Showing papers on "Open-channel flow published in 2022"

On the role of turbulent large-scale streaks in generating sediment ridges

Abstract: The role of turbulent large-scale streaks or large-scale motions in forming subaqueous sediment ridges on an initially flat sediment bed is investigated with the aid of particle resolved direct numerical simulations of open channel flow at bulk Reynolds numbers up to 9500. The regular arrangement of quasi-streamwise ridges and troughs at a characteristic spanwise spacing between 1 and 1.5 times the mean fluid height is found to be a consequence of the spanwise organisation of turbulence in large-scale streamwise velocity streaks. Ridges predominantly appear in regions of weaker erosion below large-scale low-speed streaks and vice versa for troughs. The interaction between the dynamics of the large-scale streaks in the bulk flow and the evolution of sediment ridges on the sediment bed is best described as ‘top-down’ process, as the arrangement of the sediment bedforms is seen to adapt to changes in the outer flow with a time delay of several bulk time units. The observed ‘top-down’ interaction between the outer flow and the bed agrees fairly well with the conceptual model on causality in canonical channel flows proposed by Jimenez (J. Fluid Mech., vol. 842, 2018, P1, § 5.6). Mean secondary currents of Prandtl's second kind of comparable intensity and lateral spacing are found over developed sediment ridges and in single-phase smooth-wall channels alike in averages over bulk time units. This indicates that the secondary flow commonly observed together with sediment ridges is the statistical footprint of the regularly organised large-scale streaks.

Experimental study of laminar-to-turbulent transition in pipe flow

Abstract: This paper describes an experimental study of the unforced laminar-to-turbulent transition in pipe flow. Two pipes with different length-to-diameter ratios are investigated, and the transition phenomenon is studied using pressure measurements and visual observations. The entropy change and force balance are examined, and the peak powers are measured through fast Fourier transform analysis at various Reynolds numbers. Visual observations show that the flow structure changes at the Reynolds numbers corresponding to the peak powers. There is no clear dependency of the transition on the ratio of pipe length to diameter. The flow conditions are classified as laminar flow, transitions I, II, and III, and turbulent flow, separated by Reynolds numbers of approximately 1200, 2300, 7000, and 12 000, respectively. The transition at a Reynolds number of 1200 is caused by the force balance between the laminar and turbulent flows. The other transitions are related to the flow condition in the development region upstream of the pipe flow region. That is, the laminar-to-turbulent transition in the development region affects the transition condition in the downstream pipe flow. The laminar and turbulent development length ratios derived from the entropy changes are in reasonable agreement with the formulas for both laminar and turbulent flows. At large Reynolds numbers, the laminar flow condition will be established through the creation of a laminar-flow velocity profile at the entrance to the pipe.

Direct numerical simulation of turbulent open channel flows at moderately high Reynolds numbers

Abstract: Abstract Well-resolved direct numerical simulations of turbulent open channel flows (OCFs) are performed for friction Reynolds numbers up to $Re_\tau =2000$. Various turbulent statistics are documented and compared with the closed channel flows (CCFs). As expected, the mean velocity profiles of the OCFs match well with the CCFs in the near-wall region but diverge notably in the outer region. Interestingly, a logarithmic layer with Kárman constant $\kappa =0.363$ occurs for OCF at $Re_\tau =2000$, distinctly different from CCF. Except for a very thin layer near the free surface, most of the velocity and vorticity variances match between OCFs and CCFs. The one-dimensional energy spectra reveal that the very-large-scale motions (VLSMs) with streamwise wavelength $\lambda _x>3 h$ or spanwise wavelength $\lambda _z>0.5 h$ contribute the most to turbulence intensity and Reynolds shear stress in the overlap and outer layers (where h is the water depth). Furthermore, the VLSMs in OCFs are stronger than those in CCFs, resulting in a slightly higher streamwise velocity variance in the former. Due to the footprint effect, these structures also have significant contributions to the mean wall shear stress, and the difference between OCF and CCF enlarges with increasing $Re_\tau$. In summary, the free surface in OCFs plays an essential role in various flow phenomena, including the formation of stronger VLSMs and turbulent kinetic energy redistribution.

