Assessing Predictive Capability of Selected Bed Load Equations Using Experimental and Flume Data

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Yadav Sanjay This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3714539/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Bed load transport in alluvial rivers is the principle link between river hydraulics and river form and is responsible for building and maintaining the channel geometry. Bed load prediction is of primary importance for river engineering, fluvial geomorphology, ecohydrology, environmental surveys & management and hazard prediction. In this study, for bed load transport analysis data sets and experimental data were used. The data sets of Casey, Graf & Suszka, HPY, Mavis, Paintal and MPM were used to compute bed load transport. Experimental work was carried out in advanced hydraulic laboratory in Civil Engineering Department. The bed load was measured for three mixtures. The measured bed load was compared with computed bed load using MPM, Einstein, Soulsby, Van Rijn, Parker, Ashmore and Wong & Parker approaches. The analysis of measured and computed bed load is in good agreement for MPM, Ashmore & Soulsby. At the same time for MPM data set the measured and predicted bed load is in good agreement. For all data sets and experimentally measured bed load Van Rijn approach under predicts the bed load. Bed Load transport Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Figure 26 Figure 27 Figure 28 Figure 29 I. INTRODUCTION Sediment is a naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of wind, water, or ice, and/or by the force of gravity acting on the particle itself. Sediments are most often transported by water (fluvial processes), wind (Aeolian processes) and glaciers. On an average, rivers worldwide transport around 19000 million tones of sediment annually (Knighton 1998 ). The ability to transport sediment depends on the characteristics of the flow, with rivers carrying as much sediment as the energy of the flow permits (Edwards & Glysson 1999 ). By altering the hydrology and sediment regime of a catchment there can be significant impact on the character and behavior of the river and on the fluvial ecosystem (Knighton 1998 ). Individual particles move along the bed of the water course by rolling, sliding or occasionally in jumps (saltation) which is generally termed as bed load (The Subcommittee on Sediment Terminology of the American Geophysical Union.) Bed load transport in alluvial rivers is the principle link between river hydraulics and river form and is responsible for building and maintaining the channel geometry (Parker, 1979 ; Leopold, 1994; Goodwin, 2004). Prediction of bed load is of primary importance for river engineering, fluvial geomorphology, eco-hydrology, environmental surveys and management, and hazard prediction (Recking, 2009). Until now, engineering tools have mainly used bed load equations obtained from theoretical or semi-empirical analysis, established for equilibrium conditions (stable state; where the flow energy slope is compatible with the sediment transport rate) and for uniform (or assumed to be uniform) materials. However, all natural sediments are not uniform, and properties established for flows over uniform materials may no longer be valid for flows over graded sediments. Indeed, in addition to the water sediment interaction, interactions between grains of different sizes may also influence the overall flow system’s behavior. There have been numerous studies, both in natural channels and in flumes, based on different approaches depending on the conditions under which the equations were developed. II. METHODOLOGY All runs were performed in the Advanced Hydraulic Laboratory in Sardar Vallabhbhai National Institute of Technology, Surat. With the objective to study the bed load transport, it was very important to ensure the equilibrium condition and use efficient tools to develop the experimental set up. The experimental setup The experimental setup is shown in Fig. 1 . The flume is 15 m long having 6 m working section, 0.86 m wide (slope varying from 0 to 1%). The flow rate at the upstream was controlled by two pumps, each having capacity of 1500 rpm. Discharge was measured by the flow meter situated on the inlet pipe. Each run was performed at the equilibrium condition, with the liquid and solid discharge maintained constant, over a 7 cm thick gravel bed. Sediments (Materials) Three uniform mixtures of mean diameter of 2.8284 mm (2–4 mm), 5.6564 mm (4–8 mm) and 1.41 mm (1–2 mm) (called Mixture I, II, III respectively) were selected by sieving natural sand gravel mixtures and density was 2600 kg/m 3 for Mixture I, Mixture II and Mixture III respectively. The grain sorting coefficient approximately 1.1 for each mixture shows the uniformity of all three mixtures. Uniform flow set up All the experiments were conducted under uniform flow conditions, where the surface of the water was parallel to the bed and therefore, flow depth was constant along the flume. Uniform flow conditions are important as they permit comparison of measurements of hydraulic and bed characteristics that are often taken at different locations within the flume. In addition, some formulae, including bed shear stress estimation methods, require uniform flow conditions. Uniform flow was established for each flow as follows: for a given bed slope and flow, repeat measurements of depth were taken at 10 locations along the flume at 0.5 m interval, adjusting the tailgate to produce approximate uniform flow (defined when slope of the fitted line to water levels was within ± 2% of the objective slope). Repeating this procedure for the full range of flows produced a relationship between flow, tailgate position and average flow depth. These data were subsequently used to set uniform flow conditions during the experiments and to estimate shear stress for each flow. Performance Steps of Experiment : Place the material uniformly within the working length (6m) of flume by sediment feeder. Adjust initial slope of flume and prime both pumps. Start both pumps and adjust the discharge. Make the flow uniform by adjusting tail gate at the end of the flume. After making the uniform flow saturate the mixture for at least 01 hour. After 01 hour take the wash load in the bed load trap and place uniformly in the upstream of the flume to make the equilibrium condition. Than start taking reading of Discharge, Slope, velocity, and bed load sample within the specific time limit. In this study the time limit to collect bed load sample was 20min. Then place the taken mixture in the upstream of the flume with the help of sediment feeder. Repeat step 7–8 until bed load remain constant. After completing the whole run spread the mixture in the flume to dry it for the next run. In this study slope remains constant for one run and different discharges is taken for each mixture. For the mixture of 1–2 mm initial slope was taken 0.0008 and extreme slope was 0.003. For the mixture of 2-4mm and the 4–8 mm initial slope was 0.005 and final slope was 0.008. Different types of bed load equations were used for the comparison of theoretical and experimental measurements. Table No 1 shows the details of different bed load equations used in the present study For each run the following parameters were measured: The flow discharge ,Q (m 3 /s): The flume slope, S (m/m): The outlet solid discharge (Kg/20min): from weighed samples collected at the outlet of the flume. The mean flow velocity, U (m/s). Measurements were taken for equilibrium condition. Bed Load Transport Formulae Dimensionless Quantities; Ф= \(\frac{qb}{\sqrt{\left(s-1\right)g{d}^{3}}}\) (dimensionless bed load transport) τ*= \(\frac{\tau }{P\left(s-1\right)gd}\) (dimensionless shear stress or shield stress) d*=d \(\sqrt[3]{\frac{\left(s-1\right)g}{v}}\) (dimensionless particle diameter) Table 1.0 Details of Bed Load Equations used in the present study Sr No. Scientist Equation Approach Remarks 1 Meyer-Peter and Muller (1948) Ф =8(τ*-τ* crit ) 3/2 if τ*≥ τ* crit Ф =0 if τ* < τ* crit Energy Slope Original Paper assume τ* crit =0.047 2 Einstein ( 1950 ) Ф = Kexp(− 0.391 / τ*)/0.465 if τ*<0.182 Ф =40Kθ 3 if τ*≥0.182 Where K= \(\sqrt{\frac{2}{3}+\frac{36}{{d*}^{3}}}-\sqrt{\frac{36}{{d*}^{3}}}\) Probabilistic - 3 Soulsby (1997) Ф = 5.1(τ*-τ* crit 3/2 Shear stress - 4 Van Rijn(1984) Ф = \(\frac{0.053}{{d*}^{0.3}}\) [(τ*/τ* crit )-1] Regression - 5 Parker ( 1979 ) Ф = 11.20 \(\frac{{(\tau *-0.03)}^{4.5}}{{\tau *}^{3}}\) Probabilistic - 6 Ashmore (1988) Ф = 3.11(τ*-0.045) 1.37 Shear stress - 7 Wong & Parker (2006) Ф = 3.97(τ*-0.0495) 1.5 Shear stress - III. DATA COLLECTION In this study data were collected in two parts. First part contains the data which is collected from the historical experimental data of several researchers. The second part contains the experimental data which has been collected from the hydraulic tilting flume situated in the Advanced Hydraulics Laboratory in the Sardar Vallabhbhai National Institute of Technology, Surat. Historical Data In this part various experimental flume data set has been collected. In this study collected data were which range in the moderate slope range. (Slopes varying from 0 to 1%) The data used in this study include, Casey (1935), Graf& Suzska (1987), HoPang-Yung (1939), Mavis (1937), Paintal (1971) and MPM (1948). The brief details of data set are given in Table 2.0 Experimental Data The second part contains the experimental data which were collected in hydraulic tilting flume situated at Advanced Hydraulics Laboratory, Civil Engineering Department, Sardar Vallbhbhai National Institute of Technology, Surat. The detail of mixture used in present study is detailed as Table 3.0 Table 2.0 Historical Flume Experimental Data No Author Year Diameter D (mm) Standard deviationσ Sediment Density ρs (Kg/m 3 ) Slope S(m/m) Width of flume W(m) 1 Casey 1935 2.5 mm 1.16 2650 0.00119 < S < 0.00509 0.4 1 mm 2.81 2810 0.0012 < S < 0.00519 0.4 2 Graf & Suszka 1987 12.2 mm 1.2 2716 0.005 < S < 0.015 0.6 3 Ho Pang-Yung 1939 3.1 mm 2.24 2490 