Environmental Engineering Reference
In-Depth Information
The de Chézy coefficient obtained from equation B.16 to B.19 consid-
ers only the bed forms on the bottom without taking into account the fric-
tion factor of the side banks. Therefore, it is necessary to find a weighted
value of the de Chézy coefficient for the friction of both bed and side banks.
B.2 BROWNLIE
Brownlie (1983) proposed a method to predict the flow depth (and there-
fore the friction factor) when the discharge and the slope are known. No
explicit calculation of the de Chézy coefficient is proposed, but once
the resistance to flow is determined (equations B.20 and B.21) then the
de Chézy coefficient will be calculated by equation B.22. The Brownlie
method is based on a dimensional analysis, basic principles of hydraulics
and verification with a large amount of field and flume data. Step by step,
the de Chézy coefficient in the lower flow regime can be predicted by
using the following relationships:
Q
Bg 0 . 5 d 1 . 5
q
g 0 . 5 d 1 . 5
50
q =
50 =
(B.20)
0 . 372 d 50 q 0 . 6539
S 0 . 2542
o
σ 0 . 1050
s
h
=
(B.21)
and
Ch hS o
q
h 1 . 5 S 0 . 5
0
q
=
C
=
(B.22)
where:
Q
discharge (m 3 /s)
=
unit discharge (m 2 /s)
q
=
B
=
bottom width (m)
h
=
water depth (m)
S o =
bottom slope
d 50 =
median diameter (m)
σ s =
gradation of sediment ( σ s =
½( d 84 / d 50 +
d 50 / d 16 ))
q =
dimensionless unit discharge
B.3 WHITE, PARIS AND BETTESS
White et al. (1979) describe the flow resistance by the following
dimensionless numbers:
- Particle size D
( s
1 / 3
1) g
ν 2
D =
d 35
(B.23)
 
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