in river engineering (Kennedy, 1983), which at present also relies (and
always will rely) heavily on experience.
8.2 Some basic principles of open-channel flow
8.2.1 Definitions
Open-channel flow may be laminar or turbulent, depending on the value
of the Reynolds number ReVR/v, where Vis the mean flow velocity, R
is the hydraulic radius RA/P(Ais the cross-sectional area of the flow,
andPthe wetted perimeter) and vis the coefficient of kinematic viscosity.
In rivers and canals there is invariably turbulent flow. Furthermore, open-
channel flow may be steady if the discharge, Q, is a function of distance
only (or constant), and unsteady if Qis also a function of time t. Addition-
ally, steady flow may be uniform (with Qand depth yand hence velocity
VQ/Aconstant) or non-uniform. Non-uniform flow may be rapidly or
gradually varying (Qconstant,Vandyvarying with position x) or spa-
tially varying (Qf(x)). In natural rivers flow is normally unsteady,
whereas in canalized rivers and canals flow is predominantly steady non-
uniform or uniform. The flow can be either supercritical (Fr1) or
subcritical (Fr1), where Fr is the Froude number defined by
Fr^2 Q^2 B/(gA^3 ), with Bthe water surface width and the Coriolis coeffi-
cient derived from the velocity distribution in the section. In rivers and canals
the flow is in most cases subcritical. Canals are usually prismatic open chan-
nels, while rivers are generally non-prismatic. The boundaries of open chan-
nels formed by the bed and sides may be fixed, e.g. in artificial concrete-lined
channels, or movable as in rivers or unlined canals in alluvium.
8.2.2 Some basic equations
Only a few basic concepts can be touched upon here. For further and more
detailed treatment of open-channel flow the reader is referred to books on
the subject, e.g. Henderson (1966), Chow (1983), French (1986), Graf
(1998) and Chadwick , Morfett and Borthwick (2004).
For uniform flow, the bedslope, S 0 , energy gradient, Se, and friction
slope,Sf, are all equal.
Denoting by 0 the mean shear stress on the channel perimeter Pand
the ratio A/PR(the hydraulic radius), from the balance between gravity
and frictional resistance we obtain
0 gRS 0 U^2 * (8.1)
322 RIVER ENGINEERING
