction [turbulence within bulk flow as it moves through and fitting]
The minor losses occurs at :
• Valves • Tees• Bends• Reducers• Valves• And other appurtenances
It has the common form
g
VK L 2
2
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1. Head Loss Due to a Sudden Expansion (Enlargement)
h K VgL L 12
2
K AAL
1 1
2
2
hV V
gL 1 2
2
2
or :
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2. Head Loss Due to a Sudden Contraction
h K VgL L 22
2
gVhL 2
5.02
2
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3. Head Loss Due to Gradual Enlargement (conical diffuser)
gVVKh LL 2
22
21
1.061.000.800.39KL
400300200100
Gibson Test: Loss coefficient for conical enlargement
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4. Head Loss Due to Gradual Contraction (reducer or nozzle)
gVVKh LL 2
21
22
0.350.320.280.2KL
400300200100
A different set of data is:
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