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1.
Modelling soil erosion requires an equation for predicting the sediment transport capacity by interrill overland flow on rough surfaces. The conventional practice of partitioning total shear stress into grain and form shear stress and predicting transport capacity using grain shear stress lacks rigour and is prone to underestimation. This study therefore explores the possibility that inasmuch as surface roughness affects flow hydraulic variables which, in turn, determine transport capacity, there may be one or more hydraulic variables which capture the effect of surface roughness on transport capacity suffciently well for good predictions of transport capacity to be achieved from data on these variables alone. To investigate this possibility, regression analyses were performed on data from 1506 flume experiments in which discharge, slope, water temperature, rainfall intensity, and roughness size, shape and concentration were varied. The analyses reveal that 89·8 per cent of the variance in transport capacity can be accounted for by excess flow power and flow depth. Including roughness size and concentration in the regression improves that explained variance by only 3·5 per cent. Evidently, flow depth, when used in combination with excess flow power, largely captures the effect of surface roughness on transport capacity. This finding promises to simplify greatly the task of developing a general sediment equation for interrill overland flow on rough surfaces. Copyright © 1998 John Wiley & Sons, Ltd.  相似文献   

2.
The hydraulics of overland flow on rough granular surfaces can be modelled and evaluated using the inundation ratio rather than the flow Reynolds number, as the primary dimensionless group determining the flow behaviour. The inundation ratio describes the average degree of submergence of the surface roughness and is used to distinguish three flow regimes representing partially inundated, marginally inundated and well-inundated surfaces. A heuristic physical model for the flow hydraulics in each regime demonstrates that the three states of flow are characterized by very different functional dependencies of frictional resistance on the scaled depth of flow. At partial inundation, flow resistance is associated with the drag force derived from individual roughness and therefore increases with depth and percentage cover. At marginal inundation, the size of the roughness elements relative to the depth of flow controls the degree of vertical mixing in the flow so that frictional resistance tends to decrease very rapidly with increasing depth of flow. Well-inundated flows are described using rough turbulent flow hydraulics previously developed for open channel flows. These flows exhibit a much more gradual decrease in frictional resistance with increasing depth than that observed during marginal inundation. A data set compiled from previously published studies of overland flow hydraulics is used to assess the functional dependence of frictional resistance on inundation ratio over a wide range of flow conditions. The data confirm the non-monotonic dependence predicted by the model and support the differentiation of three flow regimes based on the inundation ratio. Although the percentage cover and the surface slope may be of importance in addition to the inundation ratio in the partially and marginally inundated regimes, the Reynolds number appears to be of significance only in describing well-inundated flows at low to moderate Reynolds numbers. As these latter conditions are quite rare in natural environments, the inundation ratio rather than the Reynolds number should be used as the primary dimensionless group when evaluating the hydraulics of overland flow on rough surfaces. © 1997 by John Wiley & Sons, Ltd.  相似文献   

3.
Conventional roughness–resistance relationships developed for pipe and open‐channel flows cannot accurately describe shallow overland flows over natural rough surfaces. This paper develops a new field methodology combining terrestrial laser scanning (TLS) and overland flow simulation to provide a high‐resolution dataset of surface roughness and overland flow hydraulics as simulated on natural bare soil surfaces. This method permits a close examination of the factors controlling flow velocity and a re‐evaluation of the relationship between surface roughness and flow resistance. The aggregate effect of flow dynamics, infiltration and depression storage on retarding the passage of water over a surface is important where runoff‐generating areas are distant from well‐defined channels. Experiments to separate these effects show that this ‘effective resistance’ is dominated by surface roughness. Eight measurements of surface roughness are found to be related to flow resistance: standard deviation of elevations, inundation ratio, pit density (measured both perpendicular and parallel to the flow direction), slope, median depth, skewness of the depth distribution and frontal area. Hillslope position is found to affect the significant roughness measures. In contrast, infiltration rate has little effect on the velocity of water fronts advancing over the soil surfaces examined here and the effect of depression storage is limited. Overland flow resistance is depth dependent where complex microtopographic structures are progressively inundated. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