Confinement effect on the viscoelastic particle ordering in microfluidic flows: Numerical simulations and experiments

Abstract: Strings of equally spaced particles, also called particle trains, have been employed in several applications, including flow cytometry and particle or cell encapsulation. Recently, the formation of particle trains in viscoelastic liquids has been demonstrated. However, only a few studies have focused on the topic, with several questions remaining unanswered. We here perform numerical simulations and experiments to elucidate the effect of the confinement ratio on the self-ordering dynamics of particles suspended in a viscoelastic liquid and flowing on the centerline of a microfluidic channel. For a fixed channel size, the particles self-order on shorter distances as the particle size increases due to the enhanced hydrodynamic interactions. At relatively low linear concentrations, the relative particle velocities scale with the fourth power of the confinement ratio when plotted as a function of the distance between the particle surfaces normalized by the channel diameter. As the linear concentration increases, the average interparticle spacing reduces and the scaling is lost, with an increasing probability to form strings of particles in contact. To reduce the number of aggregates, a microfluidic device made of an array of trapezoidal elements is fabricated and tested. The particle aggregates reduce down to 5% of the overall particle number, significantly enhancing the ordering efficiency. A good agreement between numerical simulations and experiments is found.

Solute dispersion in an open channel turbulent flow: Solution by a generalized model

Abstract: • Turbulent dispersion in a typical open channel flow is analytically investigated. • Gill’s generalized dispersion model up to the fourth-order is solved and compared. • Two-dimensional concentration distribution is illustrated. • Analytical solutions are validated by numerical simulation results through RDM. • The applicable time of the fourth-order generalized dispersion model is determined. In this work, the classic problem in environmental hydraulics of solute dispersion in an open channel turbulent flow is analytically investigated by Gill’s generalized dispersion model to account for all the basic characteristics as dispersivity, skewness and kurtosis of the mean concentration evolution. A complete solution is presented for the whole process and three typical time-scales are determined: after a convection-dominated initial stage, a transient stage with essential transverse diffusion effect begins at a dimensionless time-scale of t ∼ 0.1 and gives way to an asymptotic stage of normal distribution of mean concentration from t ∼ 1 , slowly approaching to a final stage with relative uniformity in transverse concentration distribution at t ∼ 10 . Two-dimensional concentration distribution shows that there is a high concentration zone near the free water surface at a small time due to the small velocity gradient, indicating that it is not enough to characterize the dispersion process by the mean concentration, especially for the transient stage. The obtained analytical solutions of concentration distribution consist well with numerical simulation results by the random displacement method (RDM).

Dam-break flow dynamics over a stepped channel with vegetation

Abstract: In spite of the insistence of a variety of studies on floods triggered by a dam failure, the effects of channel unevenness and vegetation have not been fully explored. Some hydrological aspects, such as the sudden change in the topography of a river section, the density of vegetation, and its influence on flood development, need to be further addressed. Therefore, the present work investigates the complex effects of vegetation and channel’s step on wave propagation during a dam break across a dry downstream channel. The Flow-3d Computational Fluid Dynamics package was used to simulate the flow phenomena during a dam break, adopting different geometric conditions and a densely vegetated area of the downstream channel in the far-field. Three-dimensional flow characteristics were reproduced by solutions of Navier-Stokes equations coupled with the standard volume of fluid to track the evolution of the free surface. The turbulent flow characteristics were represented by different approaches frequently used in the scientific literature. The computational model was optimized and validated using experimental data published in the literature. The results showed that the model had high accuracy in predicting the evolution of the free surface, moving hydraulic jump, flow velocity, and flow regime. In addition, the model was able to predict the formation and development of transitional, rotational, and transverse flows, jet flow, nappe flow, wave breaking, the bore evolution in different directions, and the change of the flow regime under the influence of the channel step and vegetation. Accordingly, the flow fluctuations during dam break, wave attenuation, flow separation, and turbulence structure evolution in the vegetated area were predicted.

A data-driven model based on modal decomposition: application to the turbulent channel flow over an anisotropic porous wall

Abstract: Abstract This article presents a data-driven model based on modal decomposition, applied to approximate the low-order statistics of the spatially averaged wall-shear stress in a turbulent channel flow over a porous wall with two anisotropic permeabilities, producing drag increase or reduction when compared with the case of an isotropic porous wall. The model is comparable to a neural network architecture using a linear map to a classification. To create this model, we use high-order dynamic mode decomposition (DMD) to identify the structures describing the main flow dynamics, and then test different linear combinations of these modes to estimate the time evolution of the stress at the porous interface. The coefficients of the model are obtained by training the model against the results of direct numerical simulations over different time intervals. Depending on the number and the way of combining the DMD modes, the reduced-order models presented can reconstruct the wall-shear stress with relative error smaller than 0.01 % and reproduce its statistical variations for at least 1500 time units with relative error in the standard deviation or the mean smaller than 5 %. The model has also been tested to approximate the statistics of the wall-shear stress over the whole wall, showing that the regeneration of the flow structures can be reproduced by the nonlinear interaction of modes. Finally, considering the DMD modes as communities in a neural network, we examine the influence of the mode-to-mode interaction on the nonlinear flow dynamics, which explains the performance of the different models.

