Darcy-Weisbach Research Articles

Electrohydrodynamically-enhanced drag in a vertical pipe-flow with a concentric electrode: A One-Dimensional Turbulence study

Friction factor enhancements in pipe-flows subject to fixed electric fields are evaluated using the stochastic One-Dimensional Turbulence (ODT) model. To that extent, low Mach asymptotics are used to derive the leading order effects of the governing equations in electrohydrodynamic (EHD) flows considering low mobility ratios. Temporal and spatial ODT formulations are then carried out for three different Reynolds numbers (Re=3000, Re=4000 and Re=5000) at a set of electrohydrodynamic numbers in the range 0 ≤ NEHD≤ 600. The ODT simulation results are compared to published experimental data on Darcy friction factor enhancements of Nelson et al. (1990). The results signalize the importance of the developing flow for the EHD-enhanced drag. On one hand, the ratio NEHD2/Re2 characterizes the enhancement. On the other hand, the developing flow and the laminar-to-turbulent transition also have an important contribution to the friction factor. The ODT results presented here show that reduced order models can deliver relevant insights in otherwise numerically challenging flow simulations, therefore aiding the quantitative analysis of experimental observations in EHD flows.

Fractal Analysis of a Non-Newtonian Fluid Flow in a Rough-Walled Pipe

The fully developed laminar flow of a viscous non-Newtonian fluid in a rough-walled pipe is considered. The fluid rheology is described by the power–law model (covering shear thinning, Newtonian, and shear thickening fluids). The rough surface of the pipe is considered to be fractal, and the surface roughness is measured using surface fractal dimensions. The main focus of this study lies in the theoretical investigation of the influence of the pipe surface roughness on the velocity profile and the Darcy friction factor of an incompressible non-Newtonian fluid. The plotted results demonstrate that shear thinning fluids are the most sensitive to the surface roughness compared with Newtonian and shear thickening fluids. For a particular value of the surface fractal dimension, there exists an intersection point where shear thinning, Newtonian, and shear thickening fluids behave the same way regarding the amplitude of the velocity profile and the friction factor. This approach has a variety of potential applications, for instance fluid dynamics in hydrology, blood flow in the cardiovascular system, and many industrial applications.

Experimental and numerical investigation of turbulent flow and heat transfer characteristics in the Komax static mixer

The turbulent flow and heat transfer characteristics in the Komax static mixer are experimentally and numerically investigated in the range of Reynolds number (Re) from 2640 to 17600. The vortex evolution, Nusselt number (Nu), Darcy friction factor (f), PEC, field synergy principle and power spectrum in the Komax are evaluated based on that in Ross LPD, respectively. The Computational Fluid Dynamics (CFD) predictions of Nu and f based on SST k-ω model from ANSYS Fluent have a good agreement with the experimental results. The magnitudes of longitudinal vortices and swirl intensity in Komax are larger than those of Ross LPD. The synergy performance between velocity and temperature fields in Komax is better than that in Ross LPD due to the Dean Vortex gradually induced and weakened by the Komax inserts. The Komax static mixer has an obvious superiority in heat transfer and could enhance Nu higher than Ross by 46.7%‒49.6% at the cost of friction factor increasing 2.80‒4.37 times. Considering the PEC of both static mixers greater than 1, the Komax insert are recommended for Re<5280 and Ross LPD would be a good alternative due to much lower pressure drop for Re ≥ 5280. Based on the uniform heat flux experiments, the empirical correlations of Nu and f in both static mixers are established with the prediction errors less than ±6.20%. Turbulent kinetic energy and turbulent dissipation rate are used to evaluate the mesoscopic and microscopic mixing performance. The power spectrum and scaling relationship of outlet pressure pulsation signals are evaluated to reveal the turbulent chaotic performance which could help to enhance the mass and heat transfer. The scale relationship between power spectrum and pressure pulsation frequency satisfies power function attenuation.