0.00105 < S < 0.00336 0.339 4.4 mm 1.59 2700 0.00127 < S < 0.00336 0.339 6.3 mm 1.49 2660 0.00169 < S < 0.00504 0.339 2 mm 1.99 2450 0.00101 < S < 0.00168 0.339 6 mm 1.39 2660 0.00333 < S < 0.00501 0.339 1.4 mm 1.96 2640 0.00099 < S < 0.00102 0.339 4 Mavis 1937 4.2 mm 1.23 2660 0.00175 < S < 0.01 0.819 3.1 mm 1.25 2660 0.0017 < S < 0.00955 0.819 2 mm 1.29 2660 0.00155 < S < 0.0101 0.819 1.4 mm 1.24 2660 0.00135 < S < 0.01 0.819 3.7 mm 1.3 2660 0.0018 < S < 0.01 0.819 1.7 mm 1.36 2660 0.00165 < S < 0.01 0.819 5 Paintal 1971 22.2 mm 1.07 2650 0.0079 < S < 0.0103 0.914 8 mm 1.1 2650 0.00226 < S < 0.0052 0.914 2.5 mm 1.08 2650 0.00117 < S < 0.00213 0.914 6 MPM 1948 28.7 mm 1 2680 0.00317 < S < 0.01767 1.999 5.2 mm 1 2680 0.00128 < S < 0.0226 1.999 Table 3.0 Flume Experimental Data No Mixture Size Range Diameter D(mm) Slope S (m/m) Width of flume W(m) 1 I 1–2 mm 1.41 0.0008 < S < 0.003 0.86 2 II 2–4 mm 2.82 0.005 < S < 0.008 0.86 3 III 4–8 mm 5.65 0.005 < S < 0.008 0.86 Analysis of Data Fig. shows the best comparison curves (Φobs versus Φcal) proposed by respective investigators with data reported in the various studies for sediment bedload transport at moderate condition. The figure shows considerable compatibility with the observed Φ. The experimental data shows a marginally scatter and could be explained as a set rather than well defined curves. The discrepancy is primarily due to particle shape, random nature of the entrainment process, and the difficulty with defining criteria that adequately capture this feature, but other factors may also play a role. These comparisons show that the estimation for bedload transport may be a standardize phenomenon for studying the transport of sediments over the surface. The prediction made by Ashmore (1988) and Wong and Parker (2006b) are found to be optimal on above criterion. The higher values of R2, σ, slope, E and Id of Ashmore (1988) method shows the best predicting approach among all, having Φ values consistently close to the experimental values. Casey Data Analysis : The Analysis of Casey data is shown here. In this data the Soulsby bed load equation predicts well which is shown in Fig. 2 by comparison on actual Ф and computed Ф. In Casey data set the material used for study were having D 50 as 2.5 mm and 1 mm. For Casey data set Fig. 4 shows variation of bed load transport versus shear stress. It can be seen that the transport formulas of MPM, Soulsby and Parker predict the highest bed load transport rate. The formulas of Van Rijn and Ashmore predict medium bed load transport rates and the formulas of Einstein and Wong & Parker predict the lowest bed load transport rate. Also from the score table for the Casey data set the Soulsby bed load equation set the first position. Graf & Suszka Data Analysis : The Analysis of Graf & Suszka data is shown here. In this data the Soulsby anf Wong & Parket bed load equation predicts well which is shown in Fig. 5 and Fig. 6 by comparison on actual Ф and computed Ф. The bed load and dimensionless shear stress appear to be uniquely related for the Graf & Suszka data (Fig. 7 ). In this dataset the materials were used which have d50 as 12.2 mm. For Graf & Suszka data set Fig. 8 shows variation of bed load transport versus shear stress. It can be seen that the transport formulas of MPM, Ashmore and Parker predict the highest bed load transport rate. Also from the ranking table the Parker equation score first for the Graf & Suszka data set. Table 5 Score and Ranking of bed load transport formula for Graf Data Formulae MPM Einstein Soulsby Van Rijn Parker Ashmore Wong & Parker Score 0.334327 0.464037 0.227595 0.012647 0.5645 0.426902 0.408434 Ranking 5 2 6 7 1 3 4 HPY Data Analysis : The Analysis of HPY data is shown here. In this data the no equation is predictind well with comparison on actual Ф and computed Ф. The bed load and dimensionless shear stress appear to be uniquely related for the HoPang-Yung data (Fig. 9 ). The material for this study has selected with d 50 as 3.1 mm, 4.4 mm, 6.3 mm, 2 mm, 6 mm and 3.1 mm. for each d 50 relation has been developed between dimensionless shear stress and bed load qb and seprate predictions has been carried out for all bed load formulas. For HoPang-Yung data set Fig. 10 shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM, Soulsby, Parker and Ashmore predicts the highest bed load transport rate. Also from the score table Parker formula gives maximum score. Table 6 Score and Ranking of bed load transport formula for HPY Data Formulae MPM Einstein Soulsby Van Rijn Parker Ashmore Wong & Parker Score 0.159683 0.160783 0.152751 0.037548 0.200682 0.146404 0.076699 Ranking 3 2 4 7 1 5 6 Mavis Data Analysis : The Analysis of Mavis data is shown here. In this data the Soulsby bed load equation predicts well which is shown in Fig. 11 by comparison on actual Ф and computed Ф. The bed load and dimensionless shear stress appear to be uniquely related for Mavis data(Fig. 12 ). The author uses the material for study with having d 50 as 4.2 mm,3.1 mm. 2 mm, 1.4 mm, 3.7 mm, and 1.7 mm. for each d 50 relation has been developed between dimensionless shear stress and bed load qb and seprate predictions has been carried out for all bed load formulas. For Mavis data set Fig. 13 shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM, Ashmore and Parker predicts the highest bed load transport rate. From the table 7.0 the Einstein equation score maximum among all the formulas. Table 7.0 Score and Ranking of bed load transport formula for Mavis Data Formulae MPM Einstein Soulsby Van Rijn Parker Ashmore Wong & Parker Score 0.252058 0.383353 0.238586 0.184989 0.372242 0.26721 0.160341 Ranking 4 1 5 6 2 3 7 Paintal Data Analysis : The Analysis of Paintal data is shown here. In this data MPM equation predicts fairly well while other equations under predict by comparison on actual Ф and computed Ф. For Paintal data the bed load and dimensionless shear stress appear to be uniquely related. (Fig. 14 ). In Paintal data the different material has been used for the experimental study with having d 50 as 22.2 mm, 8 mm and 2.5 mm. For Paintal data set Fig. 15 shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM, Ashmore, Soulsby and Parker predicts the highest bed load transport rate. The formula of Wong & Parker shows the medium bed load transport rate and the formulas of Einstein and Van Rijn predict the lowest bed load transport rate. From the table 8.0 the Einstein equation score maximum. Table 8.0 Score and Ranking of bed load transport formula for Paintal Data Formulae MPM Einstein Soulsby Van Rijn Parker Ashmore Wong & Parker Score 0.023871 0.252779 0.025835 0.005925 0.153746 0.048607 0.015307 Ranking 5 1 4 7 2 3 6 Meyer-Peter Muller Data Analysis : The Analysis of MPM data is shown here. In this data Einstein,Soulsby, Ashmore and Wong & Parker equations predicts well by comparison on actual Ф and computed Ф. For MPM data the bed load and dimensionless shear stress appear to be uniquely related. (Fig. 20 ). In MPM data the different material has been used for the experimental study with having d 50 as 28.7 mm and 5.2 mm,. For MPM data set Fig. 21 shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM and Parker predicts the highest bed load transport rate. The formulas of Einstein, Soulsby, Ashmore and Wong & Parker and Soulsby show the medium bed load transport rate and the formula of Van Rijn predict the lowest bed load transport rate. From the table 9.0 the MPM equation score maximum. Table 9.0 Score and Ranking of bed load transport formula for MPM Data Formulae MPM Einstein Soulsby Van Rijn Parker Ashmore Wong & Parker Score 0.432788 0.226309 0.235399 0.074356 0.422733 0.365879 0.273715 Ranking 1 6 5 7 2 3 4 Vankar, Yadav and Samtani’s (VYS) Experimental Data Analysis In the second part following experiments were used to compute dimensionless bed load transport parameter: Mixture I (1-2mm) -Diameter of particle is 1.41 mm Mixture II (2-4mm) -Diameter of particle is 2.8284mm Mixture III(4-8mm) -Diameter of particle is 5.6564 mm Analysis for Mixture I : In this data all equations under predict by comparison on actual Ф and computed Ф. The bed load and dimensionless shear stress appear to be uniquely related for the Mixture I. (Fig. 22 ). Table 10.0 shows the score and ranking for Mixture I and the MPM formula have maximum score and first ranking in data set. For d 50 as 1.41 mm diameter Fig. 23 shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM, Einstein, Soulsby, Van Rijn, Ashmore, Parker and Wong & parker predicts the lowest bed load transport rate. Table 10.0 Score and Ranking of bed load transport formula for Mixture I Formulae MPM Van Rijn Einstein Soulsby Parker Ashmore Wong & Parker Score 0.000894204 0.00049 0.0002532 0.00078 0.00064 0.00054 0.00041 Ranking 1 5 7 2 3 4 6 Analysis for the mixture II : In this data MPM and Soulsby equations predicts well by comparison on actual Ф and computed Ф. The bed load and dimensionless shear stress appear to be uniquely related for the Mixture II. (Fig. 26 ). Table 11.0 shows the score and ranking for Mixture I and the MPM formula have maximum score and first ranking in data set. For d 50 as 2.65 mm diameter Fig. 27 shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM and Parker predicts the highest bed load transport rate. The formulas of Soulsby, Ashmore and Wong & Parker show the medium bed load transport rate and the formulas of Einstein and Van Rijn predict the lowest bed load transport rate. Table 11.0 Score and Ranking of bed load transport formula for Mixture II Formulae MPM Van Rijn Einstein Soulsby Parker Ashmore Wong & Parker Score 0.859703 0.278372 0.36126 0.714225 0.839321 0.628631 0.510371 Ranking 1 7 6 3 2 4 5 Analysis for Mixture III : In this data all equations under predict by comparison on actual Ф and computed Ф. The bed load and dimensionless shear stress appear to be uniquely related for the Mixture III. (Fig. 28 ). Table 12.0 shows the score and ranking for Mixture I and the MPM formula have maximum score and first ranking in data set. For d 50 as 5.65 mm diameter Fig. 29 shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM. Parker and Ashmore predict the highest bed load transport rate. The formulas of Einstein, Wong & Parker and Soulsby show the medium bed load transport rate and the formula of Van Rijn predict the lowest bed load transport rate. Table 12.0 Score and Ranking of bed load transport formula for Mixture III Formulae MPM Van Rijn Einstein Soulsby Parker Ashmore Wong & Parker Score 0.390465 0.005945 0.082111 0.104438 0.272161 0.320629 0.144366 Ranking 1 7 6 5 3 2 4 Conclusion Bed load equations give the relationship between hydraulic conditions, the sediment present in the liquid and the sediment transport rate (Gomez and Church 1989). However, there are many factors related to the temporal and spatial resolution and accuracy of the observation in the real flow in the river. The initial aim of this study is to calculate the degree of accuracy of the selected bed load equation by different evaluations. For that the selected sets of the flume experiment have been used for the study also the same experiments were done in the Flume available in SVNIT Surat. Results shows that for the moderate slope condition of flume the equations like Soulsby, Ashmore and Parker predicts well while MPM, Einstein and Wong & Parker fairly predicts and Van Rijn under predicts the accessibility to use. The range of slope used for this data is 0.001 to 0.01 with a uniform discharge of 0.0006 to 0.04 cumecs. It my be conclude that the proposed methods are statistically accurate with the measured bedload transport for the flume. Declarations Hereby, I Jitendra P. Vankar consciously assure that for the manuscript Assessing Predictive Capability of Selected Bed Load Equations Using Experimental and Flume Data the following is fulfilled: 1) This material is the authors' own original work, which has not been previously published elsewhere. 2) The paper is not currently being considered for publication elsewhere. 3) The paper reflects the authors' own research and analysis in a truthful and complete manner. 4) The paper properly credits the meaningful contributions of co-authors and co-researchers. 5) The results are appropriately placed in the context of prior and existing research. 6) All sources used are properly disclosed (correct citation). Literally copying of text must be indicated as such by using quotation marks and giving proper reference. 7) All authors have been personally and actively involved in substantial work leading to the paper, and will take public responsibility for its content. 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Declaration of interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data and material Availability: The Bed load data sets related to this article can be found at https://www.researchgate.net/publication/234106842_An_Experimental_Study_of_Grain_Sorting_Effects_on_Bedload. An open source by Alain Recking, French National Institute for Agriculture, Food, and Environment (INRAE), An Experimental Study of Grain Sorting Effects on Bedload, January 2006. References Benoit Camenen, Magnus Larson, (2005). A general formula for non cohesive bed load sediment transport, Estuarine, Coastal and Shelf Science 63 (2005). Page 249– 260. Brown, C.B., (1950), Sediment Transport in Engineering Hydraulics, Ch. 12, Rouse, H. (ed.), Wiley. 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Duncan and C.O. Chin, (1998), Effect of bed-load movement on flow friction factor, Journal of Hydraulic Engineering, 124, 2, 165-175. Soulsby R. L., (1997) Dynamics of Marine Sands. A Manual for Practical Applications. Thomas Telford, London, UK. Talukdar S., Bimlesh Kumar, Dutta S., (2012), Predictive capability of bed load equations using flume data J. Hydrol. Hydromech. 60, 2012, 1, 45–56. Van der Scheer P. Ribberink J.S.,. Blom A. (2002), Transport Formulas for Graded Sediment, M.Sc. Thesis, Page 34, 56 & 78.\ Van Rijn, L.C., (1984), Sediment transport, Part I: Bed load transport, ASCE J. Hydraulic Engineering, 110, 1431-1456. Wong, Y.-H.,(2006) ,Formula for predicting bed load transport rate in oscillatory sheet flow, Coastal Engineering 54, pages. 594 –601. Yager E.M., Kirchner J.W., and Dietrich W.E., (2007), Calculating bed load transport in steep boulder bed channels, Water Resources Research, Vol. 43. Yang, C.T., and S. Wan, (1991), Comparisons of selected bed material load formulas, Journal of Hydraulic Engineering, 117, 8, pages. 973-989. Yalin, M.S., (1963), An expression for bed load transportation, Proc. ASCE, 89, 221-250. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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28","display":"","copyAsset":false,"role":"figure","size":36144,"visible":true,"origin":"","legend":"\u003cp\u003eVariation of Bed load qb with Dimensionless shear stress τ* for Mixture III\u003c/p\u003e","description":"","filename":"28.png","url":"https://assets-eu.researchsquare.com/files/rs-3714539/v1/05c9edff07cf7d333b1d51ed.png"},{"id":48160573,"identity":"e71d2657-4cd9-4c88-8927-144b953c23aa","added_by":"auto","created_at":"2023-12-13 21:19:34","extension":"png","order_by":29,"title":"Figure 29","display":"","copyAsset":false,"role":"figure","size":14558,"visible":true,"origin":"","legend":"\u003cp\u003eDimensionless shear stress τ* versus Bed load qb with for D 5.65 mm\u003c/p\u003e","description":"","filename":"29.png","url":"https://assets-eu.researchsquare.com/files/rs-3714539/v1/b60b31c0e7cc4bd66d6d7e36.png"},{"id":62351484,"identity":"5b319a2b-0e27-44f1-92d6-920cf0613261","added_by":"auto","created_at":"2024-08-13 08:14:37","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1972308,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3714539/v1/09b2aaac-dec6-4775-b94b-997cb7fe6fd2.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Assessing Predictive Capability of Selected Bed Load Equations Using Experimental and Flume Data","fulltext":[{"header":"I. INTRODUCTION","content":"\u003cp\u003eSediment is a naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of wind, water, or ice, and/or by the force of gravity acting on the particle itself. Sediments are most often transported by water (fluvial processes), wind (Aeolian processes) and glaciers. On an average, rivers worldwide transport around 19000\u0026nbsp;million tones of sediment annually (Knighton \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). The ability to transport sediment depends on the characteristics of the flow, with rivers carrying as much sediment as the energy of the flow permits (Edwards \u0026amp; Glysson \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). By altering the hydrology and sediment regime of a catchment there can be significant impact on the character and behavior of the river and on the fluvial ecosystem (Knighton \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). Individual particles move along the bed of the water course by rolling, sliding or occasionally in jumps (saltation) which is generally termed as bed load (The Subcommittee on Sediment Terminology of the American Geophysical Union.) Bed load transport in alluvial rivers is the principle link between river hydraulics and river form and is responsible for building and maintaining the channel geometry (Parker, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1979\u003c/span\u003e; Leopold, 1994; Goodwin, 2004). Prediction of bed load is of primary importance for river engineering, fluvial geomorphology, eco-hydrology, environmental surveys and management, and hazard prediction (Recking, 2009). Until now, engineering tools have mainly used bed load equations obtained from theoretical or semi-empirical analysis, established for equilibrium conditions (stable state; where the flow energy slope is compatible with the sediment transport rate) and for uniform (or assumed to be uniform) materials. However, all natural sediments are not uniform, and properties established for flows over uniform materials may no longer be valid for flows over graded sediments. Indeed, in addition to the water sediment interaction, interactions between grains of different sizes may also influence the overall flow system\u0026rsquo;s behavior. There have been numerous studies, both in natural channels and in flumes, based on different approaches depending on the conditions under which the equations were developed.\u003c/p\u003e"},{"header":"II. METHODOLOGY","content":"\u003cp\u003eAll runs were performed in the Advanced Hydraulic Laboratory in Sardar Vallabhbhai National Institute of Technology, Surat. With the objective to study the bed load transport, it was very important to ensure the equilibrium condition and use efficient tools to develop the experimental set up.\u003c/p\u003e \u003cp\u003e \u003cb\u003eThe experimental setup\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThe experimental setup is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The flume is 15 m long having 6 m working section, 0.86 m wide (slope varying from 0 to 1%). The flow rate at the upstream was controlled by two pumps, each having capacity of 1500 rpm. Discharge was measured by the flow meter situated on the inlet pipe. Each run was performed at the equilibrium condition, with the liquid and solid discharge maintained constant, over a 7 cm thick gravel bed.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eSediments (Materials)\u003c/b\u003e \u003c/p\u003e \u003cp\u003eThree uniform mixtures of mean diameter of 2.8284 mm (2\u0026ndash;4 mm), 5.6564 mm (4\u0026ndash;8 mm) and 1.41 mm (1\u0026ndash;2 mm) (called Mixture I, II, III respectively) were selected by sieving natural sand gravel mixtures and density was 2600 kg/m\u003csup\u003e3\u003c/sup\u003e for Mixture I, Mixture II and Mixture III respectively. The grain sorting coefficient approximately 1.1 for each mixture shows the uniformity of all three mixtures.