<br />
<br />2042
<br />
<br />HY11
<br />
<br />NOVEMBER 1973
<br />
<br />The purpose of the present paper is to develop and examine a new framework
<br />for the analysis of transport data. This avoids refinements that may complicate
<br />the application without adding much to accuracy. The advantages of dimensional
<br />analysis are incorporated, but physical arguments are used in deriving the form
<br />of the functions to be tested. The variables are directly. related to those the
<br />engineer can readily visualize and measure. The uncertainty of slope separation
<br />procedures is avoided.
<br />
<br />SUMMARY Of BASIC THEORY
<br />
<br />Sediment Mobility.-Thc original development of the theory was given by
<br />Ackcrs (1) and is summarized in Appendix I. In essence, a coarse sediment
<br />is considered to be transported mainly as a bed process. If bed features exist,
<br />it is assumed that the effective shear stress bears a similar relationship to mean
<br />stream velocity as with a plane grain-textured surface at rest. This is given
<br />by a devclopment of the rough turbulent equation:
<br />
<br />~ 7Cg = V
<br />... ..... ..,............. .(1)
<br />P V3210g (a ;),
<br />
<br />
<br />A fine sediment is considered to be transported within the body of the flow,
<br />where it is suspended by the stream turbulence. As the intensity of turbulence
<br />is dependent on the total energy degradation, rather than on a net grain resistance,
<br />for fine grained material: '
<br />
<br />~ ~ v. = v/iiH .....,........,.............. (2)
<br />
<br />Sediment mobility is described by the ratio of the appropriate shear force on
<br />unit area of the bed to the immersed weight of a layer of grains. This mobility
<br />number is denoted Fg,,' and a general definition is:
<br />
<br />
<br />F.,~ VgD:~-I) [V3210:(~ )f'
<br />
<br />. . . . . . . . . . . . . . (J)
<br />
<br />For coarse sediments (n = 0) the expression reduces to the form
<br />
<br />V t
<br />F = . . . . . . . . . . . . . . . . . . . . . (4)
<br />.' VgD(s- I) (ad)
<br />Vlllog Ii
<br />and for fine sediments (n = 1)
<br />
<br />v.
<br />F = . . . . . . . , . . . . . . , . . . . . . . , . . . . . . . (5)
<br />g' vgD(s-l)
<br />
<br />For intermediate or transitional sizes of sediment, n may take a value between
<br />o and 1, and the hypothesis is that the value will depend primarily on a
<br />
<br />HY11
<br />
<br />SEDIMENT TRANSPORT
<br />
<br />~043
<br />
<br />dimensionless expression for grain diameter. This hypothesis has been examined
<br />by analyzing experimental data.
<br />Dimensionless Grain Diameter .-A dimensionless expression for grain diameter
<br />can be derived by eliminating shear stress from the two Shields parameters
<br />(15); or from the drag coefficient and Reynolds Number of a settling particle,
<br />by eliminating the settling velocity; or dimensionally, with immersed weight
<br />of an individual grain, fluid density, and viscosity as the variables. The dimen~
<br />sionless grain diameter is therefore generally applicable to coarse. transitional,
<br />and fine sediments and is the cube root of the ratio of immersed weight to
<br />viscous forces. Thus
<br />
<br />[g(S - I)] '/3
<br />D ~D
<br />g, v2
<br />
<br />. . . . . . . . . . . . . . . . . . . . . . . . . . . . (6)
<br />
<br />
<br />Sediment Transport.-Dimensionless expressions for sediment transport were
<br />based on the stream power concept, in the case of coarse sediments using
<br />the product of net grain shear and stream velocity as the power per unit area
<br />of bed, and for fine sediments using the total stream power. The useful work
<br />done in sediment transport in the two cases takes account of the different
<br />modes of transport assumed, and in relation to the stream power gives an
<br />expression for the efficiency of the transport process (1).
<br />The hypothesis is made that efficiency is dependent on the mobility number.
<br />Fg,. Clearly there will be a value of Fg, below which no sediment will move
<br />and efficiency will be zero. As F 8' rises above this limiting value. it is expected
<br />that the efficiency will increase.
<br />In order to separate the primary variables, the efficiency (which is dimension-
<br />less) is combined with the mobility number. F g,' to yield a general transport
<br />parameter (see Appendix I). Therefore
<br />
<br />G =Xd(~)'
<br />g, sD V
<br />
<br />. . . . . . . . . . . . . . . . . . . . . . (7)
<br />
<br />Thus, for coarse sediments (n = 0)
<br />
<br />'.'.
<br />
<br />Xd
<br />G,,=-
<br />sD
<br />
<br />. . . . . . . . . . . . . . . . . . . . . . . . . (8)
<br />
<br />and for fine sediments (n = J)
<br />
<br />Xd v.
<br />0",=--.........
<br />sD V
<br />
<br />......(9)
<br />
<br />General Transport Function.-The relationship to be tested is:
<br />
<br />G,,= II (Fg,;
<br />
<br />Dg,)
<br />
<br />(10)
<br />
<br />,,~ The definitions of G gr and F g" depend on the transition parameter, n, and
<br />,~,o the assumed relationship to be tested is:
<br />
<br />n= f,(D.,) . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . . . . . (II)
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