scholarly journals Evaluating Different Methods for Determining the Velocity-Dip Position over the Entire Cross Section and at the Centerline of a Rectangular Open Channel

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 605
Author(s):  
Zhongfan Zhu ◽  
Pengfei Hei ◽  
Jie Dou ◽  
Dingzhi Peng
Keyword(s):  
Experimental Data ◽  
Cross Section ◽  
Shannon Entropy ◽  
Open Channel ◽  
Lateral Distribution ◽  
Tsallis Entropy ◽  
The Other ◽  
Deterministic Models ◽  
Entire Cross Section ◽  
General Index

The velocity profile of an open channel is an important research topic in the context of open channel hydraulics; in particular, the velocity-dip position has drawn the attention of hydraulic scientists. In this study, analytical expressions for the velocity-dip position over the entire cross section and at the centerline of a rectangular open channel are derived by adopting probability methods based on the Tsallis and general index entropy theories. Two kinds of derived entropy-based expressions have the same mathematical form as a function of the lateral distance from the sidewall of the channel or of the aspect ratio of the channel. Furthermore, for the velocity-dip position over the entire cross section of the rectangular open channel, the derived expressions are compared with each other, as well as with two existing deterministic models and the existing Shannon entropy-based expression, using fifteen experimental datasets from the literature. An error analysis shows that the model of Yang et al. and the Tsallis entropy-based expression predict the lateral distribution of the velocity-dip position better than the other proposed models. For the velocity-dip position at the centerline of the rectangular open channel, six existing conventional models, the derived Tsallis and general index entropy-based expressions, and the existing Shannon entropy-based models are tested against twenty-one experimental datasets from the literature. The results show that the model of Kundu and the Shannon entropy-based expression have superior prediction accuracy with respect to experimental data compared with other models. With the exception of these models, the Tsallis entropy-based expression has the highest correlation coefficient value and the lowest root mean square error value for experimental data among the other models. This study indicates that the Tsallis entropy could be a good addition to existing deterministic models for predicting the lateral distribution of the velocity-dip position of rectangular open channel flow. This work also shows the potential of entropy-based expressions, the Shannon entropy and the Tsallis entropy in particular, to predict the velocity-dip position at the centerline of both narrow and wide rectangular open channels.

scholarly journals An Expression for Velocity Lag in Sediment-Laden Open-Channel Flows Based on Tsallis Entropy Together with the Principle of Maximum Entropy

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 522 ◽  
Author(s):  
Zhongfan Zhu ◽  
Jingshan Yu ◽  
Jie Dou ◽  
Dingzhi Peng
Keyword(s):  
Maximum Entropy ◽  
Shannon Entropy ◽  
Open Channel ◽  
Tsallis Entropy ◽  
Channel Flows ◽  
Test Cases ◽  
Deterministic Models ◽  
Open Channel Flows ◽  
Principle Of Maximum Entropy ◽  
Principle Of Maximum

In the context of river dynamics, some experimental results have shown that particle velocity is different from fluid velocity along the stream-wise direction for uniform sediment-laden open-channel flows; this velocity difference has been termed velocity lag in the literature. In this study, an analytical expression for estimating the velocity lag in open-channel flows was derived based on the Tsallis entropy theory together with the principle of maximum entropy. The derived expression represents the velocity lag as a function of a non-dimensional entropy parameter depending on the average and maximum values of velocity lag from experimental measurements. The derived expression was tested against twenty-two experimental datasets collected from the literature with three deterministic models and the developed Shannon entropy-based model. The Tsallis entropy-based model agreed better with the experimental datasets than the deterministic models for eighteen out of the twenty-two total real cases, and the prediction accuracy for the eighteen experimental datasets was comparable to that of the developed Shannon entropy-based model (the Tsallis entropy-based expression agreed slightly better than the Shannon entropy-based model for twelve out of eighteen test cases, whereas for the other six test cases, the Shannon entropy-based model had a slightly higher prediction accuracy). Finally, the effects of the friction velocity of the flow, the particle diameter, and the particles’ specific gravity on the velocity lag were analyzed based on the Tsallis entropy-based model. This study shows the potential of the Tsallis entropy theory together with the principle of maximum entropy to predict the stream-wise velocity lag between a particle and the surrounding fluid in sediment-laden open-channel flows.

scholarly journals Estimating the Bed-Load Layer Thickness in Open Channels by Tsallis Entropy

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 123 ◽  
Author(s):  
Zhongfan Zhu ◽  
Jingshan Yu
Keyword(s):  
Experimental Data ◽  
Shannon Entropy ◽  
Mass Density ◽  
Particle Diameter ◽  
Tsallis Entropy ◽  
Cumulative Distribution ◽  
Open Channels ◽  
Bed Load ◽  
Deterministic Models ◽  
Prediction Ability

In the research field of river dynamics, the thickness of bed-load is an important parameter in determining sediment discharge in open channels. Some studies have estimated the bed-load thickness from theoretical and/or experimental perspectives. This study attempts to propose the mathematical formula for the bed-load thickness by using the Tsallis entropy theory. Assuming the bed-load thickness is a random variable and using the method for the maximization of the entropy function, the present study derives an explicit expression for the thickness of the bed-load layer as a function with non-dimensional shear stress, by adopting a hypothesis regarding the cumulative distribution function of the bed-load thickness. This expression is verified against six experimental datasets and are also compared with existing deterministic models and the Shannon entropy-based expression. It has been found that there is good agreement between the derived expression and the experimental data, and the derived expression has a better fitting accuracy than some existing deterministic models. It has been also found that the derived Tsallis entropy-based expression has a comparable prediction ability for experimental data to the Shannon entropy-based expression. Finally, the impacts of the mass density of the particle and particle diameter on the bed-load thickness in open channels are also discussed based on this derived expression.

