Chezy Coefficient Research Articles

Estimation of Bedform Friction Factor Directly from Bathymetry Data

We present a procedure to systematically estimate the form friction factor through the analysis of spatial data obtained by acoustic Doppler current profiler. The form friction factor is related to the geometric characteristics of the bedform. The zero-crossing method was used to determine the geometric parameters of the bedform, which were then utilized to construct the probability density function for Chezy coefficients. Subsequently, Chezy coefficients were generated from the probability density function and assigned to each grid cell of a numerical model. To evaluate the performance of the presented friction factor estimation method, it was applied to the numerical simulation for the Nakdong River in South Korea. Sensitivity tests were performed to address the potential influence of random extraction from the probability density function, filtering length, and different form predictors during the estimation process. The proposed method showed more robust and accurate results compared to those with Manning's n value.

Dimensional analysis of literature formulas to estimate the characteristic flood response time in ungauged basins: A velocity-based approach

When investigating the wide literature dealing with the assessment of the critical time scale for basin hydrological response, several aspects still to be clarified can be acknowledged. Despite the high sensitivity of design flood peaks to the estimated time parameter value, there is still no agreement on the conceptual and operational definitions of the basin response time, resulting in several different approaches and formulations available.In our work, we suggest a conceptual approach to either reject or recommend formulas of the characteristic basin response time for ungauged basins, with the aim of devising some practical steps in the choice of a robust formulation to be used in hydrological modelling and flood hydrograph design. To this end, 29 empirical and semi-empirical formulas, all containing a basin length and slope, have been carefully selected and their structure compared in dimensional terms, using a simple hydraulic reasoning (e.g., the Chezy formula) as indicator of hydraulic consistency. 13 hydraulically consistent formulas have been identified.Starting from wave celerities and using the river network morphology of 135 watersheds in north-western Italy, we have then investigated and compared the variability of the average flow velocities estimated using all formulas whose input data are available within the study area. By comparing the magnitude and basin scale dependence of the inferred velocities with the values observed in the literature, which generally increase with basin size, some formulas are considered not reasonable, while 5 of them are identified as more robust, i.e. consistent with the observations. These are the formulas of Chow (1962), NERC (1975), SCS (1954), McEnroe and Zhao (1999) and Watt and Chow (1985).Our findings lead to identify analytically the relationships between the exponents of each formula and those of the scaling law linking the length and slope of the basin. These relationships, driving the increase or decrease in the velocity values with basin size, allow us to identify the range of length and slope exponents in the characteristic time formulas for which velocity increases with basin area, as literature suggests. Based on the same relationships, one of the 5 formulas above can be adopted in practical applications and a guideline for calibrating new formulations can be followed.

Mapping Mean Velocity Field over Bed Forms Using Simplified Empirical-Moment Concept Approach

The log-wake law was successful in mapping velocity fields for uniform flow over flat surfaces, even in cases of wake effects (velocity dips, wall effects, and secondary currents). However, natural riverbeds with undulations and bedforms challenge these models. This study introduces a moment-based empirical method for rough estimation of the velocity fields over stationary 2D bedforms. It proposes three polynomial velocity profile templates (first, fifth, and eighth orders) with coefficients deduced analytically while taking into account an array of flow conditions and assumptions, including slip velocity at the bed, mass and moment of momentum conservations, imposing inviscid potential flow near the water surface, and incorporation of near-bed shear stress utilizing a moment-based Chezy formula. Remarkably, the coefficients of these polynomials are primarily reliant on two crucial velocity scales, the depth-averaged velocity (uo) and the moment-derived integral velocity (u1), along with the dimensionless reattachment coefficient (Kr). Validation of the proposed approach comes from ten lab experiments, spanning Froude numbers from 0.1 to 0.32, offering empirical data to validate the obtained velocity profiles and to establish the relationship of the spatial variation in the normalized u1 velocity along bedforms. This study reveals that the assumption of a slip boundary condition at the bed generally enhances the accuracy of predicted velocity profiles. The eighth-order polynomial profile excels within the eddy zone and close to reattachment points, while the fifth-order profile performs better downstream, approaching the crest. Importantly, the efficacy of this approach extends beyond water flow to encompass airflow scenarios, such as airflow over a negative step. The research findings highlight that linear velocity, as employed in Vertically Averaged and Moment models (VAM), exhibits approximately 70% less velocity mismatch compared to constant Vertically Averaged (VA) models. Moreover, the utilization of the fifth-order and eighth-order velocity profiles results in substantial improvements, reducing velocity mismatch by approximately 86% and 90%, respectively, in comparison to VA models. The insights gained from this study hold significant implications for advancing vertically averaged and moment-based models, enabling the generation of approximate yet more realistic velocity fields in scenarios involving flow over bedforms. These findings directly impact applications related to sediment transport and mixing phenomena.