Thermal transport analysis of six circular microchannel heat sink using nanofluid

Electronics devices growth in the last decade of the twentieth century ushered in a revolution inside the electronics segment. Continuous micro-sizes and operation cause these devices to heat up, resulting in a reduction in their performance or damage to their parts. Because heat can decrease device performance and life span while also wasting energy, offering an incorporated and effective cooling system has become a significant part of the design of device equipment. One of the key challenges of modern generation technology is the cooling of electronic devices. Nanofluids have attracted attention in a broad range of engineering implementations due to their great properties, which may be used to effectively cool devices while also improving energy efficiency. In view of the above defects, this numerical research object to examine the chip surface temperature, heat transfer rate, thermal resistance, Darcy friction factor and reliability of microelectronic chips in minichannel heat sinks is scrutinized by utilizing a {text{TiO}}_{2}/water nanofluid as a coolant and comparing the nanoliquid outcomes with the outcomes of water. {text{TiO}}_{2}/Water nanofluids at 1%, 2% and 3% volume concentrations are employed for this scrutinization. Here, a commercial CFD ANSYS (R19.2) FLUENT software package is used to analyze the electronic chip performance. The CFD ANSYS (R19.2) FLUENT software package is used for modeling, meshing and simulation of the current study.

Thermal performance of Fe3O4/water nanofluid flow in a newly designed dimpled tube under the influence of non-uniform magnetic field

The effects of alternating and constant magnetic fields on heat transfer characteristics of nanofluid flow in a dimpled tube have not been investigated either numerically or experimentally. In this context, the hydrothermal performance of Fe3O4/water (1.0 vol%) ferronanofluid flow in the dimpled tube (P/d = 3.75 and 11.25) has been examined under laminar flow regime (1131 ≤ Re≤2102) in this experimental study. While the magnitudes of magnetic fields are 0.16 T, the alternating magnetic field is utilized with square wave type at frequencies of 1, 2, 5 Hz. It is concluded that the dimpled tube causes up to 78.4% increase in Nusselt number compared to the smooth tube, while up to 118.9% increase in Darcy friction factor. The constant magnetic field enhances the Nusselt number up to 4.04% compared to the absence of a magnetic field using ferronanofluid as a working fluid. Higher frequencies of the alternating magnetic field results in higher thermal performance. Alternating magnetic field effect with f = 5 Hz offers 37.3% Nusselt number enhancement compared to the constant magnetic field effect in all tube geometries. It was also seen that P/d = 11.25 gives the highest Performance Evaluation Criteria while the magnetic field effect decreases it in all tube geometries.

Influences of rock fragments on the hydraulics and erosion of concentrated runoff in steep spoil heaps on the Loess Plateau of China

The soil–rock mixed spoil heaps are prone to severe soil erosion during heavy rain, causing severe land degradation and ecological and environmental damage. Nevertheless, past research on the erosion on spoil heaps has focused on soil particles that were readily eroded and disregarded the rock fragments (RF) that were not readily eroded. To explore the effect of the RF embedded in spoil heaps on the hydraulics of and erosion caused by concentrated runoff, scour-erosion experiments were implemented on three types of spoil heaps: RF = 7%, RF = 45%, and RF = 69%. The RF clearly reduced runoff and erosion on steep spoil heaps. As the RF increased from 7% to 69%, the runoff intensity and runoff coefficient decreased by 72.9%–79.1% and 83.2%–84.1% respectively, and the sediment concentration, soil denudation rate, and total soil loss decreased by 36.0%–47.8%, 83.7%–87.1%, and 87.0%–92.3%, respectively. Narrow rills were generated during the experiments, and the RF distinctly influenced the rill characteristics. High contents of RF restrained rill retreating and undercutting, and promoted rill widening. With an increase in RF, the flow shear stress and stream power gradually decreased, and the Darcy–Weisbach roughness coefficient increased. These findings imply that the RF dissipated the flow energy and reduced soil detachment capacity and sediment transport capacity. Soil detachment is strongly related to the Darcy–Weisbach roughness coefficient, Reynolds number, and runoff intensity, which may be the preferred descriptors of soil detachment. The current findings indicate that embedded rock fragments could effectively reduce soil loss on steep spoil heaps.

