Agriculture Reference
In-Depth Information
2
z
2
d
P
d
d
=−
A
d
2
−
z
+
+
1
2
z
2
A
d
2
−
Or,
−
z
+
+
1
=
0
2
z
2
A
d
2
+
Or,
−
z
+
+
1
=
0
2
z
2
d
(
b
+
zd
)
−
Or,
+
z
=
+
1 [since
A
=
(
b
+
zd
)]
d
2
2
z
2
Or,
b
+
2
zd
d
=
+
1
2
z
2
Or,
b
+
2
zd
d
=
+
1
d
z
2
b
+
2
zd
2
=
+
1
(1.12)
Here, (
b
+2
zd
) is the top width of water; and (
d
√
z
2
1) is the single sloping side.
That is, the condition is that the sloping side is equal to half of the top width.
In this case, the hydraulic mean depth or hydraulic radius,
+
d
(
b
+
zd
)
A
P
=
=
2
d
√
z
2
R
b
+
+
1
d
(
b
+
zd
)
=
[from Eq. (1.12)]
b
+
(
b
+
2
zd
)
d
(
b
+
zd
)
d
2
=
zd
)
=
2(
b
+
d
2
That is,
R
=
(1.13)
Hence, for maximum discharge or maximum velocity, the two conditions are as
follows:
d
z
2
*
b
+
2
zd
2
=
+
1
(the sloping side is equal to half of the top width)
d
2
*
R
=
(hydraulic radius is half of flow depth)
Search WWH ::
Custom Search