4.
The Manning equation is one of the most widely used formulae for calculating the velocity of shallow overland flow in hydrological and erosion models. Precise estimation of the Manning's friction coefficient (n) is critical to determining overland flow and soil erosion processes. Few studies have been conducted to quantify the effects of sediment load on Manning's n on steep slopes. This study was conducted to investigate the potential effects of sediment load on Manning's n in a flume with a fixed bed, under wide ranges of hydraulics and sediment loads. Slope gradient varied from 8·7 to 34·2%, unit flow rate from 0·66 to 5·26 × 10?3 m2 s?1, and sediment load from 0 to 6·95 kg m?1 s?1. The Reynolds number ranged from 350 to 5899. Results showed that Manning's n varied in both sediment‐free and sediment‐laden flows ranging from 0·012 to 0·055. The apparent Manning's coefficients of sediment‐laden flow were much greater than those of sediment‐free flow. The mean Manning coefficient of sediment‐laden flow was 51·27% greater than the mean value of sediment‐free flow. For sediment‐laden flow, Manning's n could be estimated with a power function of unit flow discharge and sediment content. Further studies are needed to quantify the potential effects of sediment load on the Manning's n on erodible beds and in fields. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

5.
Effects of sediment load on hydraulics of overland flow on steep slopes   总被引：6，自引：0，他引：6  
Eroded sediment may have significant effects on the hydraulics of overland flow, but few studies have been performed to quantify these effects on steep slopes. This study investigated the potential effects of sediment load on Reynolds number, Froude number, flow depth, mean velocity, Darcy–Weisbach friction coefficient, shear stress, stream power, and unit stream power of overland flow in a sand‐glued hydraulic flume under a wide range of hydraulic conditions and sediment loads. Slope gradients were varied from 8·7 to 34·2%, unit flow rates from 0·66 to 5·26×10?3 m2 s?1, and sediment loads from 0 to 6·95 kg m?1 s?1. Both Reynolds number (Re) and Froude number (Fr) decreased as sediment load increased, implying a decrease in flow turbulence. This inverse relationship should be considered in modeling soil erosion processes. Flow depth increased as sediment load increased with a mean value of 1·227 mm, caused by an increase in volume of sediment‐laden flow (contribution 62·4%) and a decrease in mean flow velocity (contribution 37·6%). The mean flow velocity decreased by up to 0·071 m s?1 as sediment load increased. The Darcy–Weisbach friction coefficient (f) increased with sediment load, showing that the total energy consumption increased with sediment load. The effects of sediment load on f depended on flow discharge: as flow discharge increased, the influence of sediment load on f decreased due to increased flow depth and reduced relative roughness. Flow shear stress and stream power increased with sediment load, on average, by 80·5% and 60·2%, respectively; however, unit stream power decreased by an average of 11·1% as sediment load increased. Further studies are needed to extend and apply the insights obtained under these controlled conditions to real‐world overland flow conditions. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

6.
Depth profiles of particle streamwise velocity, concentration and bedload sediment transport rate were measured in a turbulent and supercritical water flow. One‐size 6 mm diameter spherical glass beads were transported at equilibrium in a two‐dimensional 10% steep channel with a mobile bed. Flows were filmed from the side by a high‐speed camera. Particle tracking algorithms made it possible to determine the position, velocity and trajectory of a very large number of particles. Approximately half of the sediment transport rate was composed by rolling grains, and the other half by saltation. This revealed a complex structure, with several concentration and flux peaks due to rolling, and one peak due to saltation. With an increase of the sediment transport rate, the depth structure remained the same at the water/granular interface, with peak value increases but with no shift in elevations. The saltation region expanded towards higher elevations with an increase of the particle velocity commensurate to the water velocity. The proportion of the sediment transport rate in saltation did not vary significantly. The particle streamwise velocity profiles exhibited three segments: an exponential decay in the bed, a linear increase where rolling and saltation co‐existed, and above this, a logarithmic‐like shape due to saltating particles. These results are comparable to profiles measured and modelled in dry granular free surface flows and in more intense bedload such as sheet flows. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

