Large-scale Roughness Elements Research Articles

Control of Propagation of Salt Wedge by using Roughness Blocks having Different Inclination

The hydraulic conditions of a flow previously proved to be changed when placing large-scale geometric roughness elements on the bed of an open channel. These elements impose more resistance to the flow. The geometry of the roughness elements, the numbers used, and the configuration are parameters that can affect the hydraulic flow characteristics. The target is to use inclined block elements to control the salt wedge propagation pointed in most estuaries to prevent its negative effects. The Computational Fluid Dynamics CFD Software was used to simulate the two-phase flow in an estuary model. In this model, the used block elements are 2 cm by 3 cm cross-sections with an inclined face in the flow direction, with a length of their sides 2 and 3 cm. These elements were placed with a constant spacing in two rows at a distance from two sides of the bed of the channel model. Six simulation runs were conducted with two different discharges and three different inclinations of the centerline of the element concerning the flow direction. The applied discharges are 30 and 45.3 l/min, and the inclination of roughness elements are 15o, 30o, and 45o. The spacing between elements in each row is kept at 3cm. The results showed that when no roughness elements were used, the propagation of the salt wedge extended to 3.9m and 3.1m at a discharge of 30 l/min and 45.31/min, respectively. The propagation of the salt wedge was reduced when using the inclined blocks roughness element. This reduction depends on the applied discharge and the angle of inclination. At the minimum applied discharge of 30 l/min, the propagation of the salt wedge was reduced by 74% at 45o inclination. In contrast, it was 69% at 30o and 64% at 15o inclination at the same discharge. When the discharge is 45.3 l/min, the propagation of the salt wedge was reduced by 85% at 45o inclinations of roughness, 84% at 30o. It was 70% at 15o inclinations. The roughness elements improve the flow turbulence that disperses and slows the salt wedge propagation beneath the fresh water.

Studies of Stable Stratification Effect on Dynamic and Thermal Roughness Lengths of Urban-Type Canopy Using Large-Eddy Simulation

Abstract Large-eddy simulations (LES) of neutrally and stably stratified turbulent flows over urban-type surfaces with relatively low plan area ratios are presented. Numerical experiments were performed for different shapes of streamlined objects and at different static stability. A new method for setting up a numerical experiment aimed at studying the heat and momentum transfer within the roughness layer and investigating the thermal and dynamic interaction between the turbulent flow and the surface as a whole has been proposed. This method enables us to obtain an equilibrium state for values of parameters determining the characteristics of the external turbulent flow chosen beforehand. A strong dependence of the thermal roughness length on stratification was found. We also discuss the physical mechanisms that lead to the maintenance of turbulence above the canopy when the ground surface is strongly cooled. Significance Statement Using LES, we identify a mechanism that contributes to the maintenance of turbulence in the atmospheric boundary layer under the condition of strong surface cooling. Although these results are obtained for an urban canopy, we believe that the qualitative conclusions should be general for a wide type of surfaces with large-scale roughness elements. We hope that the new results will be useful for improving surface flux schemes in NWP and climate atmospheric models that suffer from attenuated mixing in a very stable boundary layer and the effect of “surface decoupling.” The found effect gives a physically justified alternative way to parameterize the air–surface exchange under strong stability compared to the often ad hoc modification of the MOST universal functions.

Discharge prediction in partly vegetated channel flows: Adaptation of IDCM method with a curved interface and large-scale roughness elements

This study provides new insight into how to predict flow discharges of partly vegetated channels with emergent vegetation. By adapting for the first time the Interacting Divided Channel Method (IDCM), applied with a curved interface approach and with the presence of large-scale roughness elements (not considered in previous studies), the total and zonal discharges of partly vegetated channels were predicted based on a series of experimental results in this study together with collected data from previous studies. Consideration of transverse momentum transfer in terms of apparent shear stress at curved interface plane showed better performance with IDCM than the Divided Channel Method (DCM) with both curved and classic vertical/diagonal divisions. In this study, we also proposed a series of expressions, easily applicable, to predict the zonal discharges of a partly vegetated channel.Many experiments were carried out in a physical model of a very large rectangular channel with the presence of rows of vertical, rigid, circular, and rough steel cylinders, representing emergent rigid vegetation. The rows of cylinders were partially mounted on the bottom of the channel, leaving lateral areas of free circulation near the walls. The three-dimensional components of the flow velocity were measured using a 3D Acoustic Doppler Velocimeter (ADV)-Vectrino.

