chapter 3 hydraulics of open channel flow

3.22 Chapter Three
V2
1 V2
2
z1 � α1 �� � z2 � α2 �� � hf + he 2g
2g
(3.61)
where z1 and z2 � elevation of the water surface above a datum at Stations 1 and 2, respectively,
he � eddy and other losses incurred in the reach, and hf � reach friction loss.
The friction loss can be obtained by multiplying a representative friction slope, Sf,by the length of the reach, L. Four equations can be used to approximate the friction loss
between two cross sections:
S� f � ⎛ ⎜ �
⎝ Q1
� Q2
K �
2
(average conveyance) (3.62)
and
V2
1
α1 �� 2g
z 1
y 1
HYDRAULICS OF OPEN CHANNEL FLOW
FIGURE 3.7 Energy relationship between two channel sections.
1
�
K2 ⎞ ⎟
⎠
S� f � � Sf1 � Sf2 � (average friction slope) (3.63)
2
2 Sf1
S� f � �
S �
Sf2
� (harmonic mean friction slope) (3.64)
S
f1
Energy Grade Line (S f)
Water Surface (S w)
Channel Bottom (S o)
f2
�x�L
h f ��x
V2
2
α2 �� 2g
S� f � �S� f1 �S� f2 � (geometric mean friction slope) (3.65)
The selection of a method to estimate the friction slope in a reach is an important decision
and has been discussed in the literature. Laurenson (1986) suggested that the “true”
friction slope for an irregular cross section can be approximated by a third-degree poly-
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y 2
z 2