Effects of coupling of mass transport and blood viscosity models for microchannel flows

In this study, various aspects of a continuum transport model for blood, which is treated as a suspension of red blood cells, are thoroughly investigated. Earlier, treating blood as a suspension of rigid spherical particles in plasma was reasonably successful in mimicking flow dynamics in microchannels of size 40 μ m , comparable to 4 μ m , the dimension of a red blood cell (RBC). However, it is still not entirely clear whether such success owes to the coupling of mass and momentum transport, or to a sophisticated viscosity model for blood. To understand this in detail, we obtain semi-analytical solutions to the continuum model, in the presence and absence of the coupling of mass transport of RBCs, that connects the hematocrit concentration to the local viscosity, for fully developed blood flow in circular and rectangular microchannels. In this study, the transport of RBCs in flowing fluid is modeled by the diffusive flux model (DFM). Thus, overall, we have a hierarchy of continuum models using various viscosity models for blood, with progressive inclusion of physical complexities. Our results clearly highlight the importance of such a coupled approach, without which the results are quantitatively, and sometimes even qualitatively, different. In addition, our study serves as a thorough comparison of different viscosity models for blood, especially the steady state and transient models, recently proposed by Apostolidis and Beris (2014) and Apostolidis et al. (2015), respectively. We observe that, though the transient model reduces exactly to the description by the steady model over a range of low to moderate shear rates, the transient model shows some differences, especially for the RBC concentration in the low shear rate region. In the semi-analytical framework, the Darcy friction factor and cell free layer thickness have also been computed for circular cross-sections and a range of aspect ratios of a rectangular microchannel. Our results also indicate that the cell free layer attains a constant thickness when the aspect ratio of a rectangular microchannel reaches a critical maximum value for a specified average hematocrit. • Rectangular microchannel flow is investigated by coupling with the transport of RBC. • Even a finely tuned viscosity model without RBC transport is shown to be inadequate. • Frictional characteristics are derived in the form of a semi-analytical solution. • The model is found to predict the cell free layer thickness quite well. • The steady viscosity model overpredicts WSS when compared to the transient model.

Computational Solvers for Iterative Hydraulic loss Calculations in Pipe Systems

Abstract —The study of fluid mechanics spans several engineering disciplines including Mechanical, Civil, Aerospace, Chemical, Environmental, Petroleum, and Biomedical Engineering. In all these disciplines, hydraulic loss calculations in pipes are extremely important. However, the iterative nature of the solution to these engineering problems makes it intricate and cumbersome to solve. Further, it gets very difficult to visualize the solutions to such iterative problems for a wide variety of cases. The current paper aims to bridge this gap by the creation of two open-source Excel-VBA based computational solvers. The first tool corresponds to the determination of the Darcy-Weisbach friction factor through the Colebrook Equation and its visualization on a Moody's chart, which can be effectively employed by engineering instructors as an active learning tool. Second, a complete tool covering all four kinds of pipe flow situations (including the iterative problems) has been developed. The developed computational tools were employed in an undergraduate Fluid Mechanics classroom and the detailed student responses were collected on ten aspects related to teaching and learning divided broadly under four categories – 'overall rating', 'student perceptions on self-learning', 'Improvement in teaching delivery', and 'recommendation for other courses'. The data collected from student responses were subjected to statistical analysis. The results of hypothesis testing and the p-value calculations clearly justify the immense usefulness of this tool in the improvement of the overall teaching-learning process of Fluid Mechanics. Finally, the developed computational tools are being hosted free on the web for the benefit of engineering instructors, learners and professionals alike. Keywords:Pipe losses; computational tool; Fluid Mechanics; Hydraulic loss; Moody's chart; Excel VBA.

Determination of the Inside Diameter of Pressure Pipes for Drinking Water Systems Using Artificial Neural Networks

The fifth-degree polynomial equation determines the diameter in pressurized drinking water systems. The input variables are Q: flow (m3/s), H: pressure drop (m); L: pipe length (m); ε: roughness (m), ϑ: kinematic viscosity (m2/s), and Ʃk: sum of minor loss coefficients (dimensionless). After applying the energy equation for a hydraulic system composed of two tanks connected to a pipe of constant diameter and accepting the Colebrook-White and the Darcy-Weisbach equations, an undetermined expression is obtained since more unknowns than equations are established. This problem is solved by implementing a nested loop for the coefficient of friction and the diameter. This article proposes an Artificial Neural Network (ANN) implementing the Levenberg-Marquardt backpropagation method to estimate the diameter from the log-sigmoidal transfer function under stationary flow conditions. The training signals set consists of 5,000 random data that follow a normal distribution, calculated in Visual Basic (®Excel). The statistics used for the network evaluation correspond to the mean square error, the regression analysis, and the cross-entropy function. The architecture with the best performance had a hidden layer with 25 neurons (6-25-1) presenting an MSE equal to 5.41E-6 and 9.98E+00 for the Pearson Correlation Coefficient. The cross-validation of the neural scheme was carried out from 1,000 independent input signals from the training set, obtaining an MSE equal to 6.91E-6. The proposed neural network calculates the diameter with a relative error equal to 0.01% concerning the values ​​obtained with ®Epanet, evidencing the generalizability of the optimized system.