\u003c/p\u003e \u003cp\u003e \u003cb\u003eUniform flow set up\u003c/b\u003e \u003c/p\u003e \u003cp\u003eAll the experiments were conducted under uniform flow conditions, where the surface of the water was parallel to the bed and therefore, flow depth was constant along the flume. Uniform flow conditions are important as they permit comparison of measurements of hydraulic and bed characteristics that are often taken at different locations within the flume. In addition, some formulae, including bed shear stress estimation methods, require uniform flow conditions. Uniform flow was established for each flow as follows: for a given bed slope and flow, repeat measurements of depth were taken at 10 locations along the flume at 0.5 m interval, adjusting the tailgate to produce approximate uniform flow (defined when slope of the fitted line to water levels was within \u0026plusmn;\u0026thinsp;2% of the objective slope). Repeating this procedure for the full range of flows produced a relationship between flow, tailgate position and average flow depth. These data were subsequently used to set uniform flow conditions during the experiments and to estimate shear stress for each flow.\u003c/p\u003e \u003cp\u003e \u003cb\u003ePerformance Steps of Experiment\u003c/b\u003e:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003ePlace the material uniformly within the working length (6m) of flume by sediment feeder.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eAdjust initial slope of flume and prime both pumps.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eStart both pumps and adjust the discharge.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eMake the flow uniform by adjusting tail gate at the end of the flume.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eAfter making the uniform flow saturate the mixture for at least 01 hour.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eAfter 01 hour take the wash load in the bed load trap and place uniformly in the upstream of the flume to make the equilibrium condition.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThan start taking reading of Discharge, Slope, velocity, and bed load sample within the specific time limit. In this study the time limit to collect bed load sample was 20min.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThen place the taken mixture in the upstream of the flume with the help of sediment feeder.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eRepeat step 7\u0026ndash;8 until bed load remain constant.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eAfter completing the whole run spread the mixture in the flume to dry it for the next run.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eIn this study slope remains constant for one run and different discharges is taken for each mixture. For the mixture of 1\u0026ndash;2 mm initial slope was taken 0.0008 and extreme slope was 0.003. For the mixture of 2-4mm and the 4\u0026ndash;8 mm initial slope was 0.005 and final slope was 0.008.\u003c/p\u003e \u003cp\u003eDifferent types of bed load equations were used for the comparison of theoretical and experimental measurements. Table No 1 shows the details of different bed load equations used in the present study\u003c/p\u003e \u003cp\u003eFor each run the following parameters were measured:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe flow discharge ,Q (m\u003csup\u003e3\u003c/sup\u003e/s):\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe flume slope, S (m/m):\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe outlet solid discharge (Kg/20min): from weighed samples collected at the outlet of the flume.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe mean flow velocity, U (m/s).\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eMeasurements were taken for equilibrium condition.\u003c/p\u003e \u003cp\u003e \u003cb\u003eBed Load Transport Formulae\u003c/b\u003e \u003c/p\u003e \u003cp\u003eDimensionless Quantities;\u003c/p\u003e \u003cp\u003eФ=\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{qb}{\\sqrt{\\left(s-1\\right)g{d}^{3}}}\\)\u003c/span\u003e\u003c/span\u003e (dimensionless bed load transport)\u003c/p\u003e \u003cp\u003eτ*=\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{\\tau }{P\\left(s-1\\right)gd}\\)\u003c/span\u003e\u003c/span\u003e (dimensionless shear stress or shield stress)\u003c/p\u003e \u003cp\u003ed*=d\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sqrt[3]{\\frac{\\left(s-1\\right)g}{v}}\\)\u003c/span\u003e\u003c/span\u003e (dimensionless particle diameter)\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1.0\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cb\u003eDetails of Bed Load Equations used in the present study\u003c/b\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSr No.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eScientist\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEquation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eApproach\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRemarks\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMeyer-Peter and Muller (1948)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eФ =8(τ*-τ*\u003csub\u003ecrit\u003c/sub\u003e)\u003csup\u003e3/2\u003c/sup\u003e if τ*\u0026ge; τ*\u003csub\u003ecrit\u003c/sub\u003e\u003c/p\u003e \u003cp\u003eФ =0 if τ* \u0026lt; τ*\u003csub\u003ecrit\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEnergy Slope\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eOriginal Paper assume τ*\u003csub\u003ecrit\u003c/sub\u003e=0.047\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEinstein (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1950\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eФ = Kexp(\u0026minus;\u0026thinsp;0.391 / τ*)/0.465 if τ*\u0026lt;0.182\u003c/p\u003e \u003cp\u003eФ =40Kθ\u003csup\u003e3\u003c/sup\u003e if τ*\u0026ge;0.182\u003c/p\u003e \u003cp\u003eWhere K=\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sqrt{\\frac{2}{3}+\\frac{36}{{d*}^{3}}}-\\sqrt{\\frac{36}{{d*}^{3}}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eProbabilistic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSoulsby (1997)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eФ = 5.1(τ*-τ*\u003csub\u003ecrit\u003c/sub\u003e\u003csup\u003e3/2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eShear stress\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eVan Rijn(1984)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eФ = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{0.053}{{d*}^{0.3}}\\)\u003c/span\u003e\u003c/span\u003e[(τ*/τ*\u003csub\u003ecrit\u003c/sub\u003e)-1]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRegression\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParker (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1979\u003c/span\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eФ = 11.20\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\frac{{(\\tau *-0.03)}^{4.5}}{{\\tau *}^{3}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eProbabilistic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAshmore (1988)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eФ = 3.11(τ*-0.045)\u003csup\u003e1.37\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eShear stress\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWong \u0026amp; Parker (2006)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eФ = 3.97(τ*-0.0495)\u003csup\u003e1.5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eShear stress\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"III. DATA COLLECTION","content":"\u003cp\u003eIn this study data were collected in two parts. First part contains the data which is collected from the historical experimental data of several researchers. The second part contains the experimental data which has been collected from the hydraulic tilting flume situated in the Advanced Hydraulics Laboratory in the Sardar Vallabhbhai National Institute of Technology, Surat.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eHistorical Data\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn this part various experimental flume data set has been collected. In this study collected data were which range in the moderate slope range. (Slopes varying from 0 to 1%) The data used in this study include, Casey (1935), Graf\u0026amp; Suzska (1987), HoPang-Yung (1939), Mavis (1937), Paintal (1971) and MPM (1948). The brief details of data set are given in Table \u003cspan class=\"InternalRef\"\u003e2.0\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eExperimental Data\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe second part contains the experimental data which were collected in hydraulic tilting flume situated at Advanced Hydraulics Laboratory, Civil Engineering Department, Sardar Vallbhbhai National Institute of Technology, Surat. The detail of mixture used in present study is detailed as Table \u003cspan class=\"InternalRef\"\u003e3.0\u003c/span\u003e\u0026nbsp;\u003c/p\u003e\n\u003ctable id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2.0\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eHistorical Flume Experimental Data\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAuthor\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eYear\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDiameter\u003c/p\u003e\n \u003cp\u003eD (mm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eStandard deviation\u0026sigma;\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSediment Density\u003c/p\u003e\n \u003cp\u003e\u0026rho;s (Kg/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSlope\u003c/p\u003e\n \u003cp\u003eS(m/m)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWidth of flume\u003c/p\u003e\n \u003cp\u003eW(m)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eCasey\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" rowspan=\"2\"\u003e\n \u003cp\u003e1935\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.5 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2650\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00119\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.00509\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2810\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.0012\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.00519\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eGraf \u0026amp; Suszka\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1987\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12.2 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2716\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.005\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.015\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eHo Pang-Yung\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003e1939\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.1 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2490\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00105\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.00336\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.339\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.4 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2700\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00127\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.00336\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.339\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.3 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.49\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2660\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00169\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.00504\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.339\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2450\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00101\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.00168\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.339\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2660\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00333\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.00501\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.339\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.4 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2640\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00099\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.00102\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.339\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003eMavis\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"6\"\u003e\n \u003cp\u003e1937\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.2 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2660\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00175\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.819\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.1 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2660\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.0017\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.00955\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.819\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2660\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00155\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.0101\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.819\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.4 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2660\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00135\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.819\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.7 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2660\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.0018\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.819\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.7 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2660\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00165\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.819\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003ePaintal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"3\"\u003e\n \u003cp\u003e1971\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e22.2 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.07\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2650\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.0079\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.0103\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.914\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2650\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00226\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.0052\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.914\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.5 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2650\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00117\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.00213\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.914\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"2\"\u003e\n \u003cp\u003eMPM\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" rowspan=\"2\"\u003e\n \u003cp\u003e1948\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e28.7 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2680\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00317\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.01767\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.999\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.2 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2680\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00128\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.0226\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.999\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 3.0\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eFlume Experimental Data\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eNo\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMixture\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSize Range\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDiameter\u003c/p\u003e\n \u003cp\u003eD(mm)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSlope\u003c/p\u003e\n \u003cp\u003eS (m/m)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWidth of flume\u003c/p\u003e\n \u003cp\u003eW(m)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eI\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u0026ndash;2 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e1.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.0008\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.003\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.86\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u0026ndash;4 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e2.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.005\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.008\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.86\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eIII\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u0026ndash;8 mm\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e5.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.005\u0026thinsp;\u0026lt;\u0026thinsp;S\u0026thinsp;\u0026lt;\u0026thinsp;0.008\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\"\u003e\n \u003cp\u003e0.86\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cstrong\u003eAnalysis of Data\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFig. shows the best comparison curves (\u0026Phi;obs versus \u0026Phi;cal) proposed by respective investigators with data reported in the various studies for sediment bedload transport at moderate condition. The figure shows considerable compatibility with the observed \u0026Phi;. The experimental data shows a marginally scatter and could be explained as a set rather than well defined curves. The discrepancy is primarily due to particle shape, random nature of the entrainment process, and the difficulty with defining criteria that adequately capture this feature, but other factors may also play a role. These comparisons show that the estimation for bedload transport may be a standardize phenomenon for studying the transport of sediments over the surface. The prediction made by Ashmore (1988) and Wong and Parker (2006b) are found to be optimal on above criterion. The higher values of R2, \u0026sigma;, slope, E and Id of Ashmore (1988) method shows the best predicting approach among all, having \u0026Phi; values consistently close to the experimental values.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCasey Data Analysis\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eThe Analysis of Casey data is shown here. In this data the Soulsby bed load equation predicts well which is shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e by comparison on actual \u003cstrong\u003eФ\u003c/strong\u003e and computed \u003cstrong\u003eФ.\u003c/strong\u003e In Casey data set the material used for study were having D\u003csub\u003e50\u003c/sub\u003e as 2.5 mm and 1 mm. For Casey data set Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e shows variation of bed load transport versus shear stress. It can be seen that the transport formulas of MPM, Soulsby and Parker predict the highest bed load transport rate. The formulas of Van Rijn and Ashmore predict medium bed load transport rates and the formulas of Einstein and Wong \u0026amp; Parker predict the lowest bed load transport rate. Also from the score table for the Casey data set the Soulsby bed load equation set the first position.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eGraf \u0026amp; Suszka Data Analysis\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eThe Analysis of Graf \u0026amp; Suszka data is shown here. In this data the Soulsby anf Wong \u0026amp; Parket bed load equation predicts well which is shown in Fig. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e and Fig. \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e by comparison on actual \u003cstrong\u003eФ\u003c/strong\u003e and computed \u003cstrong\u003eФ.