Construction of a Real-Time Forecast Model for Coastal Engineering and Processes Nested in a Basin Scale Model

A numerical model was developed using Delft3D to simulate the circulation dynamics in Port Everglades, FL, and the adjacent coastal area. The model was nested within the HYCOM (Hybrid Coordinate Ocean Model), while meteorological data were obtained from the NARR (North American Regional Reanalysis) model. To evaluate the model, model outputs were compared with observed data from the NOAA. Calibration experiments were conducted on the model parameters, including the bottom friction, wind forcings, and vertical layer specification. These experiments revealed that implementing a 10-layer model slightly improved the vertical stratification, while the utilization of 2-D wind data resulted in more pronounced surface layer characteristics in temperature and velocity profiles and employing moderate values of the Chezy coefficient produced optimal outcomes for the bottom roughness parameter. The model demonstrated satisfactory performance across major parameters, including water level, salinity, temperature, and currents. A real-time forecast system has been constructed with this nested model, providing up to 3-day forecasts that are updated daily. To facilitate automated forecasting without manual intervention, an automation system has been developed using a combination of bash, MATLAB, and Python scripts. This study provides a comprehensive documentation of the concepts and detailed methods involved in developing a real-time forecast model for estuarine and coastal regions.

მდინარეთა წყალმოვარდნების მაქსიმალური ხარჯების გათვლა მდინარე ვერეს მაგალითზე

As the observations show, the hydrological regime of the Vere River, in the warm period of the year, as a result of sudden heavy rains, is characterized by large freshets. Due to global climate change, especially since the 1990s, their number and intensity have increased. Calculation of the maximum discharges of freshets using Chezy formula is mainly given in the form of Table 1. In the article, as an example, the calculation of the discharge of the catastrophic freshet on the Vere River on 14 June 2015 for the adjacent section after the connection of the Napetvrebi ravine is given by 2 methods - using the Sokolovsky and Chezy formulas, and according to the maximum discharge calculated at the Napetvrebi ravine for the laboratory section and for the entire Vere river basin using the relative coefficients of their areas, the values of the maximum discharges of the June 14 catastrophic freshet were obtained in the amount of 477 and 512 m3/s, respectively. In addition, it should be noted that comparing all three results of the maximum discharges at Napetvrebi ravine, it can be seen that they are quite close to each other, which indicates the credibility of the maximum discharges of freshets calculated by us in the laboratory section from the 1990s to the present day using the Chezy formula.

