Flow Resistance In Channels Research Articles

Experimental study on thermal–hydraulic performance of a nature-inspired mini-channel heat exchanger manufactured by 3D printing

Zigzag-channel printed circuit heat exchangers (PCHEs) are widely used in nuclear energy, solar energy, and aerospace due to their good heat transfer performance. However, the high flow resistance of zigzag channels leads to large pumping power consumption and thus limits the overall performance. Although previous modified channels could reduce the flow resistance of PCHEs, they also bring a decrease in the heat transfer efficiency. Inspired by river islands, this study proposes a novel nature-inspired channel. The nature-inspired channel heat exchanger, along with a traditional zigzag-channel heat exchanger, were manufactured by 3D printing. The high-temperature air-air flow and heat transfer experiments show that the nature-inspired channel heat exchanger increases the average heat transfer rate by 1.5% and significantly reduces the pressure drop by 34.85%. The addition of airfoil fins at the corners effectively alleviates the flow resistance caused by flow separation, reattachment, and collision, leading to a higher Nusselt number and a lower Fanning friction factor. The Nusselt number of nature-inspired channel is 59% higher than that of the zigzag channel with a 15° inclined angle. This work demonstrates that the nature-inspired channel could significantly reduce the flow resistance while maintaining high heat transfer efficiency compared with the traditional zigzag channel.

Experiments on flow velocity profiles in mountain river channels

ABSTRACT Research on the vertical profiles of flow velocity in mountainous river channels is limited, particularly in scenarios where complex bed geometries are absent. Due to the coarse roughness and seepage flow on streambeds composed of gravel, the conventional formulae for flow velocity profiles derived from fluvial river channels do not apply to mountainous river channels. Based on flume experiments with a bed packed with natural gravel and a slope ranging from 0.006 to 0.16, we derived a theoretical formula for flow velocity profiles. This new formula integrates the influence of the subsurface flow and velocity reduction near the water surface, demonstrating a strong alignment with measurements. Our findings indicate that for shallow water flow over rough bed surfaces, the turbulence intensity diminishes along the vertical direction in the near-bed region while remaining relatively constant in the upper water body. Contrary to conventional theories which attribute the increase in flow resistance and the decrease in sediment transport rates in mountainous river channels to form drag, our study emphasizes that the subsurface flow plays a significant role in the overall flow resistance of mountainous river channels and should not be overlooked.

Prediction of the flow resistance in non-prismatic compound channels

ABSTRACT Achieving an accurate estimation of the flow resistance in open channel flows is crucial for resolving several critical engineering difficulties. In instances when there is excessive flow on both banks of a river, it results in the breach of the primary channel, leading to the discharge of water into the adjacent floodplain. The alteration of floodplain geometry occurs as a consequence of agricultural and developmental practises, leading to the emergence of compound channels that exhibit converging, diverging, or skewed characteristics throughout the course of the flow. The efficacy of conventional equations in accurately forecasting flow resistance is limited due to their heavy reliance on empirical approaches. As a result of this phenomenon, there persists a significant need for methodologies that possess both novelty and precision. The objective of this work is to use the support vector machine (SVM) technique for the estimation of the Manning's roughness coefficient in a compound channel with converging floodplains. Statistical indicators are used to validate the constructed models in the experimental investigation, enabling the assessment of their performance and efficacy. The findings indicate a significant correlation between the Manning's roughness coefficient predicted by SVM and both experimental data and prior research outcomes.

Deformation of vegetated channel bed under ice-covered flow conditions

A common feature of cold regions is the presence of ice cover on water surface. In the presence of vegetation in the channel bed which is normally leafless in winter, interaction between river ice and vegetated channel bed becomes very complex. In the present study, the impacts of ice cover and submerged leafless vegetation on channel bed deformation and flow resistance have been investigated based on 144 experiments conducted in a large-scale outdoor flume. The independent variables associated with the maximum scour depth around vegetation elements have been assessed and equations have been developed. Results indicate that the most important variable affecting the maximum scour depth around vegetation under ice-covered flow conditions is the ratio of the ice cover roughness to the bed roughness (ni/nb). However, under open channel flow conditions, the flow Froude number is the most important variable influencing the maximum scour depth. The methods based on the law of the wall provide reliable Manning's coefficient for both smooth and rough ice covers in the presence of submerged vegetation in the channel bed. As the vegetation density increases, the size of scour holes becomes smaller. With the increase in vegetation density, the median grain size of the armour layer in scour holes decreases correspondingly. When vegetation elements are placed in a staggered configuration, the median grain size of the armour layer in scour holes is less than that of squared configuration of vegetation elements. Regardless of the roughness of ice cover on water surface and the grain size of sediment in the bed, the maximum depth of scour holes always occurs at the upstream front face of each vegetation element. Under the rough ice-covered flow condition, the maximum depth of scour holes is more than that under the smooth ice-covered and open flow conditions.

