Slurry 4: Gravity Transfer of Slurries in Open Channel Flow
     Part 1: Review of Pseudohomogeneous Non-Newtonian Open Channel Flow
         1 INTRODUCTION
         2 OPEN CHANNEL FLOW TERMINOLOGY
             2.1 Open Channel Hydraulics
                 2.1.1 Shape
                 2.1.2 Slope
                 2.1.3 Hydraulic Radius
                 2.1.4 Hydraulic diameter
             2.2 Types of Flow
                 2.2.1 Steady and Unsteady Flow
                 2.2.2 Uniform and Varied Flow
             2.3 Flow Regimes
                 2.3.1 Laminar, transitional and turbulent flow
                 2.3.2 Reynolds Number
                 2.3.3 Froude Number
             2.4 Wall Roughness
         3 NEWTONIAN FLOW IN OPEN CHANNELS
             3.1 Laminar Flow
             3.2 Turbulent Flow
                 3.2.1 Chézy
                 3.2.2 Manning or Gauckler-Manning
                 3.2.3 PavlovskiÐ equation
                 3.2.4 Blasius
                 3.2.5 von Karmán-Prandtl
                 3.2.6 Colebrook-White
             3.3 Laminar-Turbulent Transition
         4 NON-NEWTONIAN FLOW IN OPEN CHANNELS
             4.1 Flow curve models used
                 4.1.1 Newtonian model
                 4.1.2 Power law model
                 4.1.3 Bingham plastic model
                 4.1.4 Herschel-Bulkley model
             4.2 Laminar Flow
                 4.2.1 Kozicki and Tiu's approach
                 4.2.2 Abulnaga's approach
                 4.2.3 Coussot's approach
                 4.2.4 De Kee et al's film flow approach
                 4.2.5 Haldenwang et al.'s approach
                 4.2.6 Zhang and Ren's model
                 4.2.7 Comparison of Laminar Flow models
             4.3 Turbulent Flow
                 4.3.1 Manning
                 4.3.2 Wilson and Thomas pipe flow model adapted
                 4.3.3 Kozicki and Tiu approach
                 4.3.4 Torrance pipe flow model adapted
                 4.3.5 Slatter's pipe flow model adapted
                 4.3.6 Naik's model
                 4.3.7 Abulnaga's approach
                 4.3.8 Develter and Duffy's approach
                 4.3.9 Haldenwang's model
                 4.3.10 Yang and Zhao's model
                 4.3.11 Comparison of turbulent flow models
             4.4 Laminar-Turbulent Transition
                 4.4.1 Hao et al.'s approach
                 4.4.2 Hank's criterion adapted
                 4.4.3 Naik's approach
                 4.4.4 Coussot's adaptation of the Hanks criterion
                 4.4.5 WiIson's method for predicting transition
                 4.4.6 Haldenwang's model
                 4.4.7 Wang et al.'s model
                 4.4.8 Yang and Zhao's model
             4.5 Roughness
         5 EXPERIMENTAL STUDIES
             5.1 Zhang and Ren (1982)
             5.2 Naik (1983)
             5.3 Coussot (1994)
             5.4 Develter and Duffy (1998)
             5.5 Sanders et al. (2002)
             5.6 Haldenwang (2003) & Haldenwang et al. (2004)
         6 CASE STUDIES
             6.1 Flumes in Chile for transport of copper ore tailings
             6.2 Toquepala and Cuajone mines, Peru
             6.3 Cuyohasi copper mine, Peru
         7 CONCLUSIONS
         8 NOMENCLATURE
         9 REFERENCES
     Part 3: Review of Settling Slurry Open Channel Flow
         1 INTRODUCTION
         2 LIMIT DEPOSIT VELOCITY IN OPEN CHANNEL FLOW
         3 DESIGN PROCEDURES FOR SETTLING SLURRIES
             3.1 Green, Lamb and Taylor Approach (1978)
             3.2 Faddick's Design Procedure (1986)
             3.3 Wilson's Model (1980)
             3.4 Blench, Galay and Peterson Approach (1980)
             3.5 Joffe Approach (1965)
             3.6 Matthews Approach (1964)
             3.7 Comparison of the Available Design Procedures for Settling Slurries
         4 MECHANICAL DESIGN OF FLUMES
             4.1 Geometric Design
             4.2 Materials of Construction
             4.3 Connections between Flume Sections
             4.4 Turns and Bends
         5 FLOW MEASUREMENT OF SLURRIES IN OPEN CHANNEL FLOW
             5.1 Use of Weirs and Flumes
             5.2 Use of Ultrasonic Devices
         6 CASE STUDIES OF INDUSTRIAL SLURRY FLUME INSTALLATIONS
             6.1 Marcopper's Tailing Disposal System in the Philippines
             6.2 Copper Tailing Transport at the El Teniente Mine in Chile
             6.3 Transport of Run-of-Mine Coal at the Hansa Hydro-Mine in Dortmund, Germany
             6.4 Transport of Run-of-Mine Coal in British Columbia, Canada
             6.5 Transport of Washed Coal at Aldridge, Montana, USA
             6.6 Coal Transport in New Zealand
             6.7 Gold and Uranium Slimes Transport in South Africa
             6.8 Transport of Run-of-Mine Coal in Sunagawa Mine, Japan
         7 CONCLUDING REMARKS
         8 NOTATION
         9 REFERENCES

• Part 1 Gravity Transfer of Slurries in Open Channels

Volume SH 4: Part 1 Gravity Transfer of Slurries in Open Channels

This part is a state-of-the-art review and considers the transport of slurries along open or closed ductwork using the material head as the driving force for flow. This occurs for both open channel (or flume) flow of either "settling" or "non-settling" slurries in either the laminar or turbulent regimes. The transfer of slurries in open channels or flumes, while not as important as pipeflow, is commonplace in the mining and water industries and, as with pipeflow, can be conveniently categorised into flow of "non-settling" slurry and of "settling" slurry. For the turbulent flow of water the Chezy formula, with an appropriate Chezy coefficient depending on the flume geometry, has found widespread use for the prediction of the head/flowrate relationship. This approach can be adapted for use with "non-settling" slurries. Methods are also available for Newtonian and non-Newtonian laminar flow.

Large-scale experimental studies have been undertaken for "settling" slurries in a wide range of flume geometry. Some of these studies have resulted in procedures for correlating available head with slurry flowrate but only Wilson’s theory has provided a mechanistic insight into the flow. The choice of materials of construction for chutes and flumes is critical for a good engineering design. For chutes, linings are often employed to reduce adhesion and frictional forces between paste or cake and inner wall, although cooled steel surfaces have also been employed. For open channel flow, abrasion is generally more of a problem, particularly in the mining industry and plastic linings have been used to reduce wear rates. Test methods are available for assessing the degree of adhesion and wear for a bulk solid on different alternative linings. Good mechanical design if of prime important for continuous reliable performance of either chutes or flumes. Different chute cross-section geometries can be used including closed circular pipe and rectangular/square cross-section, while for flumes the choice generally widens to include trapezoidal and V-shapes. Chutes can be installed vertically, near vertically or deliberately inclined. They can be convergent, constant cross-sectioned or divergent. In addition, chutes can have smooth bends and much of the Roberts et al theory focuses on this situation.

The type and quality of connections between sections of chute or flume are crucial in ensuring progressive build-up and eventual blockage do not occur and in minimising wear rates at these joints. Metering of flow in chutes is occasionally required but is more important in flume flow where some type of weir can be used or alternatively an ultrasonic level detector.