Effect of walls with large scale roughness in deposition efficiency for 90-degree square bend configurations

This paper presents a numerical study of particle deposition in turbulent flow across bends with large scale roughness. The k-ε RNG model with Enhanced Wall Functions (EWF) for wall treatment and a Lagrangian point particle tracking method with a discrete random walk (DRW) model for turbulence dispersion were chosen in order to study the effect of cavities and ribs on the particle deposition efficiency in 90-degree square bends. The study is a complementary approach to previous ones performed for duct and channel flows. Results show that while cavity-type (c-type) and rib-type (r-type) large scale roughness elements in the external wall of the bend have a low effect on particle deposition, there is significant enhancement for cases in which large scale elements are located also at the inner side of the bend inducing high increments of secondary slow and turbulent kinetic energy. This, in addition to the increment of deposition area, generates a global shift of the particle deposition curve, especially for low and intermediate Stokes numbers and cases with high curvature ratio. Our study shows that bends of square cross section, similar to those used in Heating, Ventilation, and Air Conditioning (HVAC) applications but modified with large scale roughness elements in their walls, can be a potential alternative for filtering applications to be considered and studied more in depth in the future.

Investigations on Large-Scale Geometric Roughness Elements in Open Channels with Different Heights

Large-scale geometric roughness elements is one of the solutions that is used to protect openchannels from erosion. It is use to change the hydraulic characteristics of the flow. It may be concrete blocksor large stone placed at the bed of the channel to impose more resistance in the bed. The height of theseroughness elements is an important parameter that can affect the hydraulic characteristics of the flow. Usinga series of tests of T-shape roughness elements at three different heights, 3, 4.5, and 6cm, arranged in thefully rough configuration in order to investigate the velocity distributions along the flume. ANSYSParametric Design Language, APDL, and Computational Fluid Dynamics, CFD, were used to simulate theflow in an open channel with roughness elements. This simulation helps to find the best height of roughnesselements that can be used to change the hydraulic characteristics of the flow. The results showed that thevelocity values are decreased near the bed by about 61%, 58%, and 64% in case of 3cm, 4.5cm, and 6cmroughness heights consequently compared with the velocity of the control case. The velocity values areincreased near the free surface by about 32% and 19% in case of roughness elements height 6cm comparedwith 3cm and 4.5cm roughness heights respectively. The case of 6cm roughness height is considered to bethe effective case for decreasing the velocity values near the bed of the flume.

A Computational Fluid Dynamics Investigation of using Large-Scale Geometric Roughness Elements in Open Channels

The hydraulic behavior of the flow can be changed by using large-scale geometric roughness elements in open channels. This change can help in controlling erosions and sedimentations along the mainstream of the channel. Roughness elements can be large stone or concrete blocks placed at the channel's bed to impose more resistance in the bed. The geometry of the roughness elements, numbers used, and configuration are parameters that can affect the flow's hydraulic characteristics. In this paper, velocity distribution along the flume was theoretically investigated using a series of tests of T-shape roughness elements, fixed height, arranged in three different configurations, differ in the number of lines of roughness element. These elements were used to find the best configuration of roughness elements that can be applied to change the flow's hydraulic characteristics. ANSYS Parametric Design Language, APDL, and Computational Fluid Dynamics, CFD, was used to simulate the flow in an open channel with roughness elements. CFD can be used to study the hydrodynamics of open channels under different conditions with inclusive details rather than relying on the costly field and time-consuming. Runs were implemented with different conditions, the discharge, and water depth in upstream and downstream of the flume. T-shape roughness elements with height equal to 3cm placed in three different configurations, two lines, four lines, and fully rough configurations were tested. The results show that the effect of roughness elements increasing with increasing the number of lines of roughness elements. Cases of four lines and fully rough configurations have almost the same hydraulic performance by having the same results of the velocity decrease percentage, which is decreased by approximately about 66% and 61% of the control case's velocity in the zone near the roughness elements consequently. But the difference is that four lines configuration is affected in a part of the test section. This behavior increases the velocity values by about 11% in the other side and by about 10% near the free surface in the case of four lines configuration and increased by about 32% above the roughness elements in a fully rough configuration.