The hydraulic characteristics of Roman lead water pipes: An experimental investigation

An experimental investigation was conducted on two lengths of Roman lead water pipe excavated near Corbridge, Northumberland, England. The pipes date from approximately AD 80. One length of pipe contained a sleeve joint. The pipes were linked to a pump system using 3 D-printed connectors, and the hydraulic head loss along the pipe was measured. The pipe without a joint was used to determine a value for the wall roughness height, fitting the results to the Darcy-Weisbach equation. The wall roughness height obtained was assumed to apply to the pipe with the joint, and the additional head loss observed was then assumed to be due to the joint, allowing determination of a local loss coefficient. The pipes have a sinter encrustation, indicating that they had typically flowed partially full. Using this as an indication of water depth and deriving topographical information from the excavation report, the likely flow the pipes carried during their operational life was estimated. It was concluded that the pipe wall roughness coefficient ks was 0.9 mm, the joint local loss coefficient was 1.159, and that during operation the pipe probably carried around 17 litres/minute.

Topology optimization of an airfoil fin microchannel heat exchanger using artificial intelligence

High-performance microchannel heat exchangers are needed to supply heat for power conversion for nuclear microreactors. An airfoil fin microchannel design, constructed of Alloy 617 with helium as the working fluid, is analyzed and optimized using a design of experiments with artificial intelligence techniques. The use of airfoil fins offers the potential to reduce pressure drop across the heat exchanger, as compared to other types of channel configurations. A framework for topology optimization of airfoil fin printed circuit heat exchangers (PCHEs) has been developed that can be readily extended to different fin sizes and shapes, as well as different inlet and operating conditions, materials of construction, and working fluids. An optimization procedure is developed that employs computational fluid dynamics for a set of design points identified using Latin hypercube sampling. Computational fluid dynamics is used to analyze a simplified two-channel configuration where five design parameters are varied – inlet angle, fin scale, extent of staggering, transverse and longitudinal pitches. Two methods (a 5D polynomial and a regression neural network) are compared for generating surrogate models and the resulting response surface approximation is input to a genetic algorithm that is used to identify a set of optimal parameters. The optimal geometries are found across six channel Reynolds numbers ranging from 1000 to 5000, since inlet conditions affect flow through the heat exchanger. A set of optimal designs that maximizes heat transfer and minimizes pressure drop is identified, and a thermal stress analysis is performed on the optimal design. Correlations for the Nusselt number and Darcy friction factor are developed that can be useful for thermal hydraulic analyses using system codes. Thermal stresses are analyzed and a brief discussion of the status of code cases of PCHEs for nuclear applications is given. Testing and thermomechanical modeling is needed to facilitate future code compliance of PCHEs for high pressure and high temperature applications.

Flow resistance and velocity distribution in a smooth triangular channel

Abstract This study investigates the flow resistance and velocity distribution in a smooth triangular channel under varying slope conditions in a laboratory environment. For this purpose, two triangular cross-sectional shaped channels with 30° and 45° sidewall slopes were made. In various hydraulic conditions, bed slopes were carried out at different flow discharges and channels. The results have been used to test the stage-discharge curve, Manning roughness coefficient, n, the Darcy-Weisbach friction factor, f, and flow velocity profiles. By increasing the channel bed slope and flow discharge, the water surface fluctuation increased simultaneously. The fluctuation of flow surface profile in the triangular cross section (TCS) at 45° is more than in TCS 30° cases. The stage-discharge rating curve has less curvature with increasing channel bed slope. The Darcy-Weisbach f obtained from TCS 30° is higher than for TCS 45°, which means that TCS 30° has more resistance against flowing water passing through the channel than the 45° cross-section. Examination of the velocity contours shows that the maximum velocity occurred in the 30° triangular cross-section. Practical-sound findings from this research might be helpful for hydraulic engineers to design cost-effective open channels and other similar hydraulic structures.

