Equation of gradually varied flow in a reach

The canal being divided into homogeneous zones (the reaches), the problem gets reduced to calculating the water surface profile under subcritical steady flow conditions in a reach.

The classic hypotheses of unidimensional hydraulics in canals are considered to apply:

• The flow direction is sufficiently rectilinear, so that the free surface could be considered to be horizontal in a cross section.

• The transversal velocities are negligible and the pressure distribution is hydrostatic.

• The friction forces are taken into account through the MANNING-STRICKLER coefficients.

Therefore, only monodimensional steady flow is studied, and only subcritical flow is considered.