7.
Even with the flow of water over a soil surface in which roughness elements are well inundated, and in less erosive situations where erosional bed forms are not pronounced, the magnitude of resistance coefficients in equations such as those of Darcy–Weisbach, Chezy or Manning vary with flow velocity (at least). Using both original laboratory and field data, and data from the literature, the paper examines this question of the apparent variation of resistance coefficients in relation to flow velocity, even in the absence of interaction between hydraulics and resulting erosional bed forms. Resistance equations are first assessed as to their ability to describe overland flow velocity when tested against these data sources. The result is that Manning's equation received stronger support than the Darcy–Weisbach or Chezy equations, though all equations were useful. The second question addressed is how best to estimate velocity of overland flow from measurements of slope and unit discharge, recognizing that the apparent flow velocity variation in resistance coefficients is probably a result of shortcomings in all of the listed resistance equations. A new methodology is illustrated which gives good agreement between estimated and measured flow velocity for both well-inundated sheet and rill flow. Comments are given on the predictive use of this methodology. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

8.
Experiments were undertaken to determine the feasibility of tracing sediment movement in interrill overland flow. Crushed magnetite was introduced as a source-line 10 cm wide by 8 m long on a runoff plot 18 m wide by 29 m long located in southern Arizona. Initial magnetic susceptibilities along this source line, and along three transects located 0·25, 2·95 and 5 m downslope of the source-line, were measured. Movement of the magnetite in response to three rainfall simulation experiments was monitored. During the first two experiments, overland flow discharge was sampled at miniature flumes located along two cross sections on the plot downslope of the source-line, and at a supercritical flume at the plot outlet. Magnetic susceptibilities along the source-line and transects were measured after all three experiments. Results show that the magnetite moves very early in the experiments and that it reaches one of the flumes 2 m downslope of the source-line in 3 min. Most of the tracer moves a very short distance: 29·7 per cent is deposited within 25 cm of the source-line and only 2·2 per cent is deposited 2·95 m away. The deposition rate appears to decrease exponentially away from the source-line. Very little magnetite is recorded in the flow through the miniature flumes: in general it makes up less than 1 per cent of the total sediment load. No temporal pattern in these percentages is observed. Magnetite appears to be an effective tracer of sediment movement in interrill overland flow, though its higher density than natural soil may affect its detachment and transport.  相似文献   

9.
IINTRODUCTIONWhileriverflowsareusuallydeepandturbulent,overlandflowisextremelyshallowandcanbelaminar,transitionalandturbulent.Becauseoftheshallownessoftheflolw,overlandflowhydraulicsisgreatlyaffectedbysurfaceroughness,raindropimpact,andinthecaseoflaminarflow,flui(Iviscosity.Theinitiationofsedimentmovementinoverlandflowisthereforeexpectedtodifferfromthatinriverflows.InriverstUdies,bedshearStressgbhastraditionallybeenusedtocharacterizethecriticalflowconditionatwhichsedimentbeginstomove.At…  相似文献   

10.
The interactions between overland flow hydraulics and sediment yield were studied in flume experiments on erodible soil surfaces covered by rock fragments. The high erodibility of a non-cohesive fine sediment (D50 + 0·09mm) permitted the effects of local turbulence and scour on sediment yield to be examined. Overland flow hydraulics and sediment yield were compared for experiments with pebble (D50 + 1·5cm) and cobble (D50 + 8·6cm) rock fragment covers. Cover percentages range from 0 to 99 per cent. Rock fragment size strongly affects the relations between flow hydraulics and rock fragment cover. For pebbles spatially-averaged hydraulic parameters (flow velocity, flow depth, effective flow width, unit discharge, total shear stress, Darcy-Weisbach friction factor, percentage grain friction and grain shear stress) vary most rapidly within cover percentages at low covers (power functions). In contrast, for cobbles these parameters vary most rapidly within cover percentages at high covers (exponential functions). As the type of the function that describes the relation between flow hydraulics and cover percentage can be deduced from the ratio of rock fragment height to flow depth, the continuity equation can be employed to determine the actual coefficients of the functions, provided the regression of one hydraulic parameter (e.g. flow velocity) with cover percentage is known and a good estimate exists for two values of another hydraulic variable for a low and a high cover percentage. The variation of sediment yield with cover percentage is also strongly dependent on rock fragment size, but neither the convex-upward relation for pebbles, nor the positive relation for cobbles can be solely attributed to the spatially averaged hydraulics of sheet-flow. Rock fragments induce local turbulence that leads to scour hole development on the stoss side of the rock fragments while deposition commonly occurs in the wake. This local scour and deposition substantially affects sediment yield. However, scour dimensions cannot be predicted by spatially averaged flow hydraulics. An adjustment of existing scour formulas that predict scour around bridge piers is suggested. Sediment yield from non-cohesive soils might then be estimated by a combination of sediment transport and scour formulas.  相似文献   

