Correction factor to dye-measured flow velocity under varying water and sediment discharges

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Summary

Dye-tracing technique was a widely used method to determine the velocity of overland flow in soil erosion studies under both laboratory and field conditions. Few studies were performed to quantify the effects of sediment load on correction factor on steep slopes. This study was conducted to investigate the potential effects of sediment load on correction factor of overland flow to determine mean velocity in a glued hydraulic flume under a wide range of hydraulic conditions and sediment load. Slope gradient (S) varied from 8.7% to 34.2%, unit flow rate (q) from 0.66 to 5.26 × 10−3 m2 s−1, and sediment load (Qs) from 0 to 6.95 kg m−1 s−1. The Reynolds number (Re) ranged from 350 to 5899. Mean velocity was calculated from the volumetric relation using measured flow depth by a digital level probe and flow discharge. The results showed that correction factor decreased as S increased and increased as Re increased for sediment-free flow with a mean value of 0.659. Correction factor could be estimated with a logarithmic function of S and Re (R2 = 0.883). For the sediment-laden flow, correction factor varied from 0.233 to 0.682 with a mean value of 0.466. The correction factor decreased as sediment load (Qs) increased and increased as Re increased. It could be estimated with a logarithmic function of Re, and Qs (R2 = 0.796). For the combination of sediment-free and sediment-laden flows, the correction factor varied from 0.233 to 0.783 with a mean of 0.505. The correction factor was inversely related to slope gradient and sediment load, and directly to Reynolds number (R2 = 0.854). The overall results indicated that caution must be exercised and proper correction be made when using the dye tracer method to measure flow velocity in surface hydrology and erosion studies. Further studies with systematic advanced set up for sediment feeding are needed to quantify the potential effects of sediment load on correction factor under varying conditions of roughness element.

Introduction

Mean flow velocity (Vm) is one of the most important hydraulic variables in soil erosion modeling, since it is dependent upon flow discharge, slope gradient, topography, and surface condition (Zhang et al., 2002, Zhang et al., 2003). It is used to calculate friction coefficient, runoff concentration time, and other hydraulic parameters such as stream power, and unit stream power, which are used to simulate the processes of both detachment and sediment transport in the process-based erosion model (De Roo et al., 1996, Yu et al., 1997, Morgan et al., 1998, Zhang et al., 2009a, Zhang et al., 2009b). A precise measurement of mean velocity of overland flow is imperative for soil erosion studies in both laboratory and field conditions.

Many technologies have been used to measure velocity of overland flow. Among these are hot film anemometry (Robinson and Cook, 1998), Acoustic Doppler velocimetry (Gimenez et al., 2004), digital videography (Sidorchuk et al., 2008), magnetic velocimeters and particle imaging velocimetry (Raffel et al., 1998). However, most of them have certain limitations, especially in the complicated filed conditions. For example, hot film anemometry cannot be used to measure overland flow velocity carrying sediment since the thin layer of quartz that electrically insulates the platinum film can be abraded by sand particles or coated by colloidal deposits (Planchon et al., 2005). The measurements of Acoustic Doppler velocimetry and magnetic velocimeters need deeper flow depth, which is usually out of the range of overland flow.

The tracing method is widely used to measure velocity of overland flow in both laboratory and field conditions for soil erosion studies (Luk and Merz, 1992, Li et al., 1996, Nearing et al., 1999, Zhang et al., 2003, Zhang et al., 2009b). The commonly used tracer materials are dyes and salts (Horton et al., 1934, Emmett, 1970, Luk and Merz, 1992, Li et al., 1996, Lei et al., 2005). With a dye tracer, the time for the tracer to travel from the injection point to the observation point is measured visually. The ratio of the distance between the two points to the travel time to cover this span is the velocity of the leading edge of the plume, which is frequently regarded as the surface velocity of the flow (Vsurf). A correction factor α is then applied to convert Vsurf to Vm (Vm = Q/A where Q is the discharge and A is the cross-sectional area of flow).

