bed material concentration
terminal fall velocity of the particles
critical shear stress
In general, analysis of river problems is confined to flow of water over beds consisting of
quartz particles with constant ρs. The gravitational acceleration g is also constant in the
present context. The effect of other variables on the flow in alluvial channels is qualitatively
discussed in the following sections. Most of this presentation is based on laboratory studies
which have been supplemented by data from field experience when available.
With a constant slope, Sf, and bed material, Ds, an increase in depth, yo, can change a plane
bed (without movement) to ripples, and ripple-bed configuration to dunes, and a dune bed to
a plane bed or antidunes. Also, a decrease in depth may cause plane bed or antidunes to
change to a dune-bed configuration. A typical break in a depth-discharge relation caused by
a change in bed form from dunes to plane bed or from plane bed to dunes is shown in Figure
Often there is a gradual change in bed form and a gradual reduction in resistance to flow and
this type of change prevents the break in the stage-discharge relation. Nevertheless, it is
possible to experience a large increase in discharge with little or no change in stage. For this
and related reasons, development of dependable stage-discharge relations in alluvial
channels is very difficult.
Resistance to flow varies with depth even when the bed configurations do not change. When
the bed configuration is plane bed, either with or without sediment movement or ripples,
there is a decrease in resistance to flow with an increase in depth. This is a relative
Figure 3.10. Relation of depth to discharge for Elkhorn River near Waterloo, Nebraska
(after Beckman and Furness 1962).