11.
The effect of turbulent flow structures on saltation sand transport was studied during two convective storms in Niger, West Africa. Continuous, synchronous measurements of saltation fluxes and turbulent velocity fluctuations were made with a sampling frequency of 1 Hz. The shear stress production was determined from the vertical and streamwise velocity fluctuations. The greatest stress-bearing events were classified as turbulent structures, with sweep, ejection, inward interaction, and outward interaction described according to the quadrant technique. The classified turbulent structures accounted for 63·5 per cent of the average shear stress during the first storm, and 56·0 per cent during the second storm. The percentage of active time was only 20·6 per cent and 15·8 per cent, respectively. High saltation fluxes were associated with sweeps and outward interactions. These two structures contribute positively (sweeps) and negatively (outward interactions) to the shear stress, but have in common that the streamwise velocity component is higher than average. Therefore, the horizontal drag force seems primarily responsible for saltation sand transport, and not the shear stress. This was also reflected by the low correlation coefficients (r) between shear stress and saltation flux (0·12 and 0·14, respectively), while the correlation coefficients between the streamwise velocity component and saltation flux were much higher (0·65 and 0·57, respectively). © 1998 John Wiley & Sons, Ltd.  相似文献   

12.
Vegetative filter strips (VFSs) can effectively trap sediment in overland flow, but little information is available on its performance in controlling high‐concentration sediment and the runoff hydraulics in VFS. Flume experiments were conducted to investigate the sediment deposition, hydraulics of overland flow and their relationships in simulating VFS under a great range of sediment concentrations with four levels of vegetation cover (bare slope and 4%, 11% and 17%) and two flow rates (15 and 30 L min?1). Sediment concentrations varied from 30 to 400 kg m?3 and slope gradient was 9°. Both the deposited sediment load and deposition efficiency in VFS increased as the vegetation cover increased. Sediment concentration had a positive effect on the deposited load but no effect on deposition efficiency. A lower flow rate corresponded to greater deposition efficiency but had little effect on deposited load. Flow velocities decreased as vegetation cover increased. Sediment concentration had a negative effect on the mean velocity but no effect on surface velocity. Hydraulic resistance increased as the vegetation cover and sediment concentration increased. Sediment deposition efficiency had a much more pronounced relationship with overland flow hydraulics compared with deposited load, especially with the mean flow velocity, and there was a power relationship between them. Flow regime also affected the sediment deposition efficiency, and the efficiency was much higher under subcritical than supercritical flow. The results will be useful for the design of VFS and the control of sediment flowing into rivers in areas with serious soil erosion. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

13.
Partitioning resistance to overland flow on rough mobile beds   总被引：1，自引：0，他引：1  
For overland flows transporting predominantly bed load over rough mobile beds without rainfall, resistance to flow f may be divided into four components: surface resistance fs, form resistance ff, wave resistance fw, and bed‐mobility resistance fm. In this study it is assumed that f = fs + ff + fw + fm, and an equation is developed for each component. The equations for fs and ff are borrowed from the literature, while those for fw and fm are developed from two series of flume experiments in which the beds are covered with various concentrations of large‐scale roughness elements. The first series consists of 65 experiments on fixed beds, while the second series contains 194 experiments on mobile beds. All experiments were performed on the same slope (S = 0·114) and with the same size of sediment (D = 0·00074 m). The equations for fw and fm are derived by a combination of dimensional analysis and regression analysis. The analyses reveal that the major controls of fw and fm are the Froude number F and the concentration of the roughness elements Cr. When the equations for fw and fm are summed, the Cr terms cancel out, leaving fw+m = 0·63F?2. An equation is developed that predicts total f, and the contributions of fs, ff, fw and fm to f are computed from the series 1 and 2 experiments. An analysis of the first series reveals that in clear‐water flows over fixed beds, fw accounts for 52 per cent of f. A similar analysis of the second series indicates that in sediment‐laden flows over mobile beds fw comprises 37 per cent and fm 32 per cent of f, so that together fw and fm account for almost 70 per cent of f. Finally, regression analyses indicate that where F > 0·5, fw and fm each vary with F?2 and fw/fm = 1·18. The equation developed here for predicting total f applies only to the range of hydraulic, sediment, and bed roughness conditions represented by the experimental data. With additional data from a broader range of conditions the same methodology as employed here could be used to develop a more general equation. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