Hydraulic characteristics of pipelines restored using polymer hoses

Aging water supply and wastewater pipeline systems suffer from corrosion and damage. Trenchless restoration methods extend their lifespan and reduce repairing costs. However, there is no standard method for determining the hydraulic characteristics of restored pipelines, making it challenging to assess the feasibility of using different materials for restoration. This article focuses on changes in hydraulic characteristics after restoring pipelines with glass fiber and synthetic felt hoses. The study uses Bernoulli’s equation and the Chezy formula to estimate changes in the flow capacity of pipelines. Standard values for slopes, flow rates, and filling rates were used to calculate the hydraulic resistance coefficient, Chezy coefficient, and flow rate after laying polymer hoses. The results show that the flow capacity of restored pipelines increases, and there is no need for further hydraulic calculations to confirm the absence of a reduction in pipeline capacity after restoration. Therefore, trenchless restoration methods can be considered as effective means to extend the lifespan of aging pipeline systems and reduce engineering repairs costs.

Обоснование методов гидравлических расчетов оросительных каналов

Purpose: justification of the applicability of various methods of hydraulic calculations of irrigation canals of land reclamation systems. It is recommended to use five types of hydraulic tasks allowing determining the following main parameters of irrigation canals for each type: conveying capacity (first type), canal slope (second type), roughness coefficient (third type), water flow depth (fourth type), cross-section dimensions of the irrigation canal (fifth type). Materials and methods. The well-known classical methods and dependences of N. N. Pavlovsky, B. A. Bakhmetev, R. R. Chugaev, A. A. Agroskin, Shezi and other scientists were taken as a basis during the research. Results. Methods for determining the main hydraulic characteristics of irrigation canals, including: canal discharge and slope and roughness coefficient are considered. These methods allow making calculations by the selection and graphical methods. The fifth type of problems is a series of independent solutions, where the effective width also calculated graphically is used. An analysis of the calculation results shows that for problems of the first type, the Chezy coefficients and hydraulic discharge decrease with an increase in the channel roughness coefficient values. Based on the calculated data obtained, canal discharge change chart depending on the roughness coefficient of the channel was constructed. Conclusions. The conditions for application of various methods of hydraulic calculation of irrigation canals were determined based on the results of the research. The values of the roughness coefficients of irrigation canals in impervious lining – concrete monolithic and reinforced concrete from prefabricated slabs are given. Summary calculation results for six different examples are presented.

Оценка гидравлической шероховатости русла магистрального канала

The purpose of the study was to determine the roughness coefficient of the main channel bed BP-1 of the Sarpinskaya watering-irrigation system (SWIS) and to compare the data obtained with the normative values. The materials for performing the calculations were: an explanatory note to the project of the second stage of the construction of the SWIS, passports of the main and inter-farm channels of the system (2015), a technical report of the operating organization for 2021, data of full-scale measurements of the depths and velocities of the water flow in the considered alignment using the «speed-area» method, the results of full-scale surveys of the water supply network and HTS SWIS, as well as data from GIS maps and literary sources. The methodology for calculating the elements of the live section of the channels took into account the recommendations of SP 100.13330.2016. The calculation of the roughness coefficients of the channels was carried out using known dependencies, including the Chezy formula, the Manning equation, the dependencies of I.I. Agroskin and N.N. Pavlovsky. The elements of the living section are determined and the values of the roughness coeffi cient in the considered alignment of the main channel are obtained. At the same time, the calculated values of the roughness coefficient obtained have good convergence (the deviation of the results does not exceed –2.8%). However, the obtained values exceed the normative value of the roughness coefficient by 1.6-1.64 times, which is explained not only by the overgrowth of the channel bed with aquatic vegetation, but also by the peculiarity of the shape of the cross-section of this channel, which in the area under consideration has a signifi cant width along the bottom. The calculated values of the roughness coeffi cient obtained indicate the overgrowth of the main canal bed, which was confi rmed during field surveys of the water supply network of this canal in the spring of 2022. In view of this, it is necessary to carry out preventive measures in a timely manner aimed at reducing the additional hydraulic resistance caused by overgrowth of the riverbed with vegetation.

