Velocity and Concentration Distributions in Sheet Flow above Plane Beds
Publication: Journal of Hydraulic Engineering
Volume 125, Issue 2
Abstract
This paper reports the results of experiments on particle-water flow over plane-topped stationary beds. The particles used were silica sands having d50 of 0.30 and 0.56 mm and Bakelite particles having d50 of 1.05 mm. The facility was a recirculating loop with pipe of 105-mm internal diameter. Data comprised measurements of hydraulic gradient, volumetric discharge, temperature, concentration profiles, velocity profiles, and delivered concentrations. The thickness of the sheet-flow layer is found to vary in proportion to the shear stress. The velocity at the top of the layer is found to be ∼9.4 times the shear velocity, and a simple relation expresses the velocity gradient at this height. The Richardson number at the top of the sheet flow averages ∼0.035, decreasing with increasing ratio of particle fall velocity to shear velocity.
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References
1.
Ashton, G. D., ed. ( 1986). River and lake ice engineering. Water Resources Publications, Littleton, Colo., 304–318.
2.
Bagnold, R. A. ( 1954). “Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear.” Proc., Royal Soc., London, A225, 49–63.
3.
Bagnold, R. A. ( 1956). “The flow of cohesionless grains in fluids.” Philosophical Trans. Royal Soc., London, A249, 235–297.
4.
Brebner, A., and Wilson, K. C. ( 1967). “Derivation of the regime equations from relationships for pressurized flow by use of the principle of minimum energy-degradation rate.” Proc., Instn. Civ. Engrs., London, 36(January), 47–62.
5.
Czarnota, Z. ( 1986). “Hydraulics of rock tunnels.” Bull. No. TRITA-VB 1-129, Royal Institute of Technology, Stockholm.
6.
Daniel, S. M. ( 1965). “Flow of suspensions in a rectangular channel,” PhD thesis, University of Saskatchewan, Saskatoon, SK, Canada.
7.
DuBoys, P. ( 1879). “Etude du régime du Rhône et de l'action exercée par les eaux sur un lit à fond de graviers indefiniment affouillable.” Annales des Ponts et Chausées, 18(49, Part 2), 141–195.
8.
Gillies, R. G. ( 1993). “Pipeline flow of coarse particle slurries,” PhD thesis, University of Saskatchewan, Saskatoon, SK, Canada.
9.
Hanjalić, K., and Launder, B. E. ( 1972). “Fully developed asymmetric flow in a plane channel.” J. Fluid Mech., Cambridge, England, 51(2), 301–335.
10.
Hsu, S. T., Van der Beken, A., Landweber, L., and Kennedy, J. F. (1980). “Sediment suspension in turbulent pipeline flow.”J. Hydr. Div., ASCE, 106(11), 1783–1792.
11.
Johnson, J. W. ( 1942). “The importance of considering sidewall friction in bed-load investigations.” Civ. Engrg., ASCE, 12, 329–331.
12.
Larsen, P. (1973). “Hydraulic roughness of ice covers.”J. Hydr. Div., ASCE, 99(1), 111–119.
13.
Nasr-El-Din, H., Shook, C. A., and Colwell, J. M. ( 1987). “A conductivity probe for measuring local concentration in slurry flows.” Int. J. Multiphase Flow, 13, 365–378.
14.
Nnadi, F. N., and Wilson, K. C. (1992). “Motion of contact-load particles at high shear stress.”J. Hydr. Engrg., ASCE, 118(12), 1670–1684.
15.
Reynolds, A. J. ( 1974). Turbulent flows in engineering. Wiley, London.
16.
Pugh, F. J. ( 1995). “Bed-load velocity and concentration profiles in high shear stress flows,” PhD thesis, Queen's University, Kingston, ON, Canada.
17.
Shook, C. A., and Roco, M. C. ( 1991). Slurry flow principles and practice. Butterworth-Heinemann, Stoneham, Mass.
18.
Sumer, B. M., Kozakiewicz, A., Fredsøe, J., and Deigaard, R. (1996). “Velocity and concentration profiles in sheet-flows layer of movable bed.”J. Hydr. Engrg., ASCE, 22(10), 549–558.
19.
Turner, J. S. ( 1973). Buoyancy effects in fluids. Cambridge University Press, London.
20.
Vanoni, V. A., and Brooks, N. H. ( 1957). “Laboratory studies of the roughness and suspended load of alluvial streams.” Rep. E-68, California Institute of Technology Sedimentation Laboratory, Pasadena, Calif., 121.
21.
Webb, E. K. ( 1970). “Profile relationships: The log-linear range, and the extension to strong stability.” Quarterly J. Royal Meteorological Soc., Bracknell, England, 96, 67–90.
22.
Wilson, K. C. (1966). “Bed-load transport at high shear stress.”J. Hydr. Div., ASCE, 92(6), 49–59.
23.
Wilson, K. C. (1970). “Slip point of beds in solid-liquid pipeline flow.”J. Hydr. Div., ASCE, 96(1), 1–12.
24.
Wilson, K. C. (1987). “Analysis of bed-load motion at high shear stress.”J. Hydr. Engrg., ASCE, 113, 97–103.
25.
Wilson, K. C. (1989). “Mobile-bed friction at high shear stress.”J. Hydr. Engrg., ASCE, 115(6), 825–830.
26.
Wilson, K. C., Addic, G. R., Sellgren, A., and Clift, R. ( 1997). Slurry transport using centrifugal pumps, 2nd Ed., Blackic Academic & Professional, London.
27.
Wilson, K. C., and Pugh, F. J. (1988a). “Dispersive force basis for concentration profiles.”J. Hydr. Engrg., ASCE, 114(7), 806–809.
28.
Wilson, K. C., and Pugh, F. J. ( 1988b). “Dispersive force modelling of turbulent suspension in heterogeneous slurry flow.” Can. J. Chem. Engrg., Ottawa, Canada, 66(October), 721–727.
29.
Yalin, M. S. ( 1992). River mechanics. Pergamon Press, Oxford, U.K.
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Published online: Feb 1, 1999
Published in print: Feb 1999
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