Coherent Structures in Plane Channel Flow of Dilute Polymer Solutions with Vanishing Inertia

Abstract: When subjected to sufficiently strong velocity gradients, solutions of long, flexible polymers exhibit flow instabilities and chaotic motion, often referred to as elastic turbulence. Its mechanism differs from the familiar, inertia-driven turbulence in Newtonian fluids and is poorly understood. Here, we demonstrate that the dynamics of purely elastic pressure-driven channel flows of dilute polymer solutions are organized by exact coherent structures that take the form of two-dimensional traveling waves. Our results demonstrate that no linear instability is required to sustain such traveling wave solutions and that their origin is purely elastic in nature. We show that the associated stress profiles are characterized by thin, filamentlike arrangements of polymer stretch, which is sustained by a solitary pair of vortices. We discuss the implications of the traveling wave solutions for the transition to elastic turbulence in straight channels and propose ways for their detection in experiments.

Supersonic turbulent channel flows over spanwise-oriented grooves

Abstract: In the present study, we perform direct numerical simulations to study the influences of the spanwise-oriented grooves, which are emulated by the reasonably designed “relaxed” boundary conditions, on the kinetic and thermodynamic statistics in a supersonic turbulent channel flow at the Mach number of 1.5 and Reynolds number of 3000. The phase averaged flow fields show that the relaxed boundary induces compressive and expansive waves that travel across the whole channel and are reflected by the upper wall. These waves are isentropic in the average sense except in the viscous sublayer. In the near-wall region, vortices and streaks that constitute the self-sustaining cycles are less populated and less meandering, while in the outer region, especially near the channel center, the velocity divergence is as strong as the vorticity. The temperature, density, and pressure fluctuations are enhanced by these waves. The correlations between the velocity and temperature are altered, due to the counter effects caused by the vortical motions and isentropic waves.

Stability of a laminar pipe flow subjected to a step-like increase in the flow rate

Abstract: We perform the linear modal stability analysis of a pipe flow subjected to a step-like increment in the flow rate from a steady initial flow with flow rate, $Q_i$, to a final flow with flow rate, $Q_f$, at the time, $t_c$. A step-like increment in the flow rate induces a non-periodic unsteady flow for a definite time interval. The ratio, $\Gamma_a={Q}_i/{Q}_f$, parameterizes the increase in the flow rate, and it ranges between $0$ to $1$. The stability analysis for a pipe flow subjected to a step-like increment in the flow rate from the steady laminar flow ($\Gamma_a>0$) is not reported in the literature. The present work investigates the effect of varying $\Gamma_a$ on the stability characteristics of an unsteady pipe flow. The step-like increment in the flow rate for $0\leq\Gamma_a\leq0.72$ induces a viscous type instability for a definite duration and the flow is modally unstable. The non-axisymmetric disturbance with azimuthal wavenumber, $m=1$ is the most unstable mode. The flow is highly-unstable for $\Gamma_a=0$ and the flow becomes less unstable with an increase in $\Gamma_a$. The flow becomes stable before it attains the steady-state condition for all $\Gamma_a$.

Reynolds Stress Modeling of Supercritical Narrow Channel Flows using OpenFOAM: Secondary Currents and Turbulent Flow Characteristics

Abstract: In this study, the full Launder, Reece and Rodi pressure-strain model and nonlinear boundary damping functions were incorporated in OpenFOAM® to simulate the turbulence-driven secondary currents in supercritical narrow channel flows such as in sediment bypass tunnels (SBTs). Five simulations were performed under uniform flow conditions covering Froude numbers from 1.69 - 2.56 and aspect ratios (channel width to flow depth) ar from 0.9 - 1.91 to investigate the formation of secondary currents and their impacts on longitudinal velocity, turbulence characteristics, and bed shear stress distribution. The numerical results of the maximum longitudinal velocity and the average shear velocity show marginal deviations, of less than 2.6%, from two-dimensional experimental results acquired under decelerating flow conditions. However, some differences are observed for the secondary currents and for the vertical turbulence intensity and Reynolds shear stress in the outer flow region, especially for cases with higher flow nonuniformity (that can influence the surface perturbation) whose influence is missing in the numerical model. No intermediate vortex is observed for ar = 1.91. However, it develops for lower ar, and detaches from the free surface vortex when ar {less than or equal to} 1.05. Such vortex bulges the longitudinal velocity contour lines inward and the zone of higher longitudinal velocity narrows and deepens with a decrease in ar. The decrement reduces the magnitude of the normalized maximum secondary velocity. It also affects the bottom vortex which alters the bed shear stress distribution.