A Computational Fluid Dynamics Investigation of using Large-Scale Geometric Roughness Elements in Open Channels

The hydraulic behavior of the flow can be changed by using large-scale geometric roughness elements in open channels. This change can help in controlling erosions and sedimentations along the mainstream of the channel. Roughness elements can be large stone or concrete blocks placed at the channel's bed to impose more resistance in the bed. The geometry of the roughness elements, numbers used, and configuration are parameters that can affect the flow's hydraulic characteristics. In this paper, velocity distribution along the flume was theoretically investigated using a series of tests of T-shape roughness elements, fixed height, arranged in three different configurations, differ in the number of lines of roughness element. These elements were used to find the best configuration of roughness elements that can be applied to change the flow's hydraulic characteristics. ANSYS Parametric Design Language, APDL, and Computational Fluid Dynamics, CFD, was used to simulate the flow in an open channel with roughness elements. CFD can be used to study the hydrodynamics of open channels under different conditions with inclusive details rather than relying on the costly field and time-consuming. Runs were implemented with different conditions, the discharge, and water depth in upstream and downstream of the flume. T-shape roughness elements with height equal to 3cm placed in three different configurations, two lines, four lines, and fully rough configurations were tested. The results show that the effect of roughness elements increasing with increasing the number of lines of roughness elements. Cases of four lines and fully rough configurations have almost the same hydraulic performance by having the same results of the velocity decrease percentage, which is decreased by approximately about 66% and 61% of the control case's velocity in the zone near the roughness elements consequently. But the difference is that four lines configuration is affected in a part of the test section. This behavior increases the velocity values by about 11% in the other side and by about 10% near the free surface in the case of four lines configuration and increased by about 32% above the roughness elements in a fully rough configuration.

Flow Structure in a Shallow Mixing Layer Developing over 2-D Dunes

A high resolution Detached Eddy Simulation (DES) are used to characterize the evolution of a shallow mixing layer developing between two parallel streams in a long open channel over two-dimensional (2D) dunes. The study discusses the vertical non-uniformity in the mixing layer and provides a quantitative characterization of the growth of the large-scale quasi 2D coherent structures with the distance from the splitter plate. The presence of large-scale roughness elements in the form of an array of two-dimensional dunes with a maximum height of 0.25D (D is the channel depth) induces a very rapid and larger shift of the centerline of the mixing layer due to the increased influence of the bottom roughness. Results show that in streamwise sections situated after 100D (D is the channel depth) from the splitter plate, the width of the mixing layer close to the free surface stays constant. The tilting of the mixing layer interface toward the low speed stream is observed as the free surface is approached in all vertical sections.

The structure of turbulent flow around vertical plates containing holes and attached to a channel bed

High-resolution, 3-D large eddy simulations are conducted to study the physics of flow past 2-D solid and porous vertical plates of height H mounted on a horizontal surface (no bottom gap) with a fully developed, turbulent incoming flow. The porous plate consists of an array of spanwise-oriented, identical solid cylinders of rectangular cross section. The height of the solid cylinders and the spacing between the solid cylinders, corresponding to the plate’s “holes,” are kept constant for any given configuration, as the present study considers only plates of uniform porosity. The paper discusses how the mean flow and turbulence structure around the vertical plate, the unsteady forces acting on the plate, the dynamics of the large-scale turbulent eddies, the spectral content of the wake, and the distribution of the bed friction velocity on the horizontal channel bed vary as a function of the plate porosity (0% < P < 36%), the relative spacing between the solid elements of the porous plate (d/H), and the roughness of the channel bed surface. Simulation results are used to explain how the bleeding flow affects the dynamics on the larger billow eddies advected in the separated shear layer (SSL) forming at the top of the plate and the wake structure. It is found that the main recirculation eddy in the wake remains attached to the plate for P < 30%. For larger porosities, the main recirculation eddy forms away from the porous plate. The energy of the billows advected in the SSL decays monotonically with increasing plate porosity. For cases when the recirculation eddy remains attached to the plate, the larger billows advected in the downstream part of the SSL are partially reinjected inside the main recirculation eddy as a result of their interaction with the channel bed. This creates a feedback mechanism that induces large-scale disturbances of the spanwise-oriented vortex tubes advected inside the upstream part of the SSL. Results also show that the mean drag coefficient and the root-mean-square of the drag coefficient fluctuations increase mildly with increasing d/H. Meanwhile, varying d/H has a negligible effect on the position and size of the main recirculation eddy. The presence of large-scale roughness elements (2-D ribs) at the bed results in the decrease of the mean drag coefficient of the plate and, in the case of a solid plate, in a large decrease of the frequency of the large-scale eddies advected in the SSL.

