Environmental Engineering Reference
In-Depth Information
A gradually varied flow (wide rectangular channels) is based upon:
d y
d x =
S o
S f
(2.37)
Fr 2
1
where:
d y /d x
=
change of the water depth in the x -direction
d y /d x
=
slope of the water surface relative to the channel bottom
S o =
bottom slope
S f =
slope of the energy line
Fr 2
Froude number
Depending on whether d y /d x is negative or positive, the following water
surface profiles can be distinguished:
=
d y
d x > 0
==
> Backwater curve
d y
d x =
0
==
> Uniform flow
d y
d x < 0
==
> Drawdown curve
The critical slope for a given discharge Q is by definition that bottom
slope for which the normal water depth is equal to the critical depth;
S o =
y c . Any bottom slope can be compared with this critical
slope. Table 2.3 gives a classification of the bottom slopes.
S c for y n =
Table 2.3. Type of bottom slope.
Slope description
Bottom slope
Type of slope
Horizontal
S o =
0
H
Mild
0 < S o < S c
M
Critical
S o = S c
C
Steep
S o > S c
S
Adverse or negative
S o < 0
A or N
A particular discharge Q in a canal gives a normal and a critical water
depth for a given bottom slope S o . The actual water depth y in the canal
can be related to these two water depths, namely the actual water depth
can be either larger or smaller than the two water depths or is between the
two water depths (see Table 2.4).
Therefore, the actual water depth y can be classified in one of the
following three regions:
Region 1: y > y n and y > y c
Region 2: y between y n and y c
Region 3: y < y n and y < y c
 
Search WWH ::




Custom Search