v = mean velocity (m/s) 10.7 -...

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




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




3. The Manning Formula

V n R Sh1 2 3 1 2/ /

3/16

223.10

DQLnh f

2233.135.6 Vn

DLh f




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




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

.

( . )




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




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 :




2. Head Loss Due to a Sudden Contraction

h K VgL L 22

2

gVhL 2

5.02

2




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




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:




v = mean velocity (m/s) 10.7 -...

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