Estimating discharge in drainage channels through measurements of surface velocity alone: A case study

In the scientific literature it is possible to find at least two methods for estimating discharge in an open channel which represent a valid alternative to the Velocity-Area method; both offer a considerable advantage in that they are simple to apply and require knowledge solely of the channel bathymetry and maximum surface velocity. The first method is based on the entropy concept introduced into hydraulics by Chiu in the 1990s, whilst the second is focused on the reconstruction of dimensionless isovels in the channel cross-section.Both the methods have been extensively described in previous works and validated for medium/large-sized cross-sections where surface measurements are taken by current-meter or Acoustic Doppler Current Profiler (ADCP) sensor. In this technical paper, they are instead applied to a water drainage channel in a reclamation territory characterized by a very low velocity which required a particular measuring technique, called “total station”. This technique demonstrated to be reliable in situations where the velocity is very low and cannot be measured with other “no-contact” techniques, such as those based on the Doppler method, which are normally used when the use of current meters is not possible.     

Discussion of “Estimation of one-dimensional velocity distribution by measuring velocity at two points” by Yeganeh and Heidari (2020)

The concept of information entropy together with the principle of maximum entropy to open channel flow is essentially based on some physical consideration of the problem under consideration. This paper is a discussion on Yeganeh and Heidari (2020)'s paper, who proposed a new approach for measuring vertical distribution of streamwise velocity in open channels. The discussers argue that their approach is conceptually incorrect and thus leads to a physically unrealistic situation. In addition, the discussers found some wrong mathematical expressions (which are assumed to be typos) written in the paper, and also point out that the authors did not cite some of the original papers on the topic.     

Discharge prediction in flow measurement flumes with different downstream transition slopes

Experimental testing of 9 different rectangular compound cross-section flow measurement flumes with different downstream slopes was conducted to yield the coefficient of discharge and the approach velocity coefficient. The aim of the experimental research was the determination of stage–discharge relationship in compound cross-section flow measurement flumes with different downstream slopes. One empirical predictive model for each of the coefficient of discharge and the approach velocity coefficient for the 9 cross-sections have been derived using one dimensionless parameter for the coefficient of discharge and another one dimensionless parameter for the approach velocity coefficient as the single independent variable. This approach is preferred as it allows the estimation of discharge by only measuring the water depth at the head measurement section. All obtained predictive models statistics have indicated the high reliability of the derived models in estimating discharge in an open channel flume of a rectangular compound cross-section using the predicted coefficients.     

Estimating the flow velocity and discharge of ADCP unmeasured area in tidal reach

Due to the ringing and side-lobe interference, acoustic Doppler current profiler (ADCP) is unable to accurately capture the complete velocity profile in open channels near the water surface and channel bottom, which are usually called unmeasured areas. At present, the flow velocities through the unmeasured areas are most commonly estimated using the power law with the power set to be the default value. However, since the flows are unsteady and nonuniform in tidal reaches, the velocity distribution model and corresponding parameters will vary with the bathymetric, tide period, etc. Therefore, the most common estimation with the power law may not be suitable in tidal reaches. In this paper, a simple determination method of the best model is proposed. Firstly, the parameters in three classical velocity distribution models, which are called power law, logarithmic law and parabolic law models, are solved by least squares based on the ADCP measured velocity cells. Then, the corresponding root-mean-square error (RMSE) of each model is used for the quantitative indicator that the model with the minimum RMSE is chosen as the best model. At last, the flow velocity and discharge of the unmeasured area are estimated by the best model. The experiments carried out in the tidal reach of Yangtze Estuary showed that vertical flow velocity distribution various with the bathymetry and tide period, and the best models averagely improved about 2.0% of the relative standard deviation (RSD) relative to the power law method in the discharge estimation, especially at some tide period the RSD of the best model was several times better than that of power law model. For Yangtze River with an annual average discharge of 3.0×10⁴ m³/s, the improvement should not be ignored. Therefore, it will be necessary to use the best model with minimum RMSE to estimate the flow velocity in tidal reach.     