Modelling nature-like fishway flow around unsubmerged obstacles using a 2D shallow water model

n the scope to create efficient nature like fish ramps using large-scale roughness elements, the present study is an audit of modelling such complex 3D free surface flows using an industrial 2D code solving shallow water equations. Validation procedure is based upon the comparison between numerous experimental measurements and numerical runs around large-scale roughness patterns disposed on the flume bottom in order to determine what 2D reliable numerical results can be expected. In this paper, we focused on cases of unsubmerged obstacles. The results demonstrate that 2D shallow water modelling using an industrial code such as TELEMAC-2D can be a convenient way for the hydraulic engineer to help design a nature-like fishway. This article emphasizes the limitations due to 2D depth integration of velocities and turbulence modelling and gives the domain of validity of the method.

On the Need for Larger Manning's Roughness Coefficients in Depth-Integrated Tsunami Inundation Models

Manning's n values for open channel (river) flow have been studied by hydraulic engineers since the late 19th century, and a rich literature exists on the topic including large-scale laboratory experiments and actual field measurements. Both river flood models and shallow water equation tsunami inundation models incorporate the importance of varying equivalent roughness values with the large-scale roughness elements present for different land use types. However, many tsunami models (especially in Japan) use n values based on a very limited set of small-scale model laboratory experiments with inappropriate Reynolds and Weber numbers, instead of using Manning's n values from the open channel flow literature. Due to this, equivalent Manning's n values for vegetated and urban areas in these tsunami inundation models are too small, causing the mitigating effect of forests and urban regions to be underestimated. This paper presents a review of Manning's n research applied to both river flood and tsunami inundation models, and suggests values to improve the reliability of the latter.

Detached eddy simulation of shallow mixing layer development between parallel streams

Results of a high resolution Detached Eddy Simulation (DES) are used to characterize the evolution of a shallow mixing layer developing between two parallel streams in a long open channel with a smooth flat bed and medium size dunes. The study discusses the vertical non-uniformity in the mixing layer structure and provides a quantitative characterization of the growth of the large-scale quasi two-dimensional (2D) coherent structures with the distance from the splitter plate. Results show that in streamwise sections situated between 75D (D is the channel depth) and 150D from the splitter plate, the width of the mixing layer close to the free surface is 20–30% more than the width in the near-bed region. This is mostly because of the tilting of the mixing layer interface on the low-speed side toward the low speed stream as the free surface is approached. Power spectra of the horizontal velocity components near the free surface show the presence of a −3 subrange, corresponding to inverse energy cascade in two-dimensional turbulence, at streamwise locations situated more than 10D from the splitter plate, consistent with the presence of large-scale quasi 2D horizontal eddies and the transfer of energy (inverse energy cascade) from the smaller scales toward these eddies. Consistent with visualizations of the mass transport of a passive scalar within the mixing layer, close to the free surface, the estimated streamwise length of the quasi 2D mixing layer eddies is about 2.5–3.0 times larger than the local width of the mixing layer. The presence of large-scale roughness elements in the form of an array of two-dimensional dunes with a maximum height of 0.25D (D is the channel depth) induces a much more rapid and larger shift of the centerline of the mixing layer due to the increased influence of the bottom roughness.

