Agriculture Reference
In-Depth Information
dP
dd
=−
A
d
2
+
2
=
0
A
d
2
+
Or,
−
2
=
0
2
d
2
Or,
A
=
2
d
2
(since
A
Or,
bd
=
=
b
×
d
)
Or,
b
=
2
d
(1.9)
i.e., the width is double the flow depth.
To ensure that
P
is minimum value rather than maximum value, we have to
compute second derivative
d
P
2
d
d
2
. It will be minimum if the
d
P
2
d
d
2
is positive and
maximum if
d
P
2
d
d
2
is negative.
d
P
2
d
d
2
2
A
d
3
which is positive. Thus, the value of “
b
” obtained from the first
derivative of
P
is for the minimum value of
P
.
In this case, the hydraulic mean depth, or hydraulic radius,
Here,
=
A
P
=
bd
2
d
×
d
R
=
2
d
=
2
d
(since
b
=
2
d
)
+
+
b
2
d
2
d
2
4
d
=
d
2
=
d
2
i.e.,
R
=
(1.10)
Hence, for the maximum discharge conditions, the criteria of channel configurations
are as follows:
(a)
b
=
2
d
(i.e., width is twice flow depth) and
d
2
(i.e., hydraulic radius is half of flow depth)
(b)
R
=
1.2.5.2 Condition for Maximum Discharge Through a Channel of Trapezoidal
Section
Many natural and man-made channels are approximately trapezoidal. In practice,
the trapezoidal section is normally used in earthen channels. Generally, the side
slope in a particular soil is decided based on the soil type. In a loose or soft soil,
flatter side slopes are provided, whereas in a harder one, steeper side slopes are
allowed.
Search WWH ::
Custom Search