Collaborative optimization on cooling channel flow resistance and winding temperature for integrated cooling of motor and controller

The efficiency and working performance of the motor and controller system in micro-electric vehicles depends mainly on its thermal performance, which is contingent upon effective and active cooling. The working temperature of the motor and controller may be too high during operation, which properly causes motor power reduction or motor breakdowns. Therefore, it is crucial to design a good cooling channel for better cooling the integrated motor and controller system. This work proposes an integrated cooling channel of motor and controller, and the fluid-solid coupling analysis is applied for analyzing the velocity, pressure distributions of the cooling channel, and temperature distributions of motor solid components. Meanwhile, the collaborative optimization method based on the multi-island genetic algorithm (MIGA) is used to attain optimal design parameters of the integrated cooling channel of the motor and controller for obtaining a better cooling channel design with lower flow resistance and lower winding temperatures. Results show that the original cooling channel’s flow resistance and maximum winding temperature are 31.87 kPa and 120.04°C, respectively. The flow resistance and winding temperature are pretty significant. After optimization, the local vortex flow and zero velocity area in optimal cooling channel design are improved, the coolant flow velocity becomes more uniform, and the flow resistance is significantly reduced. The flow resistance and maximum winding temperature of the optimal cooling channel design are 12.5 kPa and 116.76°C, respectively, which are decreased compared with the original cooling channel structure, with a decrease of 39.4% and 2.7%, respectively. The research findings in this work can provide theoretical reference for solid components temperature evaluation of motor and give valuable data to cooling performance evaluation and optimization of integrated cooling channel for motor and controller system.

Machine learning approaches for adequate prediction of flow resistance in alluvial channels with bedforms.

In natural rivers, flow conditions are mainly dependent on flow resistance and type of roughness. The interactions among flow and bedforms are complex in nature as bedform dynamics primarily regulate the flow resistance. Manning's equation is the most frequently used equation for this purpose. Therefore, there is a need to develop alternate reliable techniques for adequate prediction of Manning's roughness coefficient (n) in alluvial channels with bedforms. Thus, the main objective of this study is to utilize machine learning (ML) models for predicting 'n' based on the six input features. The performance of ML models was assessed using Pearson's coefficient (R2), sensitivity analysis, Taylor's diagram, box plots, and K-fold method has been used for the cross-validation. Based on the output of the current work, models such as random forest, extra trees regression, and extreme gradient boosting performed extremely well (R2 ≥ 0.99), whereas, Lasso Regression models showed moderate efficiency in predicting roughness. The sensitivity analysis indicated that the energy grade line has a significant impact in predicting the roughness as compared to the other parameters. The alternate approach utilized in the present study provides insights into riverbed characteristics, enhancing the understanding of the complex relationship between roughness and other independent parameters.

Comparison of PDMS and NOA Microfluidic Chips: Deformation, Roughness, Hydrophilicity and Flow Performance.

Microfluidic devices are frequently manufactured with polydimethylsiloxane (PDMS) due to its affordability, transparency, and simplicity. However, high-pressure flow through PDMS microfluidic channels lead to an increase in channel size due to the compliance of the material. As a result, longer response times are required to reach steady flow rates, which increases the overall time required to complete experiments when using a syringe pump. Due to its excellent optical properties and increased rigidity, Norland Optical Adhesive (NOA) has been proposed as a promising material candidate for microfluidic fabrication. This study compares the compliance and deformation properties of three different characteristic sized (width of parallel channels: 100, 40 and 20 µm) microfluidic devices made of PDMS and NOA. The comparison of the microfluidics devices is made based on the Young's modulus, roughness, contact angle, channel width deformation, flow resistance and compliance. The experimental resistance is estimated through the measurement of the flow at a given pressure and a precision flow meter. The characteristic time of the system is extracted by fitting the two-element resistance-compliance (RC) hydraulic circuit model. The compliance of the microfluidics chips is estimated through the measurement of the characteristic time required for channels to achieve an output flow rate equivalent to that of the input flow rate using a syringe pump and a precision flow meter. The Young modulus was found to be 2 MPa for the PDMS and 1743 MPa for the NOA 63. The surface roughness was found to be higher for the NOA 63 than for the PDMS. The hydrophilicities of materials were found comparable with and without plasma treatment. The results show that NOA devices have lower compliance and deformation than PDMS devices.

