chapter 3 hydraulics of open channel flow

3.28 Chapter Three
TABLE 3.6 Shape Factor for Common Channel Sections
Channel Definition �
(1) (2)
Rectangle
Trapezoid
Trapezoid
with
unequal side
slopes
Circle
and if the Chezy equation is used
Ve � � 1
� �Fr (3.81b)
2
Fr should be computed using Eq. (3.11) and ��a channel shape factor (Table 3.6) or
� � 1 � R � dP
� (3.82)
dA
When Mo �� 1, flow instabilities should expected. The Montuori number is given by
Mo � � gSfL
� (3.83)
V2
It is appropriate to note that in some publications (e.g., Aisenbrey et al., 1978) Mo is
the inverse of Eq. (3.83). Figure 3.9 provides a basis for deciding whether roll waves will
form in a given situation. In the figure, data from Niepelt and Locher (1989) for a slurry
flow are also plotted. The Niepelt and Locher data suggest that flow stability also is a
function of the concentration of sediment.
3.7 CONCLUSION
HYDRAULICS OF OPEN CHANNEL FLOW
b
y
b
�� b � 2y
The foregoing sections provide the basic principles on which the following chapters on
design are based. Two observations are pertinent. First, open-channel hydraulics is incrementally
progressing. That is, over the past several decades, there have been incremental
advances that primarily have added details, often important details, but no major new
advances. Second, open-channel hydraulics remains a one-dimensional analytic approach.
However, the assumption of a one-dimensional approach may not be valid in many situations:
for example, nonprismatic channels, flow downstream of a partially breached dam,
or lateral flow over a spillway. In some of these cases, the one-dimensional approach may
provide an approximation that is suitable for design. In other cases, however, a two– or
three– dimensional approach should be used. Additional information regarding two– and
three– dimensional approaches can be found in Chaudhry (1993).
1 �
R( �1� �� z� 1 2� � �1� �� z� 2 2� )
���
T
θ�
sin(θ)
1 ��� θ[ 1�
cos(θ)]
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