Characterising englacial R-channels using artificial moulins

AbstractThe englacial and subglacial drainage systems exert key controls on glacier dynamics. However, due to their inaccessibility, they are still only poorly understood and more detailed observations are important, particularly to validate and tune physical models describing their dynamics. By creating artificial glacier moulins – boreholes connected to the subglacial drainage system and supplied with water from surface streams – we present a novel method to monitor the evolution of an englacial hydrological system with high temporal resolution. Here, we use artificial moulins as representations for vertical, pressurised, englacial R-channels. From tracer and pressure measurements, we derive time series of the hydraulic gradient, discharge, flow speed and channel cross-sectional area. Using these, we compute the Darcy–Weisbach friction factor, obtaining values which increase from 0.1 to 13 within five days of channel evolution. Furthermore, we simulate the growth of the cross-sectional area using different temperature gradients. The comparison to our measurements largely supports the common assumption that the temperature follows the pressure melting point. The deviations from this behaviour are analysed using various heat transfer parameterisations to assess their applicability. Finally, we discuss how artificial moulins could be combined with glacier-wide tracer experiments to constrain parameters of subglacial drainage more precisely.

Justifying network reconstruction when switching to low temperature district heating

The aim of the paper is to deduce a way to make low temperature district heating (LTDH) more feasible by involving operational data. Using design data only, the total network cost compared to traditional system increases by 28.4%. New assessment gives only 18.6 million EUR of costs to modernize DH network, which provide 2.4 million EUR (12.9%) as savings. The lower total network cost is achieved when the usage of existing pipes is higher. Only one section of the research brings negative trend to differential pressure head. The reason is a higher pressure drop that derives from the fact that the Colebrook-White formulae expresses the Darcy friction factor as a function of Reynolds number and pipe relative roughness. However, it does not supersede the positive effect provided by adjusting heat demands and supply/return temperatures closer to operational values. To sum up, operational data including network and outdoor temperatures, flow rate and pressure, results into more accurate evaluation. Moreover, costs for network reconstruction are sensitive to errors, when considering the overall costs to switch to low temperature technologies. This method is fast and scalable, able to include any type of a district heating system for which basic demand data is available.

Convective heat transfer and friction factor characteristics of molten salts in spirally fluted tubes

Spirally fluted tubes have been widely used for heat exchangers due to their superior heat transfer enhancement. However, most of the previous studies focused on the effects of a limited number of geometric parameters, i.e., the flute pitch and flute depth, on convective heat transfer and friction factor characteristics of low-Prandtl-number fluids, i.e., air and water. The correlations developed in these studies may not be accurate or applicable for medium-Prandtl-number fluids, such as molten salts. A numerical analysis using a Computational Fluid Dynamics (CFD) tool, STAR–CCM+, is therefore carried out in this study to systematically investigate the effects of four geometric parameters, including the flute pitch p, flute depth e, flute start number Ns (or flute helix angle θ), and trough length Ltr on convective heat transfer and friction factor characteristics of a medium-Prandtl-number fluid, FLiNaK (46.5LiF-11.5NaF-42KF mol %), in spirally fluted tubes. In addition, the convective heat transfer and Darcy friction factor correlations are proposed and validated, with ± 20% uncertainties, for medium-Prandtl-number fluids under the following conditions: Re = 88–1600, Pr = 2.5–40, p/Dc = 0.44–3.51, e/Dc = 0.10–0.40, θ/90 = 0.20–0.81, and Ltr/Dc = 0.71–2.16. The correlations proposed help improve the design of spirally fluted-tube heat exchangers.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ГАСИТЕЛЯ КОЛЕБАНИЙ ВАГОНА НА ОСНОВЕ ВЯЗКОГО ТРЕНИЯ

The work objective is to develop a mathematical model of the force characteristics of shock absorbers based on viscous friction, including elastomeric ones. For this purpose, the following tasks are solved in the work: the existing approaches to the mathematical modelling of hydraulic shock absorbers are analysed, a mathematical model based on hydraulic equations (the Darcy–Weisbach equation) is proposed, the developed mathematical model is verified and the results are compared with the results obtained based on the existing approach.&#x0D; Research methods: the equation of fluid flow through holes with hydraulic friction; D'Alembert's principle for composing the equation of car swaying motions; the Euler method for numerical integration of the differential equation.&#x0D; The novelty of the work consists in the fact that a mathematical model of the power characteristics of shock absorbers with viscous friction is proposed, based on the quadratic dependence of the reaction on the deformation rate. &#x0D; The results are the study of car swaying motions based on the traditional and proposed approaches. The proposed mathematical models can be used to develop shock absorbers with improved characteristics when designing passenger cars.