True first formula of the uniform regime

The main objective of this technical article is to redesign the first form of the uniform regimen, which during the revision and search in the International and Internet bibliography, respectively, confirms that the first formula for the evaluation of this regime is engineer Francés Antóine de Chézy in 1769, considered as a paradigm of canal hydraulics. In 1789, the Irish engineer Robert Manning presented his formula, which is currently the most widely used in the regime of this regime. The author of this technical article, to carry out an analysis of the definition of uniform regimen, considers that in addition to being similar formulas, does not represent in general terms the real conditions, because they are conceptually unique and exclusively for the fluent turbulence it is for the quadrature resistance zone (complete turbulence zone in the Moody chart), given the coefficients of Chézy (CCH) and Manning (nM), independent of the Reynolds number. It is known that the turbulent fluid is divided into three categories according to the number of Reynolds (Re) and relative rugosity (Kr), its son, full turbulent fluid, (CCH and nM), depends solely on the relative rugosity (Kr), turbulent transient fluid, (CCH and nM), its function of (Re and Kr), and the turbulent fluid is only dependent on the number of Reynolds (Re). It is concluded that the first formulation of the uniform regimen is the general formula of fluid resistance and also constitutes the origin of the Chezy formula.

Hydraulic experiment in non-pressure pipeline made of polymer material

Introduction. To solve the problem of water shortage for irrigation in the city of Kerbala (Iraq), for the first time, a decision was made to use treated wastewater from urban wastewater treatment plants. Transportation of water from treatment facilities to irrigated lands is carried out through a pipeline in a non-pressure mode. Using the Water Card simulation model, the optimal pipe diameters for two flows, 1200 and 2,200 mm, were selected. The capacity of the existing treatment plant is 1.16 m3/s or 100,000 m3/day, and after the introduction of new treatment facilities, the flow rate will increase to 4.63 m3/s or 400,000 m3/ day. The aim of the work was to experimentally confirm the choice of the optimal diameter of the pipes and determine the hydraulic characteristics of the flow in it. In this regard, in laboratory conditions, experimental studies of the hydraulic characteristics of the flow in a polyethylene pipe with a diameter of 100 mm in the range of slopes (0.005–0.03), with fluid flow in non-pressure, were carried out. Using the theory of hydrodynamic similarity, the results of experimental data were recalculated for pipe diameters of 1200 and 2,200 mm. As field data, when modeling hydrodynamic similarity, the results obtained in the simulation model are taken into account. In world practice, there is experience in the reuse of treated wastewater, but water is supplied to the place of consumption in most cases through open channels. For the first time, pipes of large diameters are used in this work, which requires a more detailed study of the hydraulic parameters of the flow in it.
 
 Materials and methods. Using the theory of hydrodynamic similarity, the results of experimentally obtained hydraulic parameters were calculated for plastic pipes with a diameter of 1200 mm at a water flow rate of 1.16 m3/s and 2,200 mm at a flow rate of 4.63 m3/s.
 
 Results. Conducting experimental studies and recalculating experimental data from a similar model to a full-scale object (the results obtained using the Water Card simulation model are used as a full-scale object) using the Froude method with similarity coefficients made it possible to obtain the following values of average flow rates, hydraulic friction coefficients λ, Chezy coefficients C, Reynolds numbers and other flow characteristics when filling the pipeline from 0.1 to 0.8 for pipes with diameters of 1200 and 2,200 mm.
 
 Conclusions. Conducting laboratory studies to determine the hydraulic characteristics of a polyethylene pipeline with a diameter of 100 mm as a model and substantiate the hydraulic similarity of the model and nature, in the form of plastic pipes with diameters of 1,200 and 2,200 mm, respectively, will allow designing a gravity system of main pipelines for transporting treated wastewater in the city of Karbala (Iraq). Further, the data of the simulation model are used as field data.