In 1934, Horton et al. showed theoretically that the correction factor α is 0.67 for the case of infinitely wide, perfectly laminar flow on a smooth and immobile bed. Emmett (1970) analyzed his dataset for the Re range of 200–2000 (Re is Reynolds number) obtained from a quasi-uniform laminar flow on a laboratory sand bed with a fixed width. The results revealed that the correction factor α varied from 0.365 to 0.825 with a mean value of 0.576. The correction factor increased with velocity or with Reynolds number for laminar flow, and could be as high as 0.83 for turbulent flow. Luk and Merz (1992) evaluated the salt tracing technique to determine mean velocity of overland flow. For their 21 data set obtained in the laboratory, correction factor varied from 0.61 to 0.86, with a mean of 0.75. For the data set of field experiments, the mean correction factor was 0.53 for all experiments, and 0.52 for laminar flow. The deviation of the correction factor was explained by the effect of raindrop impact and overestimation of mean surface velocities. The work of King and Norton (1992) indicated that the correction factor α was independent of the Reynolds number, but inversely proportional to slope gradient.

In order to investigate the relationship between correction factor, slope gradient, and Reynolds number, 40 experiments were conducted by Li et al. (1996) in a 5.2 m flume with a mobile sand bed. The slope ranged from 4.7% to 17.4% and Reynolds number from 1900 to 12,600. It was found that α did not exhibit a value of 0.67 for laminar flow, nor did it adopt the theoretical value of 0.8 for turbulent flow. The correction factor varied from 0.39 to 0.69 with a mean value of 0.53. Multiple regression analyses revealed that correction factor α varied inversely with slope and directly with Reynolds number.

Flume experiments of Li and Abrahams (1997) showed that α varied with both Reynolds number and sediment load. For sediment-free flow over a sand-cover bed, α was less than the theoretical value of 0.67 in laminar flow and increased rapidly with Reynolds number in transitional flow and more slowly with Reynolds number in turbulent flow. For sediment-laden flow, α decreased as sediment load increased in transitional and turbulent flows. The test slopes of Li and Abrahams were 2.1%, 6.1%, and 9.6% for the first set of experiments and the flume was inclined at a slope of 6.5%. The well-sorted silica testing sand with a median diameter D50 of 0.74 mm was glued to the bed of the flume. The sediment was supplied by a hopper and the sediment loads were 0.05 and 0.07 kg m−1 s−1.

Based on laboratory experiments on a glued sand bed, Dunkerley (2001) evaluated the uncertainty in the mean velocity measurement of overland flow using dye-tracing method. The experiments were conducted in a 1.2-m-long, 0.6-m-wide flume. Mean flow velocities were estimated from both dye speeds and the volumetric method with measured flow depth using a computer-controlled needle gauge at 64 points. To simulate conditions applicable to many dry land soils, the board was also roughened with plant litter and with ceramic tiles. The results demonstrated that in the range of 100 < Re < 500, there was no consistent relation between surface and mean velocities. No relationship between correction factor and Reynolds number was found in his study. The mean correction factor was 0.56 and exhibited a considerable scatter of data points that showed a dependence on flow depth. The results also showed that the size of protruding roughness elements, affected correction factor. Dunkerley concluded pessimistically regarding the usefulness of dye and salt tracing for mean velocity measurement of overland flow.

Xia et al. (2003) assessed the effect of sediment concentration on correction factor α in a 5 m flume using salt tracer. The slope gradient ranged from 0.9% to 20.8% and the sediment concentration from 0% to 60.2%. They found that the correction factor increased as sediment concentration increased. This result was not consistent with the conclusion of Li and Abrahams (1997). Planchon et al. (2005) evaluated an automated salt tracing gauge for flow velocity measurement. They found that correction factor was not a constant but depend on velocity, diffusion, and distance between two sections used to monitor velocity of dyed flow. The result confirmed the scattering of α values mentioned by Dunkerley (2001) and raised questions about the reliability of dye method to measure mean flow velocity of overland flow.

As mentioned above, the correction factor was found to be affected by Reynolds number (Emmett, 1970, Li et al., 1996), slope gradient (Li et al., 1996, Li and Abrahams, 1997), flow depth (Dunkerley, 2001), diffusion (Planchon et al., 2005), and sediment load (Li and Abrahams, 1997, Xia et al., 2003). Some studies have indicated that α decreased as sediment load increased (Li and Abrahams, 1997), while others showed that α increased as sediment load increased (Xia et al., 2003). The maximum slope gradient of prior studies was 20.8%, and limited data were available on steep slopes. Further studies are necessary to evaluate the quantitative effects of sediment load on correction factor for mean velocity determination of overland flow on steep slopes.

