chapter 3 hydraulics of open channel flow

3.10 Chapter Three
3.3.3 Hydraulic Jumps in Nonrectangular Channels
In analyzing the occurrence of hydraulic jumps in nonrectangular but prismatic channels, we
see that no equations are analogous to Eqs. (3.24) and (3.25). In such cases, Eq. (3.22) could
be solved by trial and error or by use of semiempirical equations. For example, in circular sections,
Straub (1978) noted that the upstream Froude number (Fr1 ) can be approximated by
yc
1.93
(3.26)
Fr1 � ⎛ ⎜�� ⎝y1 ⎞ ⎟
⎠
and the sequent depth can be approximated by
y2
c
Fr1 � 1.7y2 � �� (3.27
y1
Fr1 � 1.7y2 � � y1.
8
c
� 0.
73
(3.28)
y1
For horizontal triangular and parabolic prismatic channel sections, Silvester (1964,
1965) presented the following equations.
For triangular channels:
⎛
⎜
⎝ �y
2
�
y1
⎞2.5 ⎟ � 1 � 1.5 (Fr1 )
⎠
2 ⎡ ⎢ 1 �
⎣ ⎛ ⎜� ⎝ y1
�
y2
⎞2⎤⎥⎦ ⎟
⎠
(3.29)
For parabolic channels with the perimeter defined by y � aT 2 /2, where a is a
coefficient:
� y
�
2
y1
HYDRAULICS OF OPEN CHANNEL FLOW
⎛
⎜
⎝ �y
2
�
y1
⎞2.5 ⎟ � 1 � 1.67 (Fr1 )
⎠
2 ⎡ ⎢ 1 �
⎣ ⎛ ⎜� ⎝ y1
�
y2
⎞1.5 ⎤⎥⎦
⎟
⎠
FIGURE 3.3 Analytic curves for estimating sequent depths in a trapezoidal channel
(From Silvester, 1964)
(3.30)
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