Fracture conductivity management to improve heat extraction in enhanced geothermal systems

The efficiency of an enhanced geothermal reservoir (EGS) depends on the effective circulation of the working fluid through the geothermal formation. To remove the thermal shortcut that leads to thermal short-circuiting in the EGS, we present a method of fracture hydraulic conductivity management and present some practical ways to implement it in the field. The core idea is to correlate the flow resistance in different flow channels with temperature, in order to make uniform heat extraction through each flow path. The presented technique is an adaptive and reversible system and is trying to engineer the fracture system for effective delay of the early thermal breakthrough in EGS. Results indicate that the proposed fracture conductivity tuning technique (FCTT) can help to avoid flow and thermal shortcuts between the wells and maintain high heat extraction rates. The autonomous management of fracture conductivity may increase cumulative heat extraction by more than 214 %, and reduce an extra 1.06 – 3.65 Mt of greenhouse gas emission through electricity generation after 50 years of EGS development, which is highly considerable for EGS development. Besides, we found that it could be still beneficial to apply such methods solely to the injection wells, which can also bring a heat extraction improvement of 201.9 %. Furthermore, we look at the situations when the special conductivity tuning agents are placed in the middle between the wells, it is still very effective to control the fluid flow in the reservoir and enhance heat extraction. By proposing the tunable fracture conductivity, we are trying to revisit the old problem of thermal short-circuiting and provide new insight into the efficient EGS operation.

A framework approach to address the trend and causes of flood stage change in a river reach downstream of a dam influenced by tributaries

The evaluation of the trend of flood stage changes in alluvial rivers downstream of dams is important for flood management. However, the flood stage associated with a given discharge generally is nonstationary in river reaches with multiple tributaries. This is not only because of the dam-induced shifting in the cross-sectional area and/or channel roughness but also because of the backwater induced by high flows from the tributaries. To determine the total trend of the flood stage and quantify the separate contributions of hydrological and geomorphic effects, the current study proposed a framework approach consisting of hydrological analysis and multiscenario numerical modeling. By this means, the trend in the flood stage could be distinguished from the stage oscillation driven by varying factors, including extreme hydrologic events. The effects of chronic changes, including channel incision and flow resistance increase, also were quantitatively separated. This framework was applied to the Chenglingji–Datong (CD) reach downstream of the Three Gorges Dam (TGD) in the Yangtze River, China. The results indicated that the effect of the roughness increase counterbalanced the effect of channel incision when the flow discharge was beyond the bankfull level. The backwater effect induced by tributary inflow was the major cause of the flood stage rise in recent years. The method presented in the current study provides a useful tool for managers and engineers to obtain better insight into the driving mechanisms of flood stage changes in river reaches that are downstream of dams. These findings indicate that the flood stage may not decline or may even occasionally increase, although the cross-sectional area was enlarged by channel incision. Special attention should be given to the flood risk situation in the study reach after the TGD began operation.

Evaluating the influence of boulder arrangement on flow resistance in gravel-bed channels

Gravel bed flow resistance is affected by the shape and size of the roughness elements and their arrangement on the channel bed surface (spacing between elements, direction with respect to flow streamlines, and protrusion of the elements from the channel bed). Previous studies demonstrated that the flow resistance of open channel flows can be obtained by integrating the power velocity profile. This paper aims to study flow resistance in gravel-bed channels with different concentrations of boulders having staggered arrangements. At first, the equation relating Γ coefficient of the power velocity profile, and the Froude number was calibrated using measurements performed in a flume covered by hemispheric roughness elements for partially submerged and completely submerged hydraulic conditions. The roughness elements were evenly spaced (staggered) and arranged using three different concentrations of 9, 25, and 49%. Moreover, the relationship between Γ, slope, and the Froude number, calibrated using literature measurements performed with the same experimental setup but with a square arrangement, was tested for the measurements obtained with the staggered arrangement. The results showed that i) the Darcy-Weisbach friction factor can be accurately estimated by the proposed flow resistance equation, ii) the differences in flow resistance behavior between the two different investigated arrangements (staggered, square) occur only for the partially submerged hydraulic condition, and iii) for the staggered arrangement, skimming flow is reached for lower element concentrations as compared to the square one.