Применение данных SRTM для экстраполяции кривых расходов (на примере поста р. Ия – г. Тулун)

The manuscript discusses the method developed by the authors for restoring the cross-sectional area curve and extrapolate rating curves for the Iya River at the Tulun gauge, using the Shuttle Radar Topography Mission (SRTM) data. As part of the work, the systematic correction for the study area was determined to recalculate altitudes from a digital terranean model according to SRTM topographic data to the Baltic Height System. The river width data from SRTM-based information after systematic correction are in good agreement with the width from large-scale satellite images as well as with the field width measurements at appropriate levels. The paper presents the results of the extrapolation of the rating curve, using the Chezy equation approach, the Stevens-Velikanov technique and the stage-area and stage-velocity method, using the area curve and the average depth curve obtained on SRTM materials. For each research method used in the study, by comparing with the reference of rating curve, the values of the average probable deviation were calculated. As part of the study the extrapolated rating curve is presented as an analytical equation, and the approximation error is determined.

A Moment-Based Chezy Formula for Bed Shear Stress in Varied Flow

Despite its limitations, the Chezy bed shear stress formula is commonly used in depth-averaged flow numerical models as closure for estimating mutual tractive stresses with underneath boundaries. This paper proposes a novel moment-based formula that could be considered a revised version of the Chezy formula and can be used to estimate local variations of the bed shear stress under more complex and varied flow conditions with accelerating–decelerating flow fields. The formula depends on two velocity scales: the depth-averaged velocity, Uo, and a new moment-based velocity scale, u1. The new formula is calibrated using 10 experiments for flow over fixed bedforms, and the calibration coefficient is found to linearly correlate with h/Δ and h/zo ratios. The formula is also applied for the case of air flow across a negative step, jet water flow downstream a gate, and 2D water flow downstream an oblique negative step, and reasonably satisfactory agreement with the measured data is found. The new formula could be used in vertically averaged and moment models to disclose part of the information already lost by the vertical integration procedure.

A Modified Chezy Formula for One-Dimensional Unsteady Frictional Resistance in Open Channel Flow

Abstract It has been observed in literature that for unsteady flow conditions the one-to-one relationships between flow depth, cross-sectional averaged velocity, and frictional resistance as determined from steady uniform flow cases may not be appropriate for these more complex flow systems. Thus, a general friction resistance formula needs to be modified through the addition of new descriptive terms to account for flow unsteadiness, in order to eliminate errors due to uniform and steady-flow assumptions. An extended Chezy formula incorporating both time and space partial derivatives of hydraulic parameters was developed using dimensional analysis to investigate the relationship between flow unsteadiness and friction resistance. Results show that the proposed formula performs better than the traditional Chezy formula for simulating real hydrograph cases whereby both formula coefficients are individually identified for each flood event and coefficients are predetermined using other flood events as calibration cases. Although the extended Chezy formula as well as the original Chezy formula perform worse with the increasing degree of flow unsteadiness, its results are less dramatically affected by unsteadiness intensity, thereby improving estimations of flood routing. As a result, it tends to perform much better than traditional Chezy formula for severe flood events. Under more complex conditions whereby peak flooding events may occur predominantly under unsteady flow, the extended Chezy model may provide as a valuable tool for researchers, practitioners, and water managers for assessing and predicting impacts for flooding and for the development of more appropriate mitigation strategies and more accurate risk assessments.

Automatic calibration of the two-dimensional hydrodynamic and water quality model using sequential uncertainty fitting approach.

