WATER FLOW 1285
not have the same values. As the energy gradient, S, is
common to the panels in Eq. (71), water level versus energy
slope curves can be plotted for any selected discharge for
water level computations. The energy equation for the step
method of surface profile calculation can conveniently be
written in the form:WLQ
AWLQ
A
2 SL222 1212 121
21
2
gg,. (72)^
If in practice, the change in kinetic head, ()QAQ A^2 //^22 gg 222 (^12)
is small and could be removed from Eq. (72), this would
greatly simplify the work. In determining the wetted perim-
eter for the calculation of the hydraulic radius, only the
water-channel contact lines are relevant and the water-water
contact lines between panels are excluded.
FLOW IN ERODIBLE CHANNELS
Introduction
Flow in erodible channels can be divided into two types,
namely, canal and river flows. Blench describes canal flow
as possessing there degrees of freedom due to its ability to
adjust itself with respect to its flow depth, bed slope, and side
widths which are taken to be the dependent variables. River
flow, in addition to having the three degrees of freedom of
canals, has a fourth degree by virtue of its ability to meander.
It is assumed that constant maintenance of canals suppresses
the canal’s tendency to meander. The water-sediment flow is
usually regarded as the independent parameter.
In the concept of flow in mobile channels where the
transport of sediment is an integral part of the system, two
philosophies have emerged. Based on the work of Lindley
(1919), Lacey (1952), Inglis (1949), and Blench (1953, 1966)
in India and Pakistan, the regime theory has evolved. On the
other hand, the United States Bureau of Reclamation under
the direction of Lane (1952, 1953) developed the tractive
force method.
Regime Theory for Canals
The regime theory postulates that for given water-sediment
flow and bed material, there exists a regime channel which
determines uniquely the flow area, cross-sectional shape and
bed slope. The regime channel is considered a stable chan-
nel which on the average will neither silt nor scour. The flow
occupying the regime channel is the dominant discharge and
it is also variously referred to as the formative, regime, or
bank-full discharge.
Lacey ’ s Equations Based on extensive flow observations
of the canals in India, Lacey (1952) proposed a set of for-
mulae for alluvial channels with sandy mobile beds with the
discharge ranging from 25 cfs to 2500 cfs, the bed material
size varying from 0.2 mm to 0.6 mm and with the quantity
of solids conveyed being less than 50 ppm:
Wetted perimeter: PQ 267.^12 / (73)
Flow area: A
Q
f
125 56
13
. /
/
(74)
Bed slope: Sf
Q0 0054^53
16. /
/ (75)
Silt factor: fd (^8) inch1/2. (76)
From the above equations, the following two equations can
be derived:
Mean velocity: VQ0 895. r16 16//
M1
M2
M3
Mild slope Steep slope
C1
C3
Critical slope
Legend Normal depth
Critical depth
H2
H3
Adverse slope
A3
A2
S1
S3 S2
FIGURE 10 Surface water profiles.
Left
panel
Center
panel
Right
panel
FIGURE 11 River channel division.
C023_003_r03.indd 1285C023_003_r03.indd 1285 11/18/2005 11:12:15 AM11/18/2005 11:12:15 AM