A generalized log law formulation for a wide range of boundary roughness typically encountered in natural streams

AbstractApplying fluid mechanics principles to mobile bed conditions is simplified by demonstrating that fitting log profiles to streamwise velocity measurements using the plane of zero velocity is applicable to a larger range of roughness conditions than previously expected. Four sets of detailed velocity measurements obtained under the supervision of the authors were analyzed encompassing sediment‐scale roughness elements, roughness caused by rigid vegetation, and large‐scale roughness elements comprised of mobile bed forms. The analyses resulted in similar normalized zero‐plane displacements for all roughness types considered. The zero‐plane displacements, dh, normalized by roughness height, ks, were 0.20 and 0.26 for the sediment‐ and vegetation‐scale experiments, respectively. The results for two experiments with bed form dominated roughness were 0.41 and 0.34. Estimates of dh/ks ranging from 0.2 to 0.4 are therefore recommended for a range of roughness types with the higher end of the range more appropriate for the larger, bed form‐scale roughness elements, and the lower end for the sediment‐scale roughness elements. In addition, it is demonstrated that the location of the plane of zero velocity is temporally constant even when the bed height is not. The findings can be applied to field velocity measurements under mobile bed conditions facilitating the calculation of turbulence parameters such as shear velocity by using point measurements and providing guidelines for the estimation of an appropriate value for zero‐plane displacement.

Equivalent Roughness of Submerged Obstacles in Open-Channel Flows

Experimental results for flow in a 16.5% sloping channel over various kinds of submerged artificial large-scale roughness elements are presented. Eight different shapes of obstacles are tested, as follows: (1) standard baffle blocks, (2) cubes, (3) half-cubes, (4) angles, (5) cylinders, (6) vertical rods, (7) hemispheres parallel to the flow, and (8) hemispheres normal to the flow. Based on depth measurements, the effective Manning’s coefficient is determined and the respective equivalent sand roughness is evaluated. The results are given in nondimensional terms and compared with previous research. The effects of shape, size, and density of the obstacles on flow resistance are discussed.

Propagation of surge waves in channels with large-scale bank roughness

Surge waves from upstream have been studied systematically in a 40 m long channel. Its banks were equipped with large-scale rectangular roughness elements. In addition to a prismatic reference channel, 41 different configurations of rectangular bank cavities have been investigated. The purpose was to study the effect of large-scale bank roughness on steady and unsteady flows. The macro-roughness of the channel banks increases the flow resistance. Consequently, the absolute celerity of the surge wave front is also reduced by between 5 and 25%. Based on the concept of an effective channel width for the computation of the mean flow velocity, the relative celerity of the surge wave can be predicted for macro-rough channel configurations. The attenuation of the wave front height is increased by the macro-rough flow resistance as well as by the partial reflections of the surge waves in the cavities and passive retention of the latter.

Pollutant Plume Dispersion in the Atmospheric Boundary Layer over Idealized Urban Roughness

The Gaussian model of plume dispersion is commonly used for pollutant concentration estimates. However, its major parameters, dispersion coefficients, barely account for terrain configuration and surface roughness. Large-scale roughness elements (e.g. buildings in urban areas) can substantially modify the ground features together with the pollutant transport in the atmospheric boundary layer over urban roughness (also known as the urban boundary layer, UBL). This study is thus conceived to investigate how urban roughness affects the flow structure and vertical dispersion coefficient in the UBL. Large-eddy simulation (LES) is carried out to examine the plume dispersion from a ground-level pollutant (area) source over idealized street canyons for cross flows in neutral stratification. A range of building-height-to-street-width (aspect) ratios, covering the regimes of skimming flow, wake interference, and isolated roughness, is employed to control the surface roughness. Apart from the widely used aerodynamic resistance or roughness function, the friction factor is another suitable parameter that measures the drag imposed by urban roughness quantitatively. Previous results from laboratory experiments and mathematical modelling also support the aforementioned approach for both two- and three-dimensional roughness elements. Comparing the UBL plume behaviour, the LES results show that the pollutant dispersion strongly depends on the friction factor. Empirical studies reveal that the vertical dispersion coefficient increases with increasing friction factor in the skimming flow regime (lower resistance) but is more uniform in the regimes of wake interference and isolated roughness (higher resistance). Hence, it is proposed that the friction factor and flow regimes could be adopted concurrently for pollutant concentration estimate in the UBL over urban street canyons of different roughness.

