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<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) <br /> <br />>~: <br /> <br />,I <br />i+ <br /> <br />! <br />I <br />II <br />" <br />If <br />i, <br />I! <br />, <br /> <br />~ <br /> <br />': <br /> <br /> <br />.~ <br />~i <br />~;,' <br />