Stability of Hartmann shear flows in an open inclined channel

Abstract: We study the stability of laminar flows in a sheet of fluid (open channel) down an incline with constant slope angle β ∈ ( 0 , π / 2 ) assuming that the fluid is electrically conducting and subjected to a magnetic field. The basic motion (the Hartmann shear flow) is the velocity field U ( z ) i , where z is the coordinate of the axis orthogonal to the channel, and i is the unit vector in the direction of the flow, and the magnetic field B ( z ) i + B 0 k . B 0 is constant and k is the unit vector in the direction of z . U ( z ) and B ( z ) are hyperbolic functions of z : U ( z ) vanishes at the bottom of the channel and its derivative with respect to z vanishes at the top. By assuming that the boundaries are non-conducting ( B ( z ) is zero on the boundaries), we study the local (linear) stability and instability, and we obtain critical Reynolds numbers for the onset of instability by solving a generalized Sommerfeld equation. We also study the nonlinear Lyapunov stability by solving the Orr equation for the associated maximum problem of the Reynolds–Orr energy equation. As in Falsaperla et al. (2019) we finally study the nonlinear stability of tilted rolls. The critical Reynolds numbers we obtain allow us to determine, for every inclination angle β , the critical velocity.

Generation and characterization of fully developed state in open channel flow

Abstract: Abstract A fully developed approach flow is necessary in open channel studies to maintain commonality among datasets obtained from different facilities. Two-component planar particle image velocimetry is used to study the characteristics of fully developed smooth open channel flow at a constant Reynolds number of 3.9 × 104 based on the maximum velocity and flow depth. The near-bed boundary layer is tripped to achieve a fully developed state and compared with the under- and over-tripped cases. The Reynolds stresses and higher-order moments are used as indicators to establish the fully developed state. Flow properties are explored by identifying uniform momentum zones (UMZs) using the probability density function of streamwise velocities. The instances are grouped based on the number of UMZs (NUMZ) and conditional averaging of flow variables of each group is used to evaluate the difference in flow properties between the developed and the developing flow. Large-scale ejections are found in the logarithmic layer when NUMZ is higher, whereas a lower number indicates the existence of large-scale sweeping motions. The distribution of the conditionally averaged ratio of the shear contribution from ejections and sweeps and velocity deficits shows a vertical variability in the fully developed state. The large-scale and pointwise quadrant events are used simultaneously to depict variability in inner flow properties between developing and fully developed flow which cannot be recognized in the mean flow characteristics. The sweep events have much higher shear generation in the outer flow in the fully developed state whereas the shear stress contribution from ejection is lower than that in developing flow.

Direct numerical simulation of turbulent mass transfer at the surface of an open channel flow

Abstract: We present direct numerical simulation results of turbulent open channel flow at bulk Reynolds numbers up to 12 000, coupled with (passive) scalar transport at Schmidt numbers up to 200. Care is taken to capture the very large-scale motions which appear already for relatively modest Reynolds numbers. The transfer velocity at the flat, free surface is found to scale with the Schmidt number to the power ‘ $-1/2$ ’, in accordance with previous studies and theoretical predictions for uncontaminated surfaces. The scaling of the transfer velocity with Reynolds number is found to vary, depending on the Reynolds number definition used. To compare the present results with those obtained in other systems, we define a turbulent Reynolds number at the edge of the surface-influenced layer. This allows us to probe the two-regime model of Theofanous et al. ( Intl J. Heat Mass Transfer , vol. 19, 1976, pp. 613–624), which is found to correctly predict that small-scale vortices significantly affect the mass transfer for turbulent Reynolds numbers larger than 500. It is further established that the root mean square of the surface divergence is, on average, proportional to the mean transfer velocity. However, the spatial correlation between instantaneous surface divergence and transfer velocity tends to decrease with increasing Schmidt number and increase with increasing Reynolds number. The latter is shown to be caused by an enhancement of the correlation in high-speed regions, which in turn is linked to the spatial distribution of surface-parallel vortices.