Image-based river discharge estimation by merging heterogeneous data with information entropy theory

An information entropy based approach for the discharge measurements is evaluated for the gaging of the Isère river at the Grenoble university campus. Over a four month period, six discharge measurements were made using a vessel-mounted aDcp. Simultaneously, particle tracking velocimetry (PTV) from video images was used to estimate surface velocities. The surface velocities are projected along the regularly surveyed river section of the Isère-Campus gaging station. The vertical velocity profile at each stream-wise location is approximated by a 1D entropy profile. Information entropy 1D velocity vertical profile depends on two parameters which are fitted using aDcp and surface velocity measurements. The inclusion of the surface velocities reduces the dispersion of the estimated entropy parameters. The measurements show that the two parameters are linearly related with a slope that is stage dependent and thus, surface velocity dependent. From there, the information entropy theory for 1D velocity distribution offers a protocol by which surface velocities only are used to compute the discharges. The protocol is calibrated with both aDcp and surface velocity measurements. It is finally validated with several events during which only surface velocities are measured. For the high water flood event the estimated discharge falls within 2% of the one estimated with the rating curve of the gaging station.     

Flow measurement using free over-fall in generalized trapezoidal channels based on one velocity point method

A free over-fall offers the possibility of being used as a flow measuring device in hydraulic structures with a single depth measurement of the end section. Due to its practical importance, considerable attention has been paid to investigate free over-falls for different channel cross-sections using various approaches. This paper presents a new theoretical approach for computing the end depth ratio (EDR) relationship for the generalized trapezoidal channel cross-sections at free over-falls in sub critical flow regimes from which the end depth discharge (EDD) can be computed. The generalized trapezoidal channel is a geometric shape that is defined mathematically with a single equation where five widely known prismatic channel cross-sectional shapes can be generated (trapezoidal, inverted triangular (Δ), rectangular, parabolic, and triangular). This suggested theoretical approach uses one velocity point at the geometric center of the end section based on the energy and the continuity equations. Relevant experimental and theoretical results were utilized in order to examine the suggested method through the statistical measuring indices (percentage difference and the correlation coefficient (R²)). The computed results show very close agreements with the earlier works. Furthermore, simple equations are also generated using the regression curve fitting technique in order to estimate the direct discharges (Q) using the end depth (y_e) for each of the above mentioned channel cross-sections.     

Weir velocity formulation for sharp-crested rectangular weirs

Discharge in open channels can be measured by sharp-crested rectangular weirs. Generally, measured head over the weir crest is substituted into an empirical formula derived from energy considerations to calculate the discharge. Assumptions made on the derivation are taken into account by defining a discharge coefficient that fits into the experimental data. In this study, a physical quantity, the average velocity over the weir section defined as ‘weir velocity’ is directly formulated as function of weir geometry and head over the weir. Weir velocity plotted against the weir head has a universal behavior for constant weir width to channel width ratio independent of the weir size. This unique behavior is described in terms of weir parameters to calculate the discharge without involving a discharge coefficient. Combining weir velocity data for variable weir widths provides a basis for direct formulation of discharge. The weir velocity exhibits simpler functional dependency on weir parameters in contrast to the discharge coefficient.     

Analysis of acoustic Doppler current profiler mean velocity measurements in shallow flows

Acoustic Doppler current profilers (ADCPs) are commonly used instruments for measurement of natural streamflow and flow in manmade channels. Velocities measured in a profile by the instrument are used to estimate the discharge in a channel. A Teledyne RD Instruments StreamPro ADCP was used to measure the mean velocity simultaneously with a laser Doppler anemometer (LDA) in a laboratory flume. An average of 3.9% under-prediction of the mean velocity measured by the ADCP occurred when compared to the measurements of the LDA. Moreover, this study shows that the sampling duration of the measurements significantly impacts the mean point velocities measured by up to 50%.     