Flow phenomena and mechanisms in a field-scale experimental meandering channel with a pool-riffle sequence: Insights gained via numerical simulation

[1] Large-eddy simulation of turbulent flow through a natural-like meandering channel with pool-riffle sequences installed in the St. Anthony Falls Laboratory Outdoor StreamLab is carried out to elucidate the hydrodynamics at bankfull flow condition. It is shown that the shallow flow in the riffle is dominated by the presence of large-scale roughness elements that enhance turbulent mixing; increase turbulence anisotropy; and induce multiple, streamwise secondary cells driven by turbulence anisotropy. The flow in the pool, on the other hand, is dominated by the formation and interaction of the center region and outer bank secondary flow cells and the large horizontal recirculation regions along the inner bank. The collision of the counterrotating center region and outer bank cells at the water surface gives rise to a line of three-dimensional separation (flow convergence) in the time-averaged streamlines at the surface and the associated strong downward flow toward the bed that redistributes streamwise momentum and increases the bed shear stress along the channel thalweg. Intense turbulence is produced along the line of separation due to highly anisotropic velocity fluctuations. Our results make a strong case that the center region cell is driven by the curvature effects while the outer bank cell is driven by the combined effects of turbulence anisotropy and the curvature-induced centrifugal force. The inner bank horizontal recirculation zone consists of multiple eddies, which collectively span the entire point bar. A striking finding is that the center of the primary eddy is located directly above the crest of the point bar.

Flow Resistance Caused by Large-Scale Bank Roughness in a Channel

Systematic experimental investigations have been performed under steady flow conditions in a channel whose banks are equipped with large-scale rectangular roughness elements. The purpose was to determine the flow resistance owing to such macrorough banks. The practical motivation of the study is to see how morphological restoration of banks in channelized rivers, such as lateral cavities, influences the steady flow characteristics. The experiments performed in 40 different geometrical configurations revealed various two-dimensional flow characteristics in the bank cavities created by the roughness elements compared to the prismatic reference channel. The overall head loss of the flow is governed by the existence of different phenomena, such as vertical mixing layers, wake zones, recirculation gyres, coherent structures, and skin friction. The analysis of the experiments for steady flow conditions showed that the flow resistance is significantly increased in the macrorough configurations because of the disturbance of the bank geometry inducing large-scale depressions. The additional flow resistance attributable to macroroughness has been related to the forms of the banks. By separating the observed flow behavior into a normal recirculating, a reattachment and a square-grooved flow type, macrorough flow-resistance formulas according two different approaches could be developed that are in good agreement with the laboratory experiments

A Case Study of River Rehabilitation for Fish in Northern Italy: The Panaro River Project

The restoration of longitudinal connectivity of a watercourse altered by man-made obstacles is a key issue for the protection and safeguard of freshwater ecosystems and the construction of fish passes constitutes a relevant ad hoc measure. However, in many countries, like Italy, there is still not an adequate technical-scientific background and experience in this field and therefore several migratory species have become extinct or are suffering from severe impacts. The main elements of the river rehabilitation for fish project promoted by the Modena Province concerning the middle course of the Panaro River (North Italy), a watercourse characterised by high naturalistic and environmental values but fragmented by several weirs built to prevent riverbed erosion, are presented in this paper. The case study is analysed through the main steps that were carried out to define a preliminary plan for the restoration of the river continuity for the migration of four target species (South European nase (Chondrostoma genei), Italian barbel (Barbus plebejus), chub (Leuciscus cephalus cabeda) and soufie (Leuciscus souffia muticellus)) through the design of an innovative type of steep-slope fish ramp with large-scale roughness elements. The case study is part of an overall project and is the applicative section of an &#34educational&#34 document drawn up in the form of guidelines on the correct methodological approach for fish passes design, that will be addressed to professionals, technicians and local Authorities working in the field of water resource management.

Partitioning resistance to overland flow on rough mobile beds

AbstractFor 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.