Influence of submerged flexible vegetation on turbulence in an open-channel flow

Abstract: Abstract Abstract In this study, we present a three-dimensional numerical model for the interaction of flow with submerged flexible vegetation, based on a large-eddy simulation and the immersed boundary method. The model innovatively realises the interaction between the flow and highly flexible vegetation with clustered leaves. Besides being a three-dimensional model of motion with full degrees of freedom, this study improves the consideration of the motion of the vegetation in all directions, and in addition the energy and momentum transfer in the spanwise direction. Furthermore, we perform a flume experiment for the flow with submerged flexible vegetation, the results of which are used to validate the simulation effects of the numerical model. It is found that the numerical model can effectively simulate the velocity profiles and the movement of vegetation induced by the flow. Using the model to analyse the flow–vegetation interaction, we find that the movement of vegetation is closely related to the flow velocity. As the flow velocity increases, both the offset angle and the vegetation swaying amplitude increase. Compared to vertical rigid vegetation, the tilting of flexible vegetation does not significantly change the velocity difference and the magnitude of the turbulent kinetic energy between the inside and the outside of the vegetation canopy, but it does weaken the disturbance to flow, thus reducing the resistance to flow. However, the swaying of vegetation dose significantly increase the velocity difference between the inside and the outside of the canopy. It forms Kelvin–Helmholtz hairpin vortices intensifying the turbulence production, and enhancing the disturbance and resistance to flow.

Wall-attached and wall-detached eddies in proper orthogonal decomposition modes of a turbulent channel flow

Abstract: To comprehensively understand the geometric and kinematic characteristics of inertial coherent motions that conform to the attached-eddy model, proper orthogonal decomposition (POD) is applied to volumetric streamwise fluctuating velocity fields in a turbulent channel flow with Reτ=2300 being resolved by direct numerical simulation. Wall-attached POD eddies (WAPEs) or wall-detached POD eddies (WDPEs) are identified from all of the POD eigenmodes by the wall-attached or wall-detached conditions, respectively. These POD eddies can be regarded as statistical structures that make independent energy contributions. WAPEs with a wide range of scale hierarchies are found to be self-similar in both geometries and kinematics. The generalized logarithmic law of high-even-order moments contributed by self-similar WAPEs further indicates their Gaussian-like behavior. These results suggest that WAPEs are the prime statistical representatives of attached eddies. In contrast, the scale distribution of WDPEs across a wide range of flow layers are invariant and their geometric shapes are self-similar over a wide range of length scales, but the kinematic self-similarity of WDPEs is not evident.

Prediction of polymer extension, drag reduction and vortex interaction in direct numerical simulation of turbulent channel flows

Abstract: Hydrodynamic and viscoelastic interactions between turbulent fluid within a channel at and a polymeric phase are investigated numerically using a multiscale hybrid approach. Direct numerical simulations are performed to predict the continuous phase and Brownian dynamics simulations using the finitely-extensible nonlinear elastic (FENE) dumbbell approach are carried out to model the trajectories of polymer extension vectors within the flow. Impact on polymer stretching is discussed, with streamwise extension dominant close to the wall, and wall-normal extension driven by high streamwise gradients of wall-normal velocity. In this case, it is shown that chains already possessing high wall-normal extensions may attempt to orientate more in the streamwise direction, causing a curling effect. These effects are observed in instantaneous snapshots of polymer extension, and the effects of the bulk Weissenberg number show that increased leads to more stretched configurations and more streamwise orientated conformities close to the wall, whereas in the bulk flow and log-law regions, the polymers tend to trace fluid turbulence structures. Chain orientation angles are also considered, with demonstrating little influence on the isotropic distributions in the log-law and bulk flow regions. The effect of the polymer relaxation time on the turbulent drag reduction is discussed, with greater Weissenberg numbers leading to more impactful reduction. Finally, the velocity gradient tensor invariants are calculated for the drag-reduced flows, with polymers having a significant impact on the Q-R phase diagrams, with the presence of polymers narrowing the range of values in the wall regions and causing flow structures to become more two-dimensional.

