3.4.7 Shape Factor for the Reach and Cross-Section
The configuration of the reach, SR, and the shape of the cross-section, Sc, affect the energy
losses resulting from the nonuniformity of the flow in a natural stream caused by the bends
and the nonuniformity of the banks. Study of these losses in natural channels has long been
neglected. Also, flow phenomena, bed configuration, and resistance to flow vary with the
width of the stream. In narrow channels dunes and antidunes vary mainly in the downstream
direction and resistance to flow is larger than for a wide channel. Also, in wide channels
more than one bed form can occur in the cross-section.
3.4.8 Seepage Force
A seepage force, fs, occurs whenever there is inflow or outflow through the bed and banks of
a channel in permeable alluvium. The seepage flow affects the alluvial channel phenomena
by altering the velocity field in the vicinity of the bed particles and by changing the effective
weight of the bed particles. Seepage may have a significant effect on bed configuration and
resistance to flow. If there is inflow, the seepage force acts to reduce the effective weight of
the sand and, consequently, the stability of the bed material. If there is outflow, the seepage
force acts in the direction of gravity and increases the effective weight of the sand and the
stability of the bed material. As a direct result of changing the effective weight, the seepage
forces can influence the form of bed roughness and the resistance to flow for a given channel
flow. For example, under shallow flow a bed material with median diameter of 0.5 mm will be
molded into the following forms as shear stress is increased: dunes, transition, plane bed,
and antidunes. If this same material was subjected to a seepage force that reduced its
effective weight to a value consistent with that of medium sand (median diameter, Ds = 0.3
mm), the forms of bed roughness would be transition, plane bed, and antidunes for the same
range of flow conditions.
A common condition is outflow from the channel during the rising stage; this process
increases the stability of the bed and bank material but stores water in the banks. During the
falling stage, the situation is reversed; inflow to the channel reduces the effective weight and
stability of the bed and bank material and influences the form of bed roughness and the
resistance to flow.
3.4.9 Bed Material Concentration
The bed material concentration, CT, affects the fluid properties by increasing the apparent
viscosity and the density of the water-sediment mixture. However, the effect of the sediment
on viscosity and the density ρ in any resistance to flow relation is accounted for by using
their values for the water-sediment mixture instead of their values for pure water. The
presence of sediment in the flow causes a small change in the turbulence characteristics,
velocity distribution and resistance to flow.
3.4.10 Fine-Material Concentration
Fine-material concentration, cf, or washload is that part of the total sediment discharge that is
not found in appreciable quantities on the bed. If significant amounts of sediment is in
suspension, its effect on the viscosity of the water-sediment mixture should be taken into
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