14.
Rock fragments can act as a controlling factor for erosional rates and patterns in the landscape. Thus, the objective of this study is to better understand the role that rock fragments incorporated into the soil matrix play in concentrated flow hydraulics and erosion. Laboratory flume experiments were conducted with soil material that was mixed with rock fragments. Rock fragment content ranged from 0 to 40 per cent by volume. Other treatments were slope (7 and 14%) and flow discharge (5·7 and 11·4 l min?1). An increase in rock fragment content resulted in lower sediment yield, and broader width of flow. Rock fragment cover at the soil surface, i.e. surface armour, increased with time in experiments with rock fragments. Flow energy was largely dissipated by rock fragment cover. For more turbulent flow conditions, when roughness elements were submerged in the flow, hydraulic roughness was similar for different rock fragment contents. In experiments with few or no rock fragments a narrow rill incised. Flow energy was dissipated by headcuts. Total sediment yield was much larger than for experiments with rock fragments in the soil. Adding just a small number of rock fragments in the soil matrix resulted in a significant reduction of sediment yield. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

15.
A wind tunnel study examined the effect of distributions of saltating particles on sediment surfaces which were characterized by distributions of their tensile strength. The sediments consisted of varying proportions of large sand‐sized particles with a fine particle cement. The energies of the impacting particles and the surface strengths were compared with the mass of material lost from the surface. It is important to consider distributions of parameters rather than mean values only, since abrasion and erosion may occur from surfaces not predicted from average strength and saltation velocities. At the impact velocities used in this study (mean velocity 4·4 m s?1, with standard deviation of 0·51), surfaces containing less than 12 per cent fine material were easily eroded, but insignificant erosion occurred when the fine particle content exceeded 60 per cent. Small amounts of cementing material were easily ruptured, allowing the large sand grains to be moved (largely in creep) by the bombarding particles. A significant amount of energy was lost to the bed. As the percentage of fine material increased, the surface became more difficult to break up and less energy was lost to the bed. The probability that erosion will occur for known energy distributions of impacting particles and surface strength can be calculated and the mass loss increases exponentially with a decrease in the percentage of fine cementing particles. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

16.
Large roughness elements such as stones or plant stems (obstacles) influence the depth of overland flows in two ways. The first effect is a dynamic one, involving frictional retardation of the flow and associated reduction in flow speeds. The second influence is static, and arises from the upward volumetric displacement of flow depth because of the submerged volume of the obstacles. Depending upon the distribution of submerged obstacle volume with height above the soil surface, the proportion of the flow volume occupied (and so, the perturbation of flow depth arising from volumetric displacement) can vary irregularly or systematically with flow stage. Furthermore, the amount of volumetric displacement of flow depth would vary among surfaces carrying different cover fractions of identical obstacles. Consequently, estimates of the change in friction factors arising from the drag on flow traversing varying obstacle cover fractions are confounded with the parallel shift volumetric displacement. To understand the true frictional drag arising from obstacles, a correction must be made for the volumetric displacement. A method for making this correction is outlined. New laboratory experiments provide precise observations of depths and friction coefficients in laminar flows passing fields of regular obstacles. After making the proposed correction for volumetric displacement, increases of 40 to 75 per cent in the derived value of the Darcy–Weisbach friction factor, f, are found for an obstacle cover of 20 per cent. Many published studies of friction coefficients in shallow overland flows, such as those on stone‐covered dryland soils, involve larger obstacle cover fractions, and evidently involve the significant confounding effect of volumetric displacement. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