\u003c/strong\u003e The bed load and dimensionless shear stress appear to be uniquely related for the Graf \u0026amp; Suszka data (Fig. \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e). In this dataset the materials were used which have d50 as 12.2 mm. For Graf \u0026amp; Suszka data set Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e shows variation of bed load transport versus shear stress. It can be seen that the transport formulas of MPM, Ashmore and Parker predict the highest bed load transport rate. Also from the ranking table the Parker equation score first for the Graf \u0026amp; Suszka data set.\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;5 Score and Ranking of bed load transport formula for Graf Data\u003c/p\u003e\n\u003ctable id=\"Tabd\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFormulae\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMPM\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEinstein\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSoulsby\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVan Rijn\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParker\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAshmore\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWong \u0026amp; Parker\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eScore\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.334327\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.464037\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.227595\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.012647\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.5645\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.426902\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.408434\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRanking\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eHPY Data Analysis\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eThe Analysis of HPY data is shown here. In this data the no equation is predictind well with comparison on actual \u003cstrong\u003eФ\u003c/strong\u003e and computed \u003cstrong\u003eФ.\u003c/strong\u003e The bed load and dimensionless shear stress appear to be uniquely related for the HoPang-Yung data (Fig. \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e). The material for this study has selected with d\u003csub\u003e50\u003c/sub\u003e as 3.1 mm, 4.4 mm, 6.3 mm, 2 mm, 6 mm and 3.1 mm. for each d\u003csub\u003e50\u003c/sub\u003e relation has been developed between dimensionless shear stress and bed load qb and seprate predictions has been carried out for all bed load formulas. For HoPang-Yung data set Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM, Soulsby, Parker and Ashmore predicts the highest bed load transport rate. Also from the score table Parker formula gives maximum score.\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;6 Score and Ranking of bed load transport formula for HPY Data\u003c/p\u003e\n\u003ctable id=\"Tabf\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFormulae\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMPM\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEinstein\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSoulsby\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVan Rijn\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParker\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAshmore\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWong \u0026amp; Parker\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eScore\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.159683\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.160783\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.152751\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.037548\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.200682\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.146404\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.076699\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRanking\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eMavis Data Analysis\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eThe Analysis of Mavis data is shown here. In this data the Soulsby bed load equation predicts well which is shown in Fig. \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e by comparison on actual \u003cstrong\u003eФ\u003c/strong\u003e and computed \u003cstrong\u003eФ.\u003c/strong\u003e The bed load and dimensionless shear stress appear to be uniquely related for Mavis data(Fig. \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e). The author uses the material for study with having d\u003csub\u003e50\u003c/sub\u003e as 4.2 mm,3.1 mm. 2 mm, 1.4 mm, 3.7 mm, and 1.7 mm. for each d\u003csub\u003e50\u003c/sub\u003e relation has been developed between dimensionless shear stress and bed load qb and seprate predictions has been carried out for all bed load formulas. For Mavis data set Fig. \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM, Ashmore and Parker predicts the highest bed load transport rate. From the table 7.0 the Einstein equation score maximum among all the formulas.\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;7.0 Score and Ranking of bed load transport formula for Mavis Data\u003c/p\u003e\n\u003ctable id=\"Tabh\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFormulae\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMPM\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEinstein\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSoulsby\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVan Rijn\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParker\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAshmore\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWong \u0026amp; Parker\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eScore\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.252058\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.383353\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.238586\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.184989\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.372242\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.26721\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.160341\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRanking\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003ePaintal Data Analysis\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eThe Analysis of Paintal data is shown here. In this data MPM equation predicts fairly well while other equations under predict by comparison on actual \u003cstrong\u003eФ\u003c/strong\u003e and computed \u003cstrong\u003eФ.\u003c/strong\u003e For Paintal data the bed load and dimensionless shear stress appear to be uniquely related. (Fig. \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e). In Paintal data the different material has been used for the experimental study with having d\u003csub\u003e50\u003c/sub\u003e as 22.2 mm, 8 mm and 2.5 mm. For Paintal data set Fig. \u003cspan class=\"InternalRef\"\u003e15\u003c/span\u003e shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM, Ashmore, Soulsby and Parker predicts the highest bed load transport rate. The formula of Wong \u0026amp; Parker shows the medium bed load transport rate and the formulas of Einstein and Van Rijn predict the lowest bed load transport rate. From the table 8.0 the Einstein equation score maximum.\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;8.0 Score and Ranking of bed load transport formula for Paintal Data\u003c/p\u003e\n\u003ctable id=\"Tabj\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFormulae\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMPM\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEinstein\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSoulsby\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVan Rijn\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParker\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAshmore\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWong \u0026amp; Parker\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eScore\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.023871\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.252779\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.025835\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.005925\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.153746\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.048607\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.015307\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRanking\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eMeyer-Peter Muller Data Analysis\u003c/strong\u003e:\u003c/p\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eThe Analysis of MPM data is shown here. In this data Einstein,Soulsby, Ashmore and Wong \u0026amp; Parker equations predicts well by comparison on actual \u003cstrong\u003eФ\u003c/strong\u003e and computed \u003cstrong\u003eФ.\u003c/strong\u003e For MPM data the bed load and dimensionless shear stress appear to be uniquely related. (Fig. \u003cspan class=\"InternalRef\"\u003e20\u003c/span\u003e). In MPM data the different material has been used for the experimental study with having d\u003csub\u003e50\u003c/sub\u003e as 28.7 mm and 5.2 mm,. For MPM data set Fig. \u003cspan class=\"InternalRef\"\u003e21\u003c/span\u003e shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM and Parker predicts the highest bed load transport rate. The formulas of Einstein, Soulsby, Ashmore and Wong \u0026amp; Parker and Soulsby show the medium bed load transport rate and the formula of Van Rijn predict the lowest bed load transport rate. From the table 9.0 the MPM equation score maximum.