The measurement of discharge using a commercial digital video camera in irrigation canals

This paper presents measurements of the discharge by image techniques on the surface velocity field and water stage in irrigation canals. The velocity and stage gauge are obtained from a commercial digital video camera. The time series of the surface velocity and stage were collected simultaneously. Particle image velocimetry (PIV) was used to determine the surface velocities in the irrigation canal. PIV proceeds by using bubbles floating on the water surface as tracer particles, and making a cross-correlation analysis between two continuous images. The whole surface velocity distribution in the irrigation canals can be obtained. The water stage of the canal is obtained from the digital video camera images by making use of image segments to separate the stage gauge and the background. The discharge is computed by using the surface velocities and water stage via open channel velocity distribution theory. Comparing the discharge measured using image techniques with Parshall flume data shows that the differences are less then 5%. The results suggest that the image measurement techniques developed can be used in applications to estimate the discharge in irrigation canals effectively.     

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.     

Calculation of mean velocity and discharge using water surface velocity in small streams

Calculation of mean velocity and discharge are very important for demands such as water management, water supply, irrigation and flood control. This paper presents to determine the mean velocity and discharge in small streams using based water surface velocity. For this purpose, flow measurements were carried out at four different cross-sections at eighteen field measurements in central Turkey. The mean velocities (U_m) were calculated using velocity–area method. (U_m) and water surface velocities (u_ws) at these stations exhibited a linear distribution as U_m=0.552u_ws which has R²=0.99 determination coefficient. It was observed that this constant was smaller than the literature value 0.85. The advantage of this ratio is that it does not change in T/R (T; width of cross-section, R; hydraulic radius) and Froude numbers for the small streams. Using this constant, mean velocities (U_mcal) and discharges (Q_mcal) for all measurements can be calculated. The average relative error between measured and calculated discharges (Q−Q_mcal) was found to be 4.08%. The results presented that this method can be utilized to determine the mean velocity and discharge in small streams successfully.     

Measuring river velocity and discharge with acoustic Doppler profilers

Acoustic Doppler profilers and associated software packages presently are being used to measure water velocity, channel bathymetry, and river discharge. The instruments have various configurations and frequencies; choice of the appropriate instrument depends on various factors including depth, width, and sediment load of the rivers being measured. The acoustic Doppler profilers are mounted on powerboats or small remote-controlled or tethered rafts or catamarans. Profilers enable users to make fast, accurate, and economical discharge measurements on large rivers and rivers with unsteady flow conditions because of flooding or irregular releases from reservoirs. This article describes the principles of operation, application of acoustic Doppler profilers to the measurement of velocity and discharge, and calibration and verification issues.     

Modified cuckoo search algorithm in microscopic image segmentation of hippocampus

Microscopic image analysis is one of the challenging tasks due to the presence of weak correlation and different segments of interest that may lead to ambiguity. It is also valuable in foremost meadows of technology and medicine. Identification and counting of cells play a vital role in features extraction to diagnose particular diseases precisely. Different segments should be identified accurately in order to identify and to count cells in a microscope image. Consequently, in the current work, a novel method for cell segmentation and identification has been proposed that incorporated marking cells. Thus, a novel method based on cuckoo search after pre‐processing step is employed. The method is developed and evaluated on light microscope images of rats’ hippocampus which used as a sample for the brain cells. The proposed method can be applied on the color images directly. The proposed approach incorporates the McCulloch's method for lévy flight production in cuckoo search (CS) algorithm. Several objective functions, namely Otsu's method, Kapur entropy and Tsallis entropy are used for segmentation. In the cuckoo search process, the Otsu's between class variance, Kapur's entropy and Tsallis entropy are employed as the objective functions to be optimized. Experimental results are validated by different metrics, namely the peak signal to noise ratio (PSNR), mean square error, feature similarity index and CPU running time for all the test cases. The experimental results established that the Kapur's entropy segmentation method based on the modified CS required the least computational time compared to Otsu's between‐class variance segmentation method and the Tsallis entropy segmentation method. Nevertheless, Tsallis entropy method with optimized multi‐threshold levels achieved superior performance compared to the other two segmentation methods in terms of the PSNR.     

