Sediment Transport Concepts - Sediment Transport in Irrigation Canals: A New Approach - page 92

of the morphological changes in the canal bottom have shown them
to be so slow that for the computation of the water movement
the bottom can be considered to be fixed during a single time step
(de Vries, 1965).
For the assumption as to whether the unsteady flow in the irriga-
tion canal may be treated as a quasi-steady flow, two facts have to be
considered.
• In order to avoid a very wavy water surface in the canals, which will

affect the canal operation, it is recommended to maintain low Froude
numbers and to limit the number to a maximum of 0.30-0.40 (Ranga
Raju, 1981). For Froude numbers smaller than 0.4 the celerity of a
disturbance along the water surface is not influenced by the mobility of
the bed. For this condition the wave celerity is about 200 times faster
than the celerity of the bed disturbances. The relative celerity of the
disturbances along the water surface, being the ratio between the wave
celerity and the flow velocity, is to a great extent larger than 1, while
the relative celerity of the bed disturbances, being the ratio between the
celerity of these disturbances and the flow velocity, is much smaller
than 0.005. When the wave celerity along the water surface is much
larger than the celerity of the bed disturbances it can be assumed that
the disturbances of the bed will have a negligible influence on the water
movement (de Vries, 1987).

• On the other hand, control structures in irrigation networks are operated

in a very slow but sure way to avoid surges with steep wave fronts.
This means that changes in discharge are very gradual over time and
therefore the unsteady flow in an irrigation system can be approximated
by a quasi-steady flow (Mahmood and Yevjevitch, 1975).

These lecture notes focus on sediment transport processes in irrigation
canals and not on water delivery; therefore, the flow will be schematised
as a quasi-steady flow. Hence, the terms δv/δt and δA / δt in the continuity
and dynamic equation can be ignored. Figure 5.2 shows two hydrographs
in an irrigation canal: (a) a typical one; (b) a schematised one for a
quasi-steady state.
Based on these considerations the flow equations can be simplified as:
- Continuity equation:

∂Q
∂x =

0 (5.8)

Q is constant for steady flow
- Dynamic equation:

d y
d x =

S o − S f v

gh for gradually varied flow with Fr = (5.9)

Fr 2

1 −