Characterizing purely elastic turbulent flow of a semi-dilute entangled polymer solution in a serpentine channel

Abstract: Polymer solutions in the semi-dilute regime are of considerable industrial importance. The complex rheological properties of such highly viscoelastic fluids and the complexity of their flow characteristics, especially in curved geometries, necessitate a thorough experimental characterization of the dynamics of such fluid flows. We apply statistical, spectral, and structural analyses to the experimentally obtained velocity fields of a semi-dilute entangled polymer solution in a serpentine channel to fully characterize the corresponding flow. Our results show that at high Weissenberg numbers, yet vanishing Reynolds numbers, the flow resistance is significantly increased, which indicates the emergence of a purely elastic turbulent flow. Spatial flow observations, and statistical analysis of temporal flow features show that this purely elastic turbulent flow is non-homogeneous, non-Gaussian, and anisotropic at all scales. Moreover, spectral analysis indicates that compared to elastic turbulence in the dilute regime, the range of present scales of the excited fluctuations is narrower. This is partly due to the entanglement of the polymers in this concentration regime, which restricts their movement, and partly due to the mixed flow type inherent in the serpentine geometry, which can reduce the extent of polymer stretching and thus reduce the intensity of the fluctuations in the flow. Furthermore, proper orthogonal decomposition analysis is applied to directly extract the turbulent flow structure and reveals the activity of the counter-rotating vortices associated with secondary flow, which significantly contribute to the total kinetic energy of the flow.

Influence of Water Depth and Slope on Roughness—Experiments and Roughness Approach for Rain-on-Grid Modeling

Abstract: Two-dimensional (2D) models have become a well-established tool for channel flow, as well as rain-induced overland flow simulations. In channel flow simulations, slopes are usually less than a few percent and water depths are over several meters, while overland flow simulations show steep slopes and flow of a few centimeters. Despite these discrepancies, modelers transfer roughness coefficients, validated for channel flow, to overland flow. One purpose of this study is to verify whether roughness values from the literature are also valid for overland flow simulations. Laboratory experiments with different degrees of bed roughness, various discharges and a range of experimental flume slopes were carried out. For a given discharge, water depth was measured, and bed roughness was derived. Experimental results reveal that roughness shows no clear dependence on slope but is strongly dependent on water depth for vegetated surfaces. To verify the influence of different roughness approaches, they were implemented in a 2D model. A comparison of different simulation results indicates differences in the hydrograph. Here, consideration of water depth-related roughness coefficients leads to retention and translation effects. With the results of this study, modelers may enhance the precision of the hydraulic component in overland flow simulations.

Drag model from interface-resolved simulations of particle sedimentation in a periodic domain and vertical turbulent channel flows

Abstract: Abstract A drag correlation is established for laminar particle-laden flows, based on data from the interfaced-resolved direct numerical simulations (IR-DNS) of particle sedimentation in a periodic domain at density ratio ranging from 2 to 1000, particle concentration ranging from 0.59 % to 14.16 %, and particle Reynolds number below 132. Our drag decreases slightly with increasing density ratio when the other parameters are fixed. The drag correlation is then corrected to account for the turbulence effect by introducing the relative turbulent kinetic energy, from the IR-DNS data of the upward turbulent channel flows laden with the particles larger than the Kolmogorov length scale at relatively low particle volume fractions. A drift velocity model is developed to obtain the effective slip velocity from the interphase mean velocity difference for the vertical turbulent channel flow by considering the effects of particle inertia, particle concentration distribution and large-scale streamwise vortices.

Overland flow hydrodynamic characteristics in rough beds at low reynolds numbers

Abstract: This paper considers overland flow resistance at low Reynolds numbers through analysis of experimental runs carried out using water only and water/glycerol mixtures. We first examined the power relationship between the Darcy–Weisbach friction factor f and the Reynolds number Re to obtain the values of the K coefficient and b exponent. These results confirmed the applicability of the values of b suggested in literature, while K required a specific calibration for laminar open-channel flows. The analysis revealed that transition from a laminar to turbulent flow regime for water only flows occurred at a threshold value of Re equal to 500 as described historically. The estimate of f by the power relationship and the calibrated b and K values were reliable for water only runs when Re ≥ 500. The measurements were also used to test a theoretical flow resistance law based on a power-velocity distribution. The calibrated theoretical relationship between the velocity profile parameter Γv, bed slope, flow Froude number and Re enabled a good estimate of f for water flows. For mixed fluid flows, the effect of the velocity profile shape was considered calibrating this relationship by two datasets obtained setting a threshold Reynolds number equal to 7. For flows with Re < 7, the shape of the velocity profile can be linear or convex while for flows at Re ≥ 7 the shape of the velocity distribution is always concave. The theoretical flow resistance allowed an accurate estimate also for mixed fluid flows, even at Re < 7. The different shape of the power-velocity distribution highlighted that mixed flows behave differently as compared to water only flows.