particle in the formation of the bed configurations; (2) its effect on grain roughness, Ks; and
(3) its effect on the turbulent structure and the velocity field of the flow.
The physical size of the bed material, as measured by the fall diameter or by sieve diameter,
is a primary factor in determining fall velocity. Use of the fall diameter instead of the sieve
diameter is advantageous because the shape factor and density of the particle can be
eliminated as variables. That is, if only the fall diameter is known, the fall velocity of the
particle in any fluid at any temperature can be computed; whereas, to do the same
computation when the sieve diameter is known, knowledge of the shape factor and density of
the particle are also required.
The physical size of the bed material determines the friction factor mainly for the plane-bed
condition and for antidunes when they are not actively breaking. The breaking of the waves,
which increases with a decrease in the fall velocity of the bed material, causes additional
dissipation of energy.
The physical size of the bed material for a dune-bed configuration also has an effect on
resistance to flow. The flow of fluid over the back of dunes is affected by grain roughness,
although the dissipation of energy by the form roughness is the major factor. The form of the
dunes is also related to the fall velocity of the bed material.
3.4.5 Size Gradation
The gradation, G, of sizes of the bed material affects bed form and resistance to flow. Flume
experiments indicate that uniform sands (sands of practically the same size) have larger
resistance to flow (except plane bed) than graded sands for the various bed forms. Also the
transition from upper flow regime to lower flow regime occurs over a narrower range of shear
values for the uniform sand. For a plane bed with motion, resistance to flow is about the
same for both uniform or graded sand.
3.4.6 Fall Velocity
Fall velocity, ω, is the primary variable that determines the interaction between the bed
material and the fluid. For a given depth, and slope, the fall velocity determines the bed form
that will occur, the actual dimensions of the bed form and, except for the contribution of the
grain roughness, the resistance to flow.
Observations of natural streams have shown that the bed configuration and resistance to
flow change with changes in fall velocity when the discharge and bed material are constant.
For example, the Loup River near Dunning, Nebraska has bed roughness in the form of
dunes in the summer when the water is warm and less viscous but has a nearly plane bed
during the cold winter months. Similarly, two sets of data collected by Harms and
Fahnestock (1965) on a stable branch of the Rio Grande at similar discharges show that
when the water was cold, the bed of the stream was plane, the resistance to flow was small,
the depth was relatively shallow, and the velocity was large; but when the water was warm,
the bed roughness was dunes, the resistance to flow was large, the depth was large, and the
velocity was low.
3.25
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