Application of video imagery techniques for low cost measurement of water surface velocity in open channels

Developments in digital video recording technology make the video imagery tools more popular for velocity measurement in water flows. This has especially been of large interest due to its inherent advantage of non-contact nature which is quite handy in extreme flow conditions. Particle Image Velocimetry (PIV), Particle Tracking Velocimetry (PTV) and Large Scale Particle Tracking Velocimetry (LSPTV) are applied to free surface channel flow for water surface velocity measurement. Experiments are conducted to measure either a single point velocity applying PTV or velocity profiles across the channel width applying PIV on the water surface in a rectang typical velocities of nearly 1 andular tilting flume for various flow conditions. Technical issues regarding tracer particle size and type, travel distance, lighting, recording speed, camera position, image distortion and state of flow are discussed. Measured data is compared to computational results obtained from a numerical model involving a non-linear turbulence model capable of predicting turbulence driven secondary flows. Confirmation of reasonable match between computational and experimental results whereby applying mutual collaboration of them for discharge measurement has been attested. In addition to discharge, boundary roughness has also been predicted as an outcome of the numerical solution.     

基于径向基神经网络的明渠流量软测量方法

为克服现有明渠流量测量方法在监测自动化、测量准确度、测量成本和适用范围等方面存在的不足,在新兴的大尺度粒子图像测速(large-scale particle image velocimetry,LSPIV)技术的框架下,设计了一种基于径向基神经网络(radial basis function neural networ...     

Flow velocity pattern around trapezoidal piano key side weirs

In general, the side weirs are the structures installed along a channel or river. When the flow depth rises above the weir crest, the overflow passes through these weirs and enters the lateral canal. Nowadays, piano key weirs are considered as an important alternative to labyrinth weirs to modify the weirs encountering with difficulty to pass the maximum flow discharges. The present study investigates the hydrodynamic performance and the effect of the uniformity of velocity field on the resultant kinetic energy in the trapezoidal piano key side weirs with 90° installed laterally in the main channel wall. These weirs are classified as A-Type piano key weirs and two approaches (main: Mode 1 and adverse: Mode 2) were used to investigate the effect of the weirs' placement on their performance. The results showed that for velocity vectors in both modes, on average, the maximum flow discharge through the side weir occurred in the x and y directions (V_x and V_y) at Z*<0.2 and 0.2<Y*<0.7. The results also showed that at the control surface of X* = 1, the maximum values of α occur due to existing the inverse flow and increasing the deflection angle of the velocity vectors. The performance of the weir in Mode 2 was more appropriate Mode 1 due to the lack of weir base at the flow inlet, which is an obstacle for the deflection angle of the velocity vectors.     

A simple model for estimation of dimensionless isovel contours in open channels

A simple model is proposed for predicting the dimensionless isovel contours in straight ducts and open channels. It is assumed that each element of the boundary influences the velocity at an arbitrary point in the cross section. Then, the total effect of the boundary can be obtained using integration along the wetted perimeter. In this paper, power and logarithmic laws are used, while any velocity profile can be applied in the model. The model is applied to calculate the normalized isovel contours in rectangular channels. Then they are used, in combination with a single-point velocity measurement at a cross section of the uniform flow, to estimate the discharge. The kinetic energy and momentum correction factors, and the ratio of maximum to mean velocity, are also calculated from isovel patterns. Calibration and validation of the model are carried out by comparing the results obtained with measurements of the velocity in the main flow direction along the centerline of a rectangular flume as well as in the transverse direction. Each point of measurement can be used to estimate the discharge. Then, the estimated discharge is compared with the actual measured one. Depending on the position of the measurement, the deviation of the calculated and measured discharges will be altered. Model predictions are well correlated with experimental data for rectangular open channels.     

