Open Channel Flow - Sediment Transport in Irrigation Canals: A New Approach - page 45

they depend on the solution of the dependent variables at the intersection
point (see Figure 2.17). However, the solution can be found through the
Riemann invariants. The almost exactdirection of these characteristics
can then be drawn based on the average characteristic direction at the
connecting points.
The significance of the method of characteristics lies in the fact that
the characteristics are to be seen as lines along which some information on
the state of the fluid propagates. Along the characteristic lines, a special
condition is valid, which implies that these lines are unique lines and that
information only travels along these characteristics. With the characteris-
tics, it is possible to compute solutions for v and y from known conditions
at an earlier point in time.
In the derivation of the method of characteristics, the auxiliary variable

= √ gD has a special meaning as part of the direction of the character-
istics. For example when v

c

0, the direction of both characteristics is the
same in magnitude, but they have a different, opposite sign. This means
that the effect of any disturbance at a certain point in a canal propagates
in both directions (upstream and downstream) with the same speed c .
The variable c here means the celerity with which disturbances propagate
in stagnant water.
When v > 0, the characteristic directions no longer have the same mag-
nitude and at a particular point information on the fluid state travels faster
in the downstream than in the upstream direction. For smaller veloci-
ties the flow is subcritical (the Froude number is less than unity) and the
state of flow at any point in time is controlled by both the upstream and
downstream conditions.

=