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-. ,. 2046 NOVEMBER 1973 HYl1 !" approaching or exceeding unity were included: an upper limit of F 0.8 was applied in selecting data. The data for coarse material up to 4 mm median diam were taken from several sources. Fig. 2(a) shows the data for sand of diameter of 1.35 rnm (20). The curve approaches a limiting value of F Rr asymptotically at low values of the transport parameter, Gr' This asymptote therefore represents initial '. I motion, and IS denoted A. The type of relationship suggested is a power function.of G s' with (Fgr - A). This is examined in Fig. 2(b). The data/lie close to a line with slope 1.5, i.e., for 10-' < G < 2 X 10-2 . " G" ~ 0.56 (F" - A)'" . . , . . . . . . . . . . . . . . . . . , , . . . (14) in which A ~ 0.17, The type of plot in Fig. 2(b) is very searching: F" - A = 0.02A represents a 2% increase in velocity compared with the nominal start of motion, and F gr - A = O.lA is a 10% increase. Thus quite small errors in the measurement of average flow depth over an irregular bed cause a big change in the plotting position. Transport of Transitional Sizes of Sediment.-=-The analysis of data from various sources for sand sizes within the transitional zone was next attempted, using the same formula as appeared to fit coarse sediments but allowing n as well as the initial motion parameter, A. to vary with VII" An optimizing procedure obtained the values of A and n that give minimum scatter (on a least squares basis in the x coordinate direction) in plots similar to Fig. 2. The theory was well supported. There was a clear dependence of the optimum value of n on Dg,. the trend being as expected from n = 0 at Dsr values above 35, towards n = 1 for the finest sands considered. The initial motion coefficient, A, was found to depend on D s' as expected, although there were inconsistencies for the finer sizes. However. Eq. 14 was not of a sufficiently general form to describe adequately the transport of sediments towards the fine end of the transition range. The exponent should not be fixed at the value of 1.5 appropriate for coarse material: it should be higher for finer materials. The analysis was therefore extended, incorporating considerably more data, and generalizing the equation to be tested to read: (F" )m G=C--I.. I' A , , . . . . . . . . . . . . . . . . . . . . . . . . . (15) SECOND PHASE OF ANALySIS ~ '- !;-" The revised analysis was based entirely on the general function (Eq. 15) and it was assumed that C, A, m, and n would all vary with sediment size, D . In other words, the analysis optimized the values of four variable coefficients, rather than two. Some 925 individual sediment transport experiments were used in the analysis, of which 173 involved lightweight sediments of the type used in small-scale hydraulic models. Fuller details of the procedures and results are available elsewhere (20). The work of' 14 investigators, who carried out a total of 52 sets of experiments was considered: (Williams, 1966, 1970 (21,22); Laursen, 1957 (12); Mavis, ct H ,. r HY11 SEOIMENT TRANSPORT , ~ , . ~. \~ Ii i , ~ i , - < . . +---'*1' ~ ~ ~ ~ j..-A !7. ~ . ~ ~ If. s ~ // - ~~- ~- ,.I. I ."" .' e .. . : 6 6 2 ~ I"01l3J3t<1l"lIl"d /</O/JOH 7I"/JJ/o// , . , f- . , , . . , ! , ~ , 0 , ~ 0 ~ 0' . 1/ ~ 0 ,; s 0 ~ . 0 l/ .. ~ ~ ~ ~ 6 6 ~ ~ ~ ~ ~ ~ OIJ3JP'WIJI"-d NOJll<;;NYIJJ. .. , , , , , , , f-- ~ , ~ , f-c , . . ~ ,q,o ;)\g 0 ;;",-- I'-. . ~ i i "Iii == . 1 ..~... , , I-- ~~ H,,:~~ - ,.. ~ 0 .. . ;~ 1 ~ ::t W'lN?/NOd1l3 , o o o . ~ ~ " , u : i , " Ci ~ , , - ~ , '>, , <t == 0 << / I". ~ - :;t9 ~ - . ! 0 . . - ~ , .. ~ - 0 / ..... ~ --:: ~ " :0" . ... - .. ~ ~ ~ ? a o ~ ~ 8 8 ij o 0 0 , OJ.N3I:l1.:i:J30' --... . .~ iii II' ! I i 2047 .. .. .: il il 'j 1 ~ 4 'j 11 H ; ~ II II I, :1 ! ! 11 'I jl !I l' ~ i , :~ ~ . o' ... ~ - ~ '. :i . ~ ~ _ 0 ~ o 1i ~ or t: o 0. o ~ ~ t- ~ ~ . E ii <Il 'ii ~ . ~ . Cl ,5 :J ~ . 'u i o ~ ..; .lo .. ,,~ .~. .. . 'g tl -, o .; .0 ci ii: ~ !{ ': ~