Sustainable gene expression programming model for shear stress prediction in nonprismatic compound channels

Open channel flow resistance and channel stability can be determined from boundary shear stress distribution. Overbank floods cross the main channel and pours the floodplain. The momentum change between the main channel and floodplains creates complicated flow shapes in compound channels. This alters floodplain and main channel shear stress. River floodplains also support agriculture and development activities due to which floodplain shape changes along the flow length, creating a converging, diverging or skewed compound channels. Traditional empirical formulas cannot accurately estimate shear force distribution. Thus, creative and accurate methods remain in demand. Gene expression programming, an innovative approach, has been utilized in this study to develop a new equation for compound channel with converging floodplains in terms of nondimensional geometric and flow variables to estimate the boundary shear force carried by floodplains. The proposed GEP-based method is best when compared to previously developed methods. The findings indicate that the predicted percentage shear force carried by floodplains determined using GEP is in good agreement with the experimental data (R2 = 0.96 and RMSE = 3.395 for the training data and R2 = 0.95 and RMSE = 4.022 for the testing data).

Effects of Boulder Arrangement on Flow Resistance Due to Macro-Scale Bed Roughness

Flow resistance in gravel-bed channels is not only affected by the shape and size of the roughness elements, but also by their arrangement on the channel bed surface (position to flow streamlines, spacing between elements, and their protrusion from the channel bed). Many investigations proved that open channel flow resistance can be obtained by integrating the power velocity profile. For a macro-scale roughness condition, this study aims to investigate the effect of different boulder arrangements on flow resistance. First, for each arrangement, the equation relating Γ function of the power velocity profile, the Froude number, and the channel slope was calibrated using available measurements performed in a flume covered by pebbles with “Random”, “Transversal stripe”, and “Longitudinal stripe” arrangements. For each arrangement, the experimental datasets were divided to consider the effects of boulder concentration Ch. Moreover, the relationship obtained for the “Random” arrangement and element concentration lower than 48% was tested using literature measurements performed in a flume covered by coarse elements randomly arranged. Finally, the effects of the different boulder arrangements on the flow resistance law were investigated by imposing a concentration threshold. The results demonstrated that (i) the Darcy–Weisbach friction factor can be accurately estimated by the proposed flow resistance equation, (ii) the flow resistance increases with Ch for low values (<48%) of concentration, while it does not depend on Ch for high concentrations (≥48%), and (iii) the effect of the boulder arrangement on flow resistance law is more evident for low element concentrations.

Flow resistance due to shrubs and woody vegetation

In this paper, a theoretical open channel flow resistance equation was verified using flow depth and discharge measurements carried out by Freeman et al. in a large channel, 2.44 m wide, for ten different types of uniform-sized plants (shrubs and woody vegetation). The plants, which are broadleaf deciduous vegetation commonly found in floodplains and riparian zones, were placed in staggered rows inside the channel whose bed was constructed to accept plants with their root systems. For each species, the available measurements were carried out by Freeman et al. with plants having different values of plant density, height, and bending stiffness. The available literature database (87 measurements) was divided into two groups which were separately used to calibrate and test the theoretical approach. In particular, 46 measurements were used to calibrate the relationship between the scale factor Γ of the velocity profile, the Froude number, and the channel slope. This relationship was calibrated using the entire available dataset or varying the scaling coefficient a with the investigated vegetation type. The measured values of the Darcy-Weisbach friction factor, obtained by the measured flow velocity, water depth and slope values, were compared with those calculated by the theoretical flow resistance law, coupled with the relationship for estimating the Γ function having a scaling coefficient different for each investigated vegetation type. This comparison allowed to demonstrate that an accurate estimate of the Darcy-Weisbach friction factor (errors less than or equal to ±10% for 87% of the investigated cases) can be obtained. However, for the investigated vegetation species, that are characterized by a large range of bending stiffness, also a mean value of the scaling coefficient a equal to 0.3283 allows an accurate estimate of the Darcy-Weisbach friction factor.

