Open Channel Flow - Sediment Transport in Irrigation Canals: A New Approach - page 32

Gradually varied flow can be computed by three methods: direct
integration; graphical integration and numerical integration. Some

characteristics of these methods are presented in Table 2.6.

Table 2.6. Summary of the methods for computing gradually varied flow.

Distance Depth

from from Cross

Method depth distance section Remarks

Bresse O O Prismatic; Use of tables recommended

broad; Use of Chézy formula

rectangle Recommendation for computation steps :

In upstream direction for subcritical flow
In downstream direction for supercritical flow

Bakhmeteff O All shapes Use of tables recommended

Use of hydraulic exponents N and M

Graphical O Prismatic; For y → y n large errors may occur

integration non-prismatic

Direct step O Prismatic Recommendation for computation steps:

In upstream direction for subcritical flow
In downstream direction for supercritical flow

Standard O All shapes Iteration required

step Recommended for natural channels

Eddy and other losses can be included
Use of field data possible
Recommendation for computation steps :
In upstream direction for subcritical flow;
In downstream direction for supercritical flow

Predictor O All shapes Iteration not required

corrector Straightforward water depth computation

2.8 SOME GENERAL ASPECTS OF UNSTEADY FLOW

Unsteady flow in open channels occurs when the flow parameters change
with time at a fixed point, e.g. the water depth or the discharge varies
at a certain point of the canal with time. Waves travelling in canals are
examples of unsteadiness; they can be classified as:
• Translatory waves with a net transport of water in the direction of the

wave; translatory waves are the most common type of waves in open
channels.

• Oscillatory waves - a temporal variation in the water surface that is

propagated through water, for instance wind waves, without a net
transport of water. Oscillatory waves are normally ignored in the
design and operation of irrigation canals.

A translatory wave is a gravity wave with a substantial displacement
of water particles in the flow direction. The waves can be divided into