Comparing erosion and rill development processes by simulated upslope inflow in two red soils from subtropical China

Rill erosion is an important component of soil erosion, however, the process and mechanism of rill erosion on red soil slopes are not clear enough. In this paper, runoff scouring experiments were conducted with five varying inflow rates (8.5, 10, 11.5, 13, 14.5 L min−1 m−1) and one slope (8°) using two typical red soils in subtropical China: Ultisols derived from shale (UDS) and Ultisols derived from quaternary red clay (UDQ). The results showed that for the two red soils, runoff rate, sediment yield rate, and rill erosion amount were all positively correlated with inflow rates in linear relationships (p < 0.05). The high sand and low clay contents in eroded sediments were closely related to the original soil texture (dominated by clay and silt) and rill flow energy. Stream power and unit stream power were the optimal hydraulic parameters to characterize rill erosion mechanisms for UDS and UDQ, respectively. For UDQ with higher clay content and bulk density, the sediment yield process was more stable and the sand content in the eroded sediments was significantly higher than that of UDS, while the silt content was significantly lower. The rill flow of UDQ had slower velocity and larger Darcy–Weisbach resistance coefficient than that of UDS. For UDS with lower clay and higher sand content, the average sediment yield rate and rill depth were 2.26–4.71 and 2.79–6.53 times of UDQ, respectively, and the rill erodibility parameter was 1.84 times that of UDQ. The results are helpful for understanding the rill erosion mechanism and preventing soil loss in subtropical areas.

Numerical and Theoretical Investigation to Estimate Darcy Friction Factor in Water Network Problem Based on Modified Chun-Hui He’s Algorithm and Applications

In this work, we applied the modified Chun-Hui He’s algorithm to evaluate for estimation of flow friction factor f for value of friction factor by using Colebrook–White relation. The speedy, precise, and consistent evaluation of flow friction factor f are essential for evaluation of pressure dips and streams in complex network prototypes at distinct values of diameters of pipes. Friction factor estimated outcomes are applied in everyday engineering routine. Numerous computational systems tested for distinguishing of water pipe networks resolution, such as Hardy Cross method (HCM), Newton method (NM), and modified Newton method (MNM), are presented. As a novelty, a modified Newton method tabulated data, graphical results, and comparisons that are presented with different numerical schemes.

Experimental and numerical study of a 3D-printed aluminium cryogenic heat exchanger for compact Brayton refrigerators

Some cryogenic applications, such as for superconducting generators of wind power plants, require compact refrigerators. Heat exchangers are the most bulky components within the cold box of a cryogenic refrigerator. Thus, a reduction of their size would be advantageous for the development of a compact system. Volume and performance of a heat exchanger depend strongly on the hydraulic diameter of the channels and of the efficiency of the heat transfer surface. To improve the performance, a concept of aluminium 3D printed heat exchanger with optimised fin geometry has been developed. A fin design with hydraulic diameters of 1.48 mm and 1.07 mm for the high and low pressure sides, respectively, has been realized.Two prototype aluminium heat exchangers with improved fins have been produced by 3D printing and studied within this project. The accuracy of the geometry reproduction within the printing process has been investigated. The heat exchangers have successfully withstood pressure tests. The pressure drop has been measured at atmospheric and at higher pressure using helium and air as working fluids. Furthermore, the heat transfer with a temperature difference of 40 K along the heat exchanger has been investigated using helium. The Colburn and Darcy friction factors of designed and printed fin geometry have been calculated using Ansys CFX. A full heat exchanger simulation model with consideration of longitudinal heat conduction through inner and outer walls has been developed in Python. The results of the numerical simulations have been successfully validated against measurements. Based on the obtained data, suggestions for an improved heat exchanger geometry for cryogenic applications have been worked out.

Overland flow hydrodynamic characteristics in rough beds at low Reynolds numbers

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.