A two-dimension velocity field measurement method for the thermal smoke basing on the optical flow technology

The confine and heat are remarkable features in building fire research, as well as is a barrier for flow velocity profiles measurement, which the general method is unsuitable for this experimental environment. Therefore, this paper develops a measurement method for the acquisition of the thermal smoke flow velocity profiles in the fire building experiment. Firstly, we utilize the smoke itself particle distribution to replace the manual track particles in which reduce the complexity of the measurement method for fire experiments system. Secondly, we optimize the non-uniform distribution of smoke soot particle and utility the smoke stratification characteristics basing on the optical flow technology. The four optimized methods were compared to acquire reasonable smoke velocity distributions. Finally, we take advantage of filter post-process method to smooth the smoke velocity profiles in the main transportation direction. Moreover, a series of experiments and simulations show the feasibility of this image-based method in which the pre-process, optical calculation and smooth methods were established to denote reasonably the smoke flow velocity gradient and inclined upward trend nearby the corridor open. Meanwhile, it is not only in acquiring two-dimension smoke field velocity, while also can fulfill the other particle flow movement.     

Synchronous measurements of the velocity and concentration in low density turbidity currents using an Acoustic Doppler Velocimeter

Low density turbidity currents have been investigated in a laboratory flume. An Acoustic Doppler Velocimeter (ADV) was used to measure the velocity. The dimensionless velocity profiles were compared with previous studies to check the accuracy of acoustic measuring techniques for turbidity currents. Successful use of the ADV to measure the current velocity has led to interest in the technique of using acoustic sensors to estimate concentrations. Acoustic backscattering analyses are used for estimating the sediment concentration in turbidity currents. With this approach, concentration measurements can be reasonably well represented by a similarity profile. Using this technique, an accurate estimation of the concentration close to the bed, where obtaining reliable concentration data by sampling techniques is difficult, is possible. The results show that a power relation is a good estimate for the concentration distribution in this region, for which no reliable expressions have been provided previously.Successful estimation of the velocity and concentration, in the present experiments, indicates that this technique could be appropriate and useful for determining the flow structure in turbidity currents.     

Flow resistance law under suspended sediment laden conditions

The uniform flow resistance equation, in the form due to Manning or Darcy-Weisbach, is widely applied to establish the stage-discharge relationship of a river cross-section. The application of this equation, namely the slope-area method, allows to indirectly measure the corresponding river discharge by measurements of bed slope, water level, cross-section area, wetted perimeter and an estimate of channel roughness. In this paper, a recently deduced flow resistance equation for open channel flow was tested during conditions of suspended sediment-laden flow. First, the flow resistance equation was determined by dimensional analysis and by applying the condition of incomplete self-similarity for the flow velocity profile. Then the analysis was developed by the following steps: (i) for sediment-laden flows characterized by known values of mean diameter and concentration of suspended sediments, a relationship (Eq. (28)) between the Γ function of the velocity profile, the channel slope and the Froude number was calibrated by the available measurements; and (ii) a relationship for estimating the Γ function (Eq. (29)) which also takes into account the mean concentration of suspended particles was also established. The theoretical flow resistance law (Eq. (26)) coupled with the relationship for estimating the Γ function (Eq. (28) or Eq. (29)), which is characterized by the applicability of a wide range of flow conditions, allowed to estimate the Darcy-Weisbach friction factor for flows with suspended-load. The analysis showed that for large-size mixtures the Darcy-Weisbach friction factor can be accurately estimated neglecting the effect of mean concentration of suspended sediments while for small-size mixtures the friction factor decreases when the mean sediment concentration increases.