Encyclopedia of Environmental Science and Engineering, Volume I and II

1278 WATER FLOW

The dimension of the roughness coefficient, N, is frequently

taken as L 1/6 as the equation by itself is not dimensionally

homogenous. Table 3 provides values of Manning’s N for the

more widely used pipe materials.

Hazen-William ’ s Equation This equation is used mainly in

sanitary engineering.

V  0.36 CR 0.63 S 0.54 , (18)

where C  roughness coefficient. Typical values of the

Hazen-William’s C is given in Table 4.

Energy Losses Due to Cross-Sectional Changes,

Bends and Valves

Cross-Sectional Changes

Expansion Energy loss in an expansion is principally a

form loss:

h

D

D

V

exp^12 ,

1

2

2 2

1

⎛^2

⎝⎜

⎞

⎠⎟

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥ g

(19)

in which D  diameter of the conduit, and subscripts 1 and

2 denote upstream and downstream values. From Eq. (19), if

D 2 is very large compared to D 1 , such as the discharge into a

reservoir, the entire velocity head is lost.

Contraction The contraction loss equation can be expres sed

in terms of the downstream velocity, V 2 , as:

H

C

V

c

con

1

1

2

(^22)
⎛
⎝⎜
⎞
⎠⎟ g

. (20)

Typical values of the coefficient of contraction, C c , are given

in Table 5.

Entrance Loss The head loss at the entrance of a conduit

can be compared to that of a short tube:

h

C

V

ent

1

1

(^22)
2
⎛
⎝⎜
⎞
⎠⎟ g
(21)
hK
V
ent end
2
2 g
, (22)^
in which C  coefficient of discharge, K  entrance loss
coefficient. Typical values of C and K are given in Table 6.
Transition In gradual contractions and expansions, the
lead losses are calculated in terms of the difference of veloc-
ity heads in the upstream and downstream pipes:
Gradual contraction: hK
VV
tcte
2
2
1
2
22 gg
⎛
⎝⎜
⎞
⎠⎟
, (23)
Gradual expansion: hK
VV
tcte
22
22 gg
⎛
⎝⎜
⎞
⎠⎟

. (24)

K tc values vary from 0.1 to 0.5 for gradual to sudden contrac-

tions. Values of K tc range from 0.03 to 0.80 for flare angles of

2 
 to 60
.

TABLE 4

Hazen-William’s C

Material (new) C

Cast iron 130

Welded steel 119

Riveted steel 110

Concrete 130

Wood-stave 120

Vitrified clay 110

TABLE 3

Normal values of Manning’s N

Material N

Brass 0.010

Corrugated metal 0.024

Glass 0.010

Concrete, unfinished 0.014

Vitrified clay 0.014

Steel 0.012

Cement 0.012

Brick 0.013

TABLE 5

Coefficient of contraction

A 2 /A 1 Cc

0.25 0.64

0.50 0.68

0.75 0.78

1.00 1.00

TABLE 6

Values of C and Kent

Type of entrance C Kent

Circular bellmouth 0.98 0.05

Square bellmouth 0.93 0.16

Fully rounded 0.95 0.10

Moderately rounded 0.89 0.25

Sharp cornered 0.82 0.50

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