17.
Water erosion on hillslopes is a worldwide environmental problem, which is a rainfall‐induced process, especially extreme rainfall. The great intensity of extreme rainfall strongly enhances the power of overland flow to detach soil and transport sediment. Plant litter is one of the most important constituents of ecosystems that often covers the soil surface and can be incorporated into topsoil. However, little attention has been paid to its effect on flow hydraulics owing to the veiled nature. This study aimed to examine the effects of incorporated litter on the hydraulic properties under extreme rainfall condition. To reach this goal, six litter rates of 0, 0.05, 0.10, 0.20, 0.35, and 0.50 kg m?2 and four litter types collected from deciduous trees, coniferous trees, shrubs, and herbs were incorporated into topsoil. Then, simulated rainfall experiments were performed on five slope gradients (5°, 10°, 15°, 20°, and 25°) with an extreme rainfall intensity of 80 mm h?1. The results showed that Froude number and flow velocity of the overland flow decreased, whereas flow resistance increased exponentially with litter incorporation rate. Litter type had an influence on flow hydraulics, which can mainly be attributed to the variations in surface coverage of the exposed litter and the litter morphology. Flow velocity and Darcy–Weisbach coefficient increased markedly with slope gradient. However, the variation of slope gradient did not modify the relationships between flow hydraulics and incorporated litter rate. The random roughness, resulting from heterogeneous erosion due to the uneven protection of surface exposed litter, increased linearly with litter incorporated rate. As rainfall proceeded, flow hydraulics varied with incorporated litter rate and slope gradient complicatedly due to the increases in flow rate and coverage of the exposed litter and the modification of soil surface roughness.  相似文献   

18.
There is a dearth of knowledge on the runoff processes of eucalypt woodland communities in the semi-arid tropics of Australia. The work was undertaken on a 100 m transect of a 0·8 degree hillslope typical of the ‘smooth plainlands’ of central-north Queensland. This paper introduces a new experimental design for measuring overland flow in such areas by way of a cascade system of unbounded runoff plots which allow the inputs and outputs between troughs to be calculated. Most storms generate overland flow. Time to overland flow ranges between 1 and 18 min where rain intensities are above 10mm hr−1 and when the average detention storage of 3·6 mm is exceeded. The bare soil surfaces within the scattered grass understory control the runoff generation process through the temporal variability of field saturated hydraulic conductivity. The study demonstrated that overland flow is mainly redistributed over the freely-draining oxic soil. Some areas export more overland flow than they gain from upslope (runoff), others gain more overland flow than they export (runon). Over the study period only 2 per cent of total rain is transferred out of this 100 m transect as overland flow due to the short duration of storms, the relatively high soil permeability, and the low slope angle. The remainder adds to the large soil water store or deep drainage. The variability of runoff–runon over these ‘smooth plainlands’ highlights how results from bounded plots would be misleading in such areas.  相似文献   

19.
This study examines how the sediment transport capacity of interrill overland flow varies with stone cover and stone size at two flow intensities. Six series of flume experiments were conducted on two slopes (2° and 10°) with stones of three sizes (28·0, 45·5 and 91·3 mm) serving as roughness elements. Bed sediment size, water discharge and simulated rainfall intensity were the same in all experiments. It was found (1) that transport capacity is positively related to stone size, with the relation becoming stronger as stone cover increases and flow intensity decreases; and (2) that transport capacity is negatively related to stone cover at the high flow intensity and curvilinearly related to stone cover at the low flow intensity. The curvilinear relations are concave‐upward with the lowest transport capacities occurring at stone covers between 0·40 and 0·60. The highest transport capacities are found at stone covers of 0 and 1, with the transport capacity being greater at the former stone cover than at the latter. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

20.
When sediment grains are transported as bed load in overland flow, there is a net transfer of momentum from the flow to the grains. When these grains collide with other grains, whether on the bed or in the flow, streamwise flow velocity decreases and resistance to flow increases. Resistance to flow generated in this manner is termed bed‐load transport resistance. Resistance to flow f over a plane bed may be partitioned into grain resistance fg and bed‐load transport resistance fbt. We use the symbols fbtf and fbtm to denote fbt for flows over fixed beds and over mobile beds, respectively, and we compute the effect of bed mobility on flow resistance fmob by subtracting fbtf from fbtm. The data for this study come from 54 flume experiments with fixed beds and 38 with mobile beds. On average fmob is approximately equal to half of fbtm, which is about one‐quarter of f. Hence, fmob is about one‐tenth of f. Predictive equations are developed for fbtf, fbtm and fmob using dimensional analysis to identify the relevant independent variables and regression analysis to evaluate the coefficients associated with these variables. Values of fmob are always positive which implies that mobile beds offer greater resistance to flow than do fixed beds. Evidently bed‐load grains colliding with mobile beds lose more momentum to the bed than do grains colliding with fixed beds. In other words, grain collisions with mobile beds are less elastic than those with fixed beds. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

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