\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003eTable\u0026nbsp;9.0 Score and Ranking of bed load transport formula for MPM Data\u003c/p\u003e\n\u003ctable id=\"Tabl\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFormulae\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMPM\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEinstein\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSoulsby\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVan Rijn\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParker\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAshmore\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWong \u0026amp; Parker\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eScore\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.432788\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.226309\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.235399\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.074356\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.422733\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.365879\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.273715\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRanking\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eVankar, Yadav and Samtani\u0026rsquo;s (VYS) Experimental Data Analysis\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn the second part following experiments were used to compute dimensionless bed load transport parameter:\u003c/p\u003e\n\u003col class=\"decimal_type\" style=\"list-style-type: lower-roman;\"\u003e\n \u003cli\u003eMixture I (1-2mm) \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;-Diameter of particle is 1.41 mm\u003c/li\u003e\n \u003cli\u003eMixture II (2-4mm)\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;-Diameter of particle is 2.8284mm\u003c/li\u003e\n \u003cli\u003eMixture III(4-8mm) \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;-Diameter of particle is 5.6564 mm\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003e\u003cstrong\u003eAnalysis for Mixture I\u003c/strong\u003e :\u003c/p\u003e\n\u003cp\u003eIn this data all equations under predict by comparison on actual \u003cstrong\u003eФ\u003c/strong\u003e and computed \u003cstrong\u003eФ.\u003c/strong\u003e The bed load and dimensionless shear stress appear to be uniquely related for the Mixture I. (Fig. \u003cspan class=\"InternalRef\"\u003e22\u003c/span\u003e). Table\u0026nbsp;10.0 shows the score and ranking for Mixture I and the MPM formula have maximum score and first ranking in data set. For d\u003csub\u003e50\u003c/sub\u003e as 1.41 mm diameter Fig. \u003cspan class=\"InternalRef\"\u003e23\u003c/span\u003e shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM, Einstein, Soulsby, Van Rijn, Ashmore, Parker and Wong \u0026amp; parker predicts the lowest bed load transport rate.\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;10.0 Score and Ranking of bed load transport formula for Mixture I\u003c/p\u003e\n\u003ctable id=\"Tabn\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFormulae\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMPM\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVan Rijn\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEinstein\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSoulsby\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParker\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAshmore\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWong \u0026amp; Parker\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eScore\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.000894204\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00049\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.0002532\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00078\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00064\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00054\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.00041\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRanking\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eAnalysis for the mixture II\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eIn this data MPM and Soulsby equations predicts well by comparison on actual \u003cstrong\u003eФ\u003c/strong\u003e and computed \u003cstrong\u003eФ.\u003c/strong\u003e The bed load and dimensionless shear stress appear to be uniquely related for the Mixture II. (Fig. \u003cspan class=\"InternalRef\"\u003e26\u003c/span\u003e). Table\u0026nbsp;11.0 shows the score and ranking for Mixture I and the MPM formula have maximum score and first ranking in data set. For d\u003csub\u003e50\u003c/sub\u003e as 2.65 mm diameter Fig. \u003cspan class=\"InternalRef\"\u003e27\u003c/span\u003e shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM and Parker predicts the highest bed load transport rate. The formulas of Soulsby, Ashmore and Wong \u0026amp; Parker show the medium bed load transport rate and the formulas of Einstein and Van Rijn predict the lowest bed load transport rate.\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;11.0 Score and Ranking of bed load transport formula for Mixture II\u003c/p\u003e\n\u003ctable id=\"Tabp\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFormulae\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMPM\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVan Rijn\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEinstein\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSoulsby\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParker\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAshmore\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWong \u0026amp; Parker\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eScore\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.859703\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.278372\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.36126\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.714225\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.839321\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.628631\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.510371\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRanking\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eAnalysis for Mixture III\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eIn this data all equations under predict by comparison on actual \u003cstrong\u003eФ\u003c/strong\u003e and computed \u003cstrong\u003eФ.\u003c/strong\u003e The bed load and dimensionless shear stress appear to be uniquely related for the Mixture III. (Fig. \u003cspan class=\"InternalRef\"\u003e28\u003c/span\u003e). Table\u0026nbsp;12.0 shows the score and ranking for Mixture I and the MPM formula have maximum score and first ranking in data set. For d\u003csub\u003e50\u003c/sub\u003e as 5.65 mm diameter Fig. \u003cspan class=\"InternalRef\"\u003e29\u003c/span\u003e shows variation of bed load transport versus shear stress. It can be seen that for the transport formulas of MPM. Parker and Ashmore predict the highest bed load transport rate. The formulas of Einstein, Wong \u0026amp; Parker and Soulsby show the medium bed load transport rate and the formula of Van Rijn predict the lowest bed load transport rate.\u003c/p\u003e\n\u003cp\u003eTable\u0026nbsp;12.0 Score and Ranking of bed load transport formula for Mixture III\u003c/p\u003e\n\u003ctable id=\"Tabr\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFormulae\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eMPM\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eVan Rijn\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eEinstein\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eSoulsby\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eParker\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eAshmore\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eWong \u0026amp; Parker\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eScore\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.390465\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.005945\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.082111\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.104438\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.272161\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.320629\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0.144366\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRanking\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e"},{"header":"Conclusion","content":"\u003cp\u003eBed load equations give the relationship between hydraulic conditions, the sediment present in the liquid and the sediment transport rate (Gomez and Church 1989). However, there are many factors related to the temporal and spatial resolution and accuracy of the observation in the real flow in the river. The initial aim of this study is to calculate the degree of accuracy of the selected bed load equation by different evaluations. For that the selected sets of the flume experiment have been used for the study also the same experiments were done in the Flume available in SVNIT Surat. Results shows that for the moderate slope condition of flume the equations like Soulsby, Ashmore and Parker predicts well while MPM, Einstein and Wong \u0026amp; Parker fairly predicts and Van Rijn under predicts the accessibility to use. The range of slope used for this data is 0.001 to 0.01 with a uniform discharge of 0.0006 to 0.04 cumecs. It my be conclude that the proposed methods are statistically accurate with the measured bedload transport for the flume.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eHereby, I Jitendra P. Vankar consciously assure that for the manuscript Assessing Predictive Capability of Selected Bed Load Equations Using Experimental and Flume Data the following is fulfilled:\u003c/p\u003e\n\u003cp\u003e1) This material is the authors\u0026apos; own original work, which has not been previously published elsewhere.\u003c/p\u003e\n\u003cp\u003e2) The paper is not currently being considered for publication elsewhere.\u003c/p\u003e\n\u003cp\u003e3) The paper reflects the authors\u0026apos; own research and analysis in a truthful and complete manner.\u003c/p\u003e\n\u003cp\u003e4) The paper properly credits the meaningful contributions of co-authors and co-researchers.