Reservoir hydrodynamic and water quality modeling, in conjunction with the monitoring programs, is one of the essential tools for controlling the pollution of these types of water bodies. The complexity of the model, data scarcity, and the variable nature of natural phenomena lead to uncertainty in models, which should be considered in the calibration process of these models. Uncertainty-based automatic calibration is one of the methods that can be effective in achieving a high-reliability model. In this paper, the Sequential Uncertainty Fitting (SUFI-2) algorithm was used for the automatic calibration of the two-dimensional hydrodynamic and water quality model (CE-QUAL-W2) for the reservoir under parameter uncertainty conditions. To this end, the CE-QUAL-W2 model was developed to simulate the temperature and water surface elevation of the Karkheh Dam reservoir (western Iran). The parameters affecting temperature were regarded as uncertain parameters in the calibration process, including the coefficients of longitudinal eddy viscosity, longitudinal eddy diffusivity, Chezy coefficient or Manning, wind sheltering, solar radiation absorbed in the surface layer, extinction coefficient for pure water, and the experimental coefficients of wind speed function. The developed method demonstrated a high potential for matching the simulated temperature and water surface elevation for the reservoir with the measured data. Averagely, 69% of the simulated temperature and 90% of the simulated water surface elevation were located within the 95% confidence interval. The SUFI-2 algorithm also showed better performance in terms of the convergence rate compared with the particle swarm optimization (PSO) algorithm, which indicated a lower number of calls (80 calls compared to 2000 calls) and could reduce the total root-mean-square error by 9.6%.

Simple Semi-analytical Solutions Using the Perturbation Method for Gradually Varied Flow Profile in Triangular Channels

In hydraulic engineering, the steady non-uniform flow in a channel with the gradual changes at the water surface level is introduced as the Gradually Varied Flow (GVF). For the design of open channels, it is necessary to calculate the GVF profile along the channel flow. The GVF profile is described by a nonlinear Ordinary Differential Equation (ODE). Because this equation is strongly nonlinear, providing new analytical and/or semi-analytical solutions for this equation without any simplifications and/or linearizations would be necessary and helpful. In this research, the Perturbation Method (PM) is proposed to present a semi-analytical solution for solving the GVF equation in the prismatic triangular channel. A total of two cases are studied in this paper. In case 1, the Manning equation and in case 2, the Chezy equation are applied as the resistance equations. The GVF profiles in the two cases are compared with the Finite Difference Method (FDM) profiles. Also, the effect of the summation truncation in the PM is studied for these cases. The results show that by increasing the terms approximation in the PM, the GVF profile converges to the FDM profile. A reference solution for efficiency assessment of numerical techniques can be provided by presented semi-analytical solutions in this paper. Furthermore, the proposed method in this paper can be used as a new idea in providing semi-analytical solutions to other open channel works.

Solutions for Gradually Varied Flow Profiles in Prismatic and Wide Rectangular Channels by Perturbation Method

Gradually varied flow (GVF) in open channel hydraulics occurs when free water surface level gradually varies in a steady flow due to geometry alteration in the channel. Investigation of GVF profile is important because water depth along the channel should be determined when designing the channel. Mathematically, GVF profile is obtained by solution of a nonlinear ordinary differential equation. However, due to extreme nonlinearity of the equation, providing an analytical solution is practically unattainable unless under highly simplified conditions. The current study presents semi-analytical solutions for the equation in prismatic ordinary and wide rectangular channels by perturbation method (PM). At the first step, a perturbation solution is derived for wide rectangular channels using a constant Chezy coefficient. At the second step, the wide rectangular channel is investigated using Manning equation as the resistance equation. Finally, the perturbation solution is presented for an ordinary rectangular channel using Manning equation. Obtained GVF profiles using the perturbation solutions are compared with finite difference method (FDM) profiles. Results show that PM profiles are in excellent agreements with FDM ones, and therefore, PM solutions may be used to obtain GVF profiles in mentioned cases with high levels of accuracy. It was concluded that developed semi-analytical solutions may be used as reference solutions for efficiency assessment in various numerical techniques that provide solution for GVF profile in open channels.

