chapter 3 hydraulics of open channel flow

3.18 Chapter Three
HYDRAULICS OF OPEN CHANNEL FLOW
FIGURE 3.6 Definition of variables for gradually varied flow through contracting
and expanding channel sections.
3. If dz/dx � 0 (downward step) and Fr � 1, then dy/dx must be greater than zero—
depth of flow increases as x increases.
4. If dz/dx � 0 (downward step) and Fr � 1, then dy/dx must be less than zero—depth
of flow decreases as x increases.
In the case of a channel of constant width with a positive or negative step, the relation
between the specific energy upstream of the step and the specific energy downstream of
the step is
E1 =E2 + ∆z (3.55)
In the case dz/dx � 0, if the channel is rectangular in shape but the width of the channel
changes, it can be shown (French, 1985) that the governing equation is
(1 � Fr2 )� dy
� � Fr
dx
2 y dT
�� �� � 0 (3.56)
b dx
The following observations also apply to channels of arbitrary shape:
1. If db/dx � 0 (width increases) and Fr � 1, then dy/dx must be greater than
zero–depth of flow increases as x increases.
2. If db/dx � 0 (width increases) and Fr � 1, then dy/dx must be less than zero—depth
of flow decreases as x increases.
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