Flow Resistance in Very Rough Channels

AbstractFlow resistance in open channels determines the average flow velocity in a river, with important implications for downstream and at‐a‐station hydraulic geometry and sediment transport in natural channels. However, flow resistance in steep mountain channels is challenging to understand and predict due to heterogeneous channel morphology and spatially variable flow. Using a double‐averaging approach appropriate for very rough channels, the width, reach, and double‐averaged variables for steady, uniform flow in an open channel are derived. Using an empirical model for the coefficient of form drag, a flow resistance model is derived that compares well to a large data set of flow velocity in natural channels. Several parameters that together describe bed morphology are observed to be relatively consistent in the data set used and compare well to previous estimates of their values. This implies a degree of self‐organization in bed morphology that may simplify the challenging problem of predicting flow resistance in steep mountain rivers.

Flow effects of finite-sized tidal turbine arrays in the Chacao Channel, Southern Chile

To characterize energy resources and study of hydrodynamic effects induced by marine hydrokinetic devices in tidal channels, numerical models need to provide reliable representations of turbine arrays. In regions disconnected from the grid, near coastal protected areas and other relevant economic activities, there is a pressing need to evaluate the impacts of limited-size arrays. Here, we use the emblematic Chacao Channel in Southern Chile to understand the effects of bathymetry and array placement on energy extraction in strongly tidal channels. We implement in FVCOM a parameterization from a previously derived high-resolution model to represent a group of turbines in different locations. We first analyze the complexity of the bathymetry to define the appropriate grid size and obtain a correct representation of the interaction of turbines with the bed morphology. We simulate a base case to identify three suitable locations in the channel where we analyze the effects of the turbines: From simulations we compute the changes in the mean velocity, turbulent kinetic energy (TKE), and bed shear stress. The results show that baseline velocities and TKE are the main factors on the momentum extraction despite the bed complexity. However, in flatter bathymetries, changes on TKE and bottom shear are significantly larger compared to complex morphologies, since turbine arrays modify considerably the original flow conditions. Simulations also provide additional insights that are critical to evaluate the local impacts, showing the directionally-dependent flow resistance of tidal channels, in which the interactions with bathymetry change the downstream effects of turbine arrays in flood or ebb regimes.

An unconventional vertical fluidic-controlled wearable platform for synchronously detecting sweat rate and electrolyte concentration

Epidermal microfluidic devices with long microchannels have been developed for continuous sweat analysis, which are crucial to assess personal hydration status and underlying health conditions. However, the flow resistance in long channels and the ionic concentration variation significantly affect the accuracy of both the sweat rate and electrolyte concentration measurements. Herein, we present a novel fluidic-controlled wearable platform for synchronously dropwise-detecting the sweat rate and total electrolyte concentration. The unconventional platform consisting of a vertically shortened channel, a pair of embedded electrodes and an absorption layer, is designed to minimize the flow resistance and transform sweat fluidics into uniform micro-droplets for chronological and dropwise detection. Real-time sweat conductance is decoupled from a square-wave-like curve, where the sweat rate and electrolyte concentration can be derived from the interval time and peak value, respectively. Flexible and wearable band devices are demonstrated to show their potential application for hydration status assessment during exercises.

Numerical and Experimental Studies of Transpiration Cooling Film Effectiveness over Porous Materials

Comprehensive experimental and numerical studies were performed to determine cooling film effectiveness of transpiration cooling over porous materials. The cooling film effectiveness was evaluated experimentally using pressure-sensitive paint by invoking heat/mass transfer analogy over the surface of the porous samples. It was found that transpiration cooling can reduce total surface heat flux by two to three times and provide solid surface cooling film effectiveness on average 40% higher than the state-of-the-art multihole effusion cooling. This improvement increases to 200% when high coolant flow rates are used due to effusion cooling film liftoff. Numerical simulations allowed detailed investigations of the flow evolution in the porous media and its ability to create a thermal protection film. Modeling results revealed slight lateral motion of the flow inside the porous media in the same direction as the main flow. This was attributed to the viscous effect of the channel flow and low flow resistance of the porous samples. As a result, a larger portion of coolant exits the porous transpiration cooling surface toward the trailing edge of the test coupon, creating a nonuniform cooling film over the test samples surface. The model also suggested that cooling film effectiveness is a function of the porous media physical properties (permeability and inertia coefficient). In contrast to the reduction in cooling film effectiveness in multihole effusion cooling resulting from cooling film liftoff at high coolant flow rates, this study indicates that high coolant flow rates enhance cooling film protection in transpiration cooling.

