SETRIC, a Mathematical Model for Sediment Transport in Irrigation Canals - Sediment Transport in Irrigation Canals: A New Approach - page 161

Continuity equation at confluences and/or bifurcations:
inflow

= outflow

(6.2)

Q ± q 1 = 0

Dynamic equation:

d h
d x =

S o − S f

(6.3)

Fr 2

1 −

Q 2 B s
gA 3

Fr 2 = (6.4)

Several methods are available to solve the dynamic equation of grad-
ually varied flow for prismatic canals. Henderson (1966), Chow (1983),
Depeweg (1993) and Rhodes (1995) present a comprehensive description
of the available methods, including graphical integration, direct integra-
tion, direct step, standard step, the Newton-Raphson solution and the
predictor-corrector method. A summary of these methods is given in
Chapter 2.

6.1.3 Sediment transport equations

The analysis of the sediment transport process is based on the following
assumptions:
- the sediment particles can be characterized by a single representative
size;
- the size and gradation of the sediment remain constant along the whole
length of the canal and throughout the irrigation season;
- the canal bed is composed of the same material as that of the inflowing
sediment.

The numerical solution of the one-dimensional sediment equations
that include the friction factor predictor, continuity equation for sediment
and the sediment transport predictor (see Chapter 5) requires boundary
conditions for the hydraulic and sediment transport calculations.
These conditions are:
- the geometrical variables of the canal: bottom width, side slope and
level of the bottom;
- the flow conditions along the entire canal during a time step: discharge,
velocity, roughness, water depth and slope of the energy line;
- specific confluences and bifurcations can be incorporated by applying
continuity for water flow and sediment load;
- the characteristics of the incoming sediment, namely the sediment load
(ppm) and sediment size d 50 at the upstream boundary; there will be no
entrainment of the original bottom material;