Morphometric elements of the channel and hydraulic flow parameters in the zone of the river backwater

The article is devoted to the analysis of the dynamics of the morphometry of the river bed and the hydraulic parameters of the flow under conditions of flow regulation. For the analysis of the dynamics of the bed morphometry and hydraulic elements of the flow, the Nietbaitas hydro-array located in the zone of the sub-flow of the lower reaches of the Amudarya river in Uzbekistan was selected. As a result of the analysis of data from long-term field studies and hydrometric measurements at the Nietbaitas hydrostorm of the Amudarya river, functional relationships were established between the morphometric elements of the channel and the hydraulic parameters of the flow. The dynamics of the Chezy coefficient, hydraulic resistance, and the roughness coefficient of the channel in conjunction with the hydrodynamic characteristic of the flow are established. Adapted formulas are recommended for determining the calculated values of the Chezi coefficients, roughness, and average flow velocity, taking into account the decelerating effect of the banks of the Amudarya river bed

Dynamics of hydraulic resistance in the zone of constraint of the riverbed

The article is devoted to the analysis of the dynamics of the morphometric parameters of the river channel and the hydraulic parameters of the flow under constrained conditions. The Kipchak hydraulic track located in the lower reaches of the Amu Darya River, constrained by the pontoon bridge, is characterized by intensive channel processes. The dynamics of the hydraulic resistance of the channel depending on the flow during the periods of observation in a confined section of the river has a wide range of 0.045 to 0.068, with a change in the roughness of the channel within 0.0195 to 0.065. The calculated values of the flow rates, taking into account the inhibitory effect of the river banks, gave a satisfactory agreement with the measured ones, the hydraulic resistance of the channel, depending on the value of this parameter, varied within 0.045 to 0.068 with the dynamics of the Chezy coefficient from 27 to 67 m0.5 / s

ASSESSMENT OF ROUGHNESS COEFFICIENT VALUE

The article considers one of the main parameters while conducting water management calculations – the roughness coefficient. Up-to-date assessment of its value is carried out according to special tables or by calculation. Article presents various methods for calculating the roughness coefficient – from the reverse evaluation using the Chezy formula by the measurements to the empirical relations obtained by various specialists on the basis of field studies. In addition, the authors considered formulas for calculating the roughness coefficient based on physics. The results of calculations obtained for such formulas best fit their values obtained in the inverse way from the Chezy formula. The calculation methods presented in the article were tested on the data of gauging station on the river Polist' – near the settlement Podtopol'e for the period of 1954 year and on the river Gozovka – near the settlement Goza for the period 2014-2017. Behind comparing the results of measurements, calculations for various formulas and estimated tabular data, the authors made the following conclusions. Pressure losses in explicit depends on the depth of the stream and the slope of the free surface, the last one implicitly characterizes the frictional of the channel. At the same water flow rates, a change in the roughness coefficient can reach tens of percent. With different filling of the channel, the roughness coefficient can change by several times, which predetermines the corresponding errors in the tabular estimation of the roughness coefficient, even for a simplified case – only for an open channel. Therefore, all the dependencies, taking into account only the granulometric of riverbed deposits, basically can not have practical application. General conclusion: even with the same water level for simplified conditions of an open channel without vegetation, the roughness coefficient can differ by several times, which nullifies all attempts to theoretically evaluate it in the absence of direct measurements of slope, speed, and average depth.

Maximum water level calculation based on 2-dimensional DELFT-3D model, the case study of the Oka river

This research represents methodical approach and main results of water level hydrodynamic modeling for real summer low-water season and extreme spring flood of 1% probability. The object of modeling is 105 km length section of the Oka River in Moscow region between Kashira and Kolomna urban districts. Modeling object includes also the Moscow River section downstream the Severka River mouth. Two-dimensional hydrodynamic model constructed using DELFT-3D. To build the model we used the detailed elevation model and hydrological conditions based on in-situ measurements in 2019, special estimated discharge and water level time-series of 1% exceedance probability based on reference year observations and distributed Chezy coefficient calibration. The model implementation resulted in the actual detailed distribution of the water discharge, velocity and level along the Oka River section (including the downstream Moscow River) for low-water and extremely high water periods. These results are used for the flood zone delineation in the Kashira and Kolomna urban districts.