Bipolar Electrode Array for Multiplexed Detection of Prostate Cancer Biomarkers

Owing to the characteristics of high throughput, high flexibility, and convenient separation of the sensing and reporting reactions, the bipolar electrode (BPE) shows great potential in clinical analysis. However, there are some difficulties in the combination of BPEs and multiplex electrochemiluminescence (ECL) biosensing, such as the need for small sample consumption, multistep operations, and separated sample loading. In this paper, a microfluidic BPE array chip was fabricated toward multiplex detection of cancer biomarkers. With a special channel structure and the difference in flow resistance of channels of different sizes, the direction of liquid flow was successfully controlled. In this way, rapid and automatic multiplex sampling was achieved on the array, which would help improve the sensing efficiency and reduce the reagent consumption. The ECL BPE array chip served as an immunosensor for multiple prostate cancer biomarkers including prostate-specific antigen (PSA), interleukin-6 (IL-6), and prostate-specific membrane antigen (PSMA). The microfluidic BPE chip shows good reproducibility and high sensitivity. The limits of detection for PSA, IL-6, and PSMA are 0.093 ng/mL, 0.061 pg/mL, and 0.059 ng/mL, respectively. It also exhibits excellent performance in real sample analysis. The integrated ECL BPE array shows a good application prospect in clinical sensing of cancer biomarkers, as well as point-of-care testing.

Using Structure-from-Motion Photogrammetry to Improve Roughness Estimates for Headwater Dryland Streams in the Pilbara, Western Australia

There are numerous situations where engineers and managers need to estimate flow resistance (roughness) in natural channels. Most estimates of roughness in small streams come from humid areas. Ephemeral streams in arid and semi-arid areas have different morphology and vegetation that leads to different roughness characteristics, but roughness in this class of stream has seldom been studied. A lack of high-resolution spatial data hinders our understanding of channel form and vegetation composition. High resolution structure-from-motion (SfM)-derived point clouds allow us to estimate channel boundary roughness and quantify the influence of vegetation during bankfull flows. These point clouds show individual plants at centimetre accuracy. Firstly, a semi-supervised machine learning procedure called CANUPO was used to identify and map key geomorphic features within a series of natural channels in the Pilbara region of Western Australia. Secondly, we described the variation within these reaches and the contribution of geomorphic forms and vegetation to the overall in-channel roughness. Channel types are divided into five reach types based on presence and absence of geomorphic forms: bedrock; alluvial single channel (≥cobble or sand dominated); alluvial multithread; composed of either nascent barforms or more established; stable alluvial islands. Using this reach classification as a guide, we present estimates of Manning’s roughness within these channels drawing on an examination of 650 cross sections. The contribution of in-channel vegetation toward increasing channel roughness was investigated at bankfull flow conditions for a subset of reaches. Roughness within these channels is highly variable and established in-channel vegetation can provide between a 35–55% increase in total channel roughness across all channel types. This contribution is likely higher in shallow flows and identifies the importance of integrating vegetation and geomorphic features into restorative practices for these headwater channels. These results also guide Manning’s selection for these semi-arid river systems and contribute to the vegetation-roughness literature within a relatively understudied region.

Flow resistance in channels with large emergent roughness elements

Reducing uncertainty in flow resistance estimation in natural channels requires elucidation of contributing influences. Surface shear and form drag are the major contributors in channels containing large roughness elements under emergent flow conditions. The two effects can be accounted for in the Darcy-Weisbach and Manning equations by adding their associated, separate friction factors or taking the square root of the sum of the squares of the corresponding Manning coefficients. The friction factor for form drag can be estimated from the drag coefficient and areal density of the roughness elements and the flow depth. Predictions of the combined effect are tested against results of laboratory experiments with different arrangements of emergent cylinders on smooth and rough beds, using experimentally determined drag coefficients for the cylinders. The variation of the overall resistance coefficient with flow condition depends on the dominant influence, decreasing with flow depth when surface shear dominates, and increasing with depth when form drag dominates.