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<br />768
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<br />HYDRAULIC ENGINEERING '94
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<br />Beghmlng movement of' the bottom bed _terial
<br />The conditions of' the beginning movement of the individual bed load
<br />fractions were det~rllllned directly In the measurellents on rivers
<br />recording behavior of the grains traced by tantalum-182 isotope
<br />and simultaneously measuring the hydraulic parameters. Such a hind
<br />of measurements for the bed load were conducted four Urnes on the
<br />Raba river what made the hiding function, determine accurately and
<br />it turned out to be the same as the Dlplas function (Diplas
<br />1986).Th& movement limiting quantities resulted from the
<br />measurelllenls on Ra.ba are presented in Table 1.
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<br />Table 1
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<br />year. nUlllber d h T v
<br />of run I LI c,
<br /> 5 C c,
<br />river . . L kPa I
<br /> m/s
<br /> 0.0025 0,70 0.00300 2,100 0,509 -
<br /> 0,02 1.07 0.00315 3.386 0,103 1.84
<br />1987, I 0.04 1.07 0.00287 3.071 0.047 1.80
<br />Raba 0.06 1.10 0.00298 3.278 0.033 1.83
<br /> 0.07 1.18 0.00315 3.717 0.032 1.97
<br /> 0.18 1.15 0.00333 3.830 0,013 1.98
<br /> 0,0025 1.15 0,00315 3,822 0,878 -
<br /> 0,02 1.26 O. 00267 3,378 0,102 1.89
<br />1987,2 0.04 1.34 0.00279 3.082 0.047 2.01
<br />!laba 0,06 1.12 0.00284 3.180 0.032 1.80
<br /> 0,07 1.20 0.00315 3,780 0,033 1.99
<br /> 0.08 1.32 0.00267 3.538 0.027 1.95
<br /> 0.18 1.31 0.00302 3.950 0.013 2.09
<br /> 0,02 1.43 0.0025 3.575 0.108 1.81
<br />1988.3 0,04 1.21 0,0023 2.783 0,042 1.71
<br />!laba 0.08 0.95 0.00335 3.183 0.032 I. 79
<br /> 0.07 0.90 0.0375 3.375 0.029 I. 74
<br /> 0.08 0.90 0.00370 3.330 0.025 I. 71
<br /> 0.18 1.35 0.00301 4.070 0.014 2.10
<br /> 0.03 0.57 0.0029 1.653 0.333 1.19
<br />1991. 4 0.05 0.81 0.0029 2.349 0.030 I. 47
<br />!laba I
<br />0,07 0.71 i 0.0028 1.988 0,017 1.32
<br />> 0,08 0.78 0,0028 2,128 0,013 1.39
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<br />where:dt grain diameter of a friction
<br />hLl- critical depth at which the movement of" the dt began
<br />SL - slope of water surface at the IIOment the grains started
<br />Ter- shear stress
<br />fl = Ter /(78 -7) - nondllllentional shear stress
<br />VL - mean limiting rate of" f"low in the river cross section
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<br />FLUVIAL HYDRAULICS
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<br />769
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<br />It was found that in all cases nondlmenslonal tangent stress f..,
<br />for the aean diameter of the grains d. was f-= 0.030 (tn the
<br />~8Surements 1987.1 , 1987.2 and 1988.3 d. = 0.072 m and in 1991.4
<br />d... 0.05 m), therefore, significantly less them in the Heyer -
<br />Peter and Muller equation, where according to ann accept
<br />deslgnation f.. = 0.047.
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<br />Roughness of the bed under the incipient movement condition
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<br />To determlne resistance of floW' the Prandtl equation of velocity
<br />distribution was applied. After transformation , analogically Graf
<br />(1981) the following equation was obtained:
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<br />v/v .- ~ 8/A = C/-/'8= 5,751g (h Id)+ B (t)
<br />er LI t
<br />The B .coefficient was determined on the basis of the measurements
<br />and B = 2.5J.Consequently, the equation (1) is as follows:
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<br />v/Ver-= ~ alA = C/vg= 5,751g (hLl /dl)+ 2.53 (2)
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<br />Wherei v - average velocity ,Ver- - critical shear velocity
<br />A - friction factor
<br />The equation (2) presented aboVe is derlvated for the beginning
<br />aovelllent of the bed load, then, for the flow conditions under which
<br />roughness is equilibrated by force of gravity.
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<br />The gratn shape effect on the incIpient movetnent of the bed load.
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<br />It was found that the crItical stress depended mainly, the grain
<br />stze, the hiding coefficient, the flow velocity and turbulence
<br />Intensities. The grain shape effects essentially on the critical
<br />stresses value. The More flate (board) grains creating the bottom
<br />the less shear stress are necessary to make gra1ns move. If it
<br />accepted that the resistance coefficients of unbounded falling of
<br />grains In water and. grain moving on the bottom are the same
<br />(Bartnik 93) and both of them depended on the gratn shape, it can
<br />asSUIle that the falling velocity of grain"w" and the critical
<br />velocity llVL" derived frOM the resistance flow equation are equal: w
<br />. VL. After appropriate transformation, the nondluns10nal stress
<br />depended On the resistance coefficient of grains for different
<br />shapes, is expressed by the equat Ion:
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<br />,14/38 die. lJ,p./p = v_{S,75Ig (hLl /dl) + 2,53]
<br />and
<br /> 4 phLl 51.
<br /> . C (3)
<br />3cv(S,751g hLI Idl+ 2.53)2 dl Ap I
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<br />where:cw- resistance coefficient of grains
<br />According to this equation, the nondilRensional shear stress were
<br />calculated for the grain shapes appearing 1n the bed loads of the
<br />studied rivers.The results are presented 1n Table 2.
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