\u003c/p\u003e\n\u003cp\u003e5) The results are appropriately placed in the context of prior and existing research.\u003c/p\u003e\n\u003cp\u003e6) All sources used are properly disclosed (correct citation). Literally copying of text must be indicated as such by using quotation marks and giving proper reference.\u003c/p\u003e\n\u003cp\u003e7) All authors have been personally and actively involved in substantial work leading to the paper, and will take public responsibility for its content.\u003c/p\u003e\n\u003cp\u003eThe violation of the Ethical Statement rules may result in severe consequences.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePatient\u0026rsquo;s Consent to Publication\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTitle of product: \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;Assessing Predictive Capability of Selected Bed Load Equations Using Experimental and Flume Data\u003c/p\u003e\n\u003cp\u003eAuthor/Developer: \u0026nbsp; \u0026nbsp; \u0026nbsp;Jitendra p. Vankar\u003c/p\u003e\n\u003cp\u003eThis is to state that I give my full permission for the publication, reproduction, broadcast and other use of photographs, recordings and other audio-visual material of myself (including of\u0026nbsp;my face) and textual material (case histories) in all editions of the above-named product and in any other publication (including books, journals, CD-ROMs, online and internet), as well as in any advertising or promotional material for such product or publications.\u003c/p\u003e\n\u003cp\u003eI declare, in consequence of granting this permission, that I have no claim on ground of breach of confidence or any other ground in any legal system against \u0026mdash; Jitendra P. Vankar \u0026mdash; and its agents, publishers, successors and assigns in respect of such use of the photograph(s) and textual material\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eI hereby agree to release and discharge (Jitendra P. Vankar) and any editors or other contributors and their agents, publishers, successors and assigns from any and all claims, demands or causes of action that I may now have or may hereafter have for libel, defamation, invasion of privacy, copyright or moral rights or violation of any other rights arising out of or relating to any use of my image or case\u0026nbsp;history.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contribution:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eJitendra P. Vankar\u003c/strong\u003e: Methodology, Validation, Investigation, Formal Analysis, Writing-Original Draft, Visualization, Data Curation.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDr. Sanjay M. Yadav:\u003c/strong\u003e Conceptualization, Resources, Supervision, Project administration.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding Information:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo funding was received for this work.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of interests:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData and material Availability:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe Bed load data sets related to this article can be found at https://www.researchgate.net/publication/234106842_An_Experimental_Study_of_Grain_Sorting_Effects_on_Bedload. An open source by Alain Recking, French National Institute for Agriculture, Food, and Environment (INRAE), An Experimental Study of Grain Sorting Effects on Bedload, January 2006.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBenoit Camenen, Magnus Larson, (2005). A general formula for non cohesive bed load sediment transport, Estuarine, Coastal and Shelf Science 63 (2005). Page 249\u0026ndash; 260.\u003c/li\u003e\n\u003cli\u003eBrown, C.B., (1950), Sediment Transport in Engineering Hydraulics, Ch. 12, Rouse, H. (ed.), Wiley.\u003c/li\u003e\n\u003cli\u003eBogen Jim, Moen Knut, (2003), Bed load measurements with a new passive acoustic sensor, IAHS Publ. 283\u003c/li\u003e\n\u003cli\u003eChegini A.H.N., Pender, G.,(2012), Determination of small size bed load sediment transport and its related bed form under different uniform flow conditions, Wseas transactions on environment and development, Issue 4, Volume 8.\u003c/li\u003e\n\u003cli\u003eColby B.R. (1963), Fluvial sediments a summary of source, transportation, deposition, and measurement of sediment discharge, United States Geological Survey Bulletin 1181-A.\u003c/li\u003e\n\u003cli\u003eDietrich W.E., Kirchner J.W., Ikeda H., and Iseya F., (1987), The origin of coarse surface layer in gravel bedded streams: the role of sediment supply, Geological Society of America Bulletin, 19, 642.\u003c/li\u003e\n\u003cli\u003eEdwards, T.K., and Glysson, G.D., 1999, Field Methods for Measurement of Fluvial Sediment: U.S. Geological Survey Techniques of Water-Resources Investigations, Book 3, Chapter C2, 89 p\u003c/li\u003e\n\u003cli\u003eEINSTEIN H. A., (1942) Formulas for the transportation of bed load Transport, American Society of Civil Engineers., 107\u003c/li\u003e\n\u003cli\u003eEinstein, H.A., (1950), The Bed load function for sediment transportation in open channel flows. United State Department of Agriculture \u0026ndash; Soil Conservation Service, Washington pp71.\u003c/li\u003e\n\u003cli\u003eEinstein, H.A., and N.L. Barbarossa, (1951), River Channel Roughness, American Society of Civil Engineers, Paper N2528, 1121-1146.\u003c/li\u003e\n\u003cli\u003eEngelund F. and Hansen E. (1967), A Monograph on sediment Transport in Alluvial streams, Technical University of Denmark, Hydraulic Laboratory. Pg. 634\u003c/li\u003e\n\u003cli\u003eFernandez R. Luque, Van Beek R., (2010), Erosion and Transport of Bed Load Sediment, Journal of Hydraulic Research, 14:2, 127-144.\u003c/li\u003e\n\u003cli\u003eGomez, B., Richard L.N, and Hubbell D.W, (1989), Temporal variations in bed load transport rates associates with the migration of bed forms , Earth Surface processes and Landforms, Vol. 14, 135-156.\u003c/li\u003e\n\u003cli\u003eGraeme M. Smart., (1982), Sediment transport formula for steep channels, Journal of Hydraulic Engineering, Vol. 110, No.3.\u003c/li\u003e\n\u003cli\u003eHuang Jinchi,(1992), Application of sand wave measurements in calculating bed load discharge, IAHS Publ. no. 210.\u003c/li\u003e\n\u003cli\u003eJaber H. Almedeij and Panayiotis Diplas, (2003), Bed load Transport in Gravel-Bed Streams with Unimodal Sediment, Journal of Hydraulic Engineering, Vol. 129, No. 11\u003c/li\u003e\n\u003cli\u003eJackson, W.L., and R.L. Beschta, (1984), Influence of increased sand delivery on the morphology of sand and gravel channels, Water Resource. Bull., 20, 4, 527-533.\u003c/li\u003e\n\u003cli\u003eJau-Yau Lu, Chih-Chiang Su and I-Yu Wu, (2004), Transport of Gravels with Different Ranges of Grain Sizes in a Steep Channel, Journal of Hydraulic Engineering, ASCE.\u003c/li\u003e\n\u003cli\u003eJeffrey J. Barry, John M. Buffington and John G. King, (2004), A general power equation for predicting bed load transport rates in gravel bed rivers, Water Resources Research, Vol. 40.\u003c/li\u003e\n\u003cli\u003eKazemi Younes, Salajegheh Ali, Mahdavi Mohammad and Rostami Noredin,(2011), Estimating the bed load to suspended load ratio in central Alborz rivers; Iran (case study: Taleghan and Jajroud rivers), International Journal of Agriculture Research and Review. Vol., 1 (1), 44-47.\u003c/li\u003e\n\u003cli\u003eKnighton D. (1998), Fluvial Forms and Processes, Arnold, London, 383 pg.\u003c/li\u003e\n\u003cli\u003eKuhnle, R.A., (1996), unsteady transport of sand and gravel mixtures. Pages 183-201 in P.C.A.M. Dawson, editor. Advances in fluvial dynamics and Stratigraphy (Chap 5). John Wiley \u0026amp; Sons Ltd.\u003c/li\u003e\n\u003cli\u003eLeo C. Van Rijn, (1982), Sediment transport, Part I: Bed load transport, Journal of Hydraulic Engineering, Vol. 110, No. 10, Paper No. 19220.\u003c/li\u003e\n\u003cli\u003eLeopold, L.B., M.G. 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ASCE, 89, 221-250.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Bed Load transport","lastPublishedDoi":"10.21203/rs.3.rs-3714539/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3714539/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBed load transport in alluvial rivers is the principle link between river hydraulics and river form and is responsible for building and maintaining the channel geometry. Bed load prediction is of primary importance for river engineering, fluvial geomorphology, ecohydrology, environmental surveys \u0026amp; management and hazard prediction. In this study, for bed load transport analysis data sets and experimental data were used. The data sets of Casey, Graf \u0026amp; Suszka, HPY, Mavis, Paintal and MPM were used to compute bed load transport. Experimental work was carried out in advanced hydraulic laboratory in Civil Engineering Department. The bed load was measured for three mixtures. The measured bed load was compared with computed bed load using MPM, Einstein, Soulsby, Van Rijn, Parker, Ashmore and Wong \u0026amp; Parker approaches. The analysis of measured and computed bed load is in good agreement for MPM, Ashmore \u0026amp; Soulsby. At the same time for MPM data set the measured and predicted bed load is in good agreement. For all data sets and experimentally measured bed load Van Rijn approach under predicts the bed load.\u003c/p\u003e","manuscriptTitle":"Assessing Predictive Capability of Selected Bed Load Equations Using Experimental and Flume Data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-12-13 21:19:28","doi":"10.21203/rs.3.rs-3714539/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ed32bdd1-0d36-4687-a12e-de47c4cc90d2","owner":[],"postedDate":"December 13th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-08-13T08:06:27+00:00","versionOfRecord":[],"versionCreatedAt":"2023-12-13 21:19:28","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3714539","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3714539","identity":"rs-3714539","version":["v1"]},"buildId":"FbvkV6FR0MCFSLy54lSbu","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}