The objective of this study was to investigate the potential effects of Reynolds number, slope gradient, flow depth, and sediment load on correction factor α of overland flow to determine mean velocity in a glued hydraulic flume under a wide range of hydraulic conditions and sediment loads. The study provided useful information to insight the complicate relationship between correction factor and sediment load on steep slopes and was helpful to use dye method to measure velocity of overland flow with high sediment concentration.

Section snippets

Materials and methods

The experiments were conducted in a 5-m-long, 0.4-m-wide hydraulic flume (Fig. 1). The bed slope of the flume could be adjusted up to 60%. Test sediment was collected from the bed of Yongding River near Beijing, China. The test sediment was air-dried and sieved. Particles less than 2 mm were used as the test materials. The diameter of test sediment varied from 0.02 to 2 mm with a median diameter D50 of 0.28 mm. Test sediment was glued to the flume bed to simulate the grain roughness of natural

Sediment-free flow

The measured depth of sediment-free flow varied from 1.38 to 6.36 mm and the measured surface velocity from 0.56 to 1.65 m s−1. The Reynolds number ranged from 664 to 5899. The calculated mean velocity was within the range of 0.346 to 1.139 m s−1. The statistical properties of correction factor α were given in Table 3. The correction factor α of sediment-free flow varied from 0.510 to 0.783 with a mean value of 0.659. The measured range included the Horton’s theoretical value of 0.67 for laminar

Summary and conclusions

Dye tracers are widely used to measure velocity of overland flow in soil erosion studies. Few studies were conducted to quantify the effects of sediment load on correction factor on steep slopes and at high sediment load. The results showed that correction factor varied from 0.510 to 0.783 with a mean value of 0.659 for sediment-free flow. The correction factor αsf decreased as slope gradient increased and increased as Reynolds number increased for sediment-free flow. The αsf could be estimated

Acknowledgements

The experiments were conducted at the Fangshan Field Station of Beijing Normal University. Financial assistance for this work was provided by the National Key Basic Research Special Foundation Project (2007CB407204) and the National Key Technologies R&D Program (2006BA09B05).

References (26)

  • A.D. Abrahams et al.

    Effect of saltating sediment on flow resistance and bed roughness in overland flow

    Earth Surface Processes and Landforms

    (1998)
  • A.P. De Roo et al.

    LISEM: a single-event physically based hydrological and soil erosion model for drainage basins: I: theory, input and output

    Hydrological Processes

    (1996)
  • D. Dunkerley

    Estimating the mean speed of laminar overland flow using dye injection-uncertainty on rough surfaces

    Earth Surface Process and Landforms

    (2001)
  • W.W. Emmett

    The hydraulics of overland flow on hill slope

    US Geological Professional Paper

    (1970)
  • R. Gimenez et al.

    Longitudinal velocity patterns and bed morphology interaction in a rill

    Earth Surface Processes and Landforms

    (2004)
  • R.E. Horton et al.

    Laminar sheet flow

    Transactions of the American Geophysical Union

    (1934)
  • S.X. Hu et al.

    Partitioning resistance to overland flow on rough mobile beds

    Earth Surface Processes and Landforms

    (2006)
  • King, K.W., Norton, L., 1992. Methods of Rill Flow Velocity Dynamics. American Society of Agricultural Engineers,...
  • T.W. Lei et al.

    Method for measuring velocity of shallow water flow for soil erosion with an electrolyte tracer

    Journal Hydrology

    (2005)
  • G. Li et al.

    Effect of saltating sediment load on the determination of the mean velocity of overland flow

    Water Resource Research

    (1997)
  • G. Li et al.

    Correction factors in the determination of mean velocity of overland flow

    Earth Surface Processes and Landforms

    (1996)
  • S.H. Luk et al.

    Use of the salt tracing technique to determine the velocity of overland flow

    Soil Technology

    (1992)
  • R.P. Morgan et al.

    The European soil erosion model (EUROSEM): a dynamic approach for predicting sediment transport from fields and small catchments

    Earth Surface Processes and Landforms

    (1998)
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