A comparative study of two experimental techniques for the measurement of residual stresses in circular rods and tubes of perspex

1989 ◽  
Vol 24 (3) ◽  
pp. 163-171
Author(s):  
R K Mittal ◽  
I A Khan
Keyword(s):  
Residual Stresses ◽  
Cross Section ◽  
The Other ◽  
Experimental Techniques ◽  
Entire Cross Section ◽  
Sum Rule ◽  
Thin Walled ◽  
Removal Technique ◽  
Non Destructive ◽  
Distribution Of Stresses

Two experimental techniques have been used to measure residual stresses in circular rods and tubes of perspex, i.e., polymethyl methacrylate (PMMA). The first technique, based on photoelasticity, is non-destructive and easy to apply. It gives distribution of stresses over the entire cross-section. The analysis of this technique has been improved to relax some restrictions. The other technique is the layer removal technique. A serious drawback of this technique is that it fails to give the distribution of stresses over the entire cross-section and its accuracy for thin walled tubes is doubtful. A simplification of this technique is possible if the kinematic assumption introduced by Nishimura is replaced by one using the sum rule of stresses.

Numerical Computation of Flow in Rotating Ducts

1977 ◽  
Vol 99 (1) ◽  
pp. 148-153 ◽  
Author(s):  
A. K. Majumdar ◽  
V. S. Pratap ◽  
D. B. Spalding
Keyword(s):  
Experimental Data ◽  
Kinetic Energy ◽  
Finite Difference ◽  
Numerical Computation ◽  
Cross Section ◽  
Dissipation Rate ◽  
Rectangular Cross Section ◽  
Longitudinal Direction ◽  
The Other ◽  
Constant Area

A finite-difference procedure is employed to predict the turbulent flow in ducts of rectangular cross-section, rotating about an axis normal to the longitudinal direction. The flows were treated as “parabolic” and the turbulence model used involved the solution of two differential equations, one for the kinetic energy of the turbulence and the other for its dissipation rate. Agreement with experimental data is good for a constant-area duct at low rotation, but less satisfactory for a divergent duct at larger rotation. It is argued that a “partially-parabolic” procedure will be needed to predict the latter flow correctly.

The origin of the epidermis in the supernumerary regenerates of triple legs in cockroaches (Blattaria)1

Development ◽  
1972 ◽  
Vol 28 (1) ◽  
pp. 185-208
Author(s):  
Horst Bohn
Keyword(s):  
Cross Section ◽  
The Other ◽  
Entire Cross Section ◽  
Leucophaea Maderae ◽  
Gromphadorhina Portentosa ◽  
Anterior Posterior

An attempt has been made to clarify the origin of the supernumerary regenerates of triple legs by transplantations between two species of cockroaches, Gromphadorhina portentosa and Leucophaea maderae. The three ways of combining stump and transplant tissues were: heteropleural, dorso-dorsal, antero-posterior (I); heteropleural, dorso-ventral, antero-anterior (II); homopleural, dorso-ventral, antero-posterior (III). The transplantations have been performed at the level of the tibia as well as at the level of the coxa. (1) The supernumerary regenerates were partly mixed, i.e were composed of a mosaic of the tissues of both species of cockroach, partly homogeneously built up by the tissues of only one of the two species. In combination I nearly all regenerates were mixed; in the other two combinations homogeneous regenerates were relatively numerous, sometimes even the most numerous. Both supernumerary regenerates of a triple leg might be mixed; or one was homogeneous and the second mixed; or they were both homogeneous. In the latter case one regenerate was built up by Gromphadorhina tissues, the other by Leucophaea tissues, or, more rarely, both were built by up Gromphadorhina tissues. (2) The intraspecific transplantations simultaneously done in Leucophaea gave results which correspond in general with the results of the interspecific transplantations. (3) From the composition of the supernumerary regenerates it must be concluded that the four different properties of a cross-section (anterior, posterior, etc.) are not yet determined irreversibly in the tissues of the cockroach legs. Thus, missing properties may be completed by the other properties to give an entire cross-section.

scholarly journals Comparison of Conventional Deterministic and Entropy-Based Methods for Predicting Sediment Concentration in Debris Flow

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 439 ◽  
Author(s):  
Zhongfan Zhu ◽  
Hongrui Wang ◽  
Bo Pang ◽  
Jie Dou ◽  
Dingzhi Peng
Keyword(s):  
Debris Flow ◽  
Maximum Entropy ◽  
Shannon Entropy ◽  
Sediment Concentration ◽  
Tsallis Entropy ◽  
Principle Of Maximum Entropy ◽  
General Index ◽  
Deterministic Methods ◽  
The Mean ◽  
Principle Of Maximum

In this study, the distribution of sediment concentration and the mean sediment concentration in debris flow were investigated using deterministic and probabilistic approaches. Tsallis entropy and Shannon entropy have recently been employed to estimate these parameters. However, other entropy theories, such as the general index entropy and Renyi entropy theories, which are generalizations of the Shannon entropy, have not been used to derive the sediment concentration in debris flow. Furthermore, no comprehensive and rigorous analysis has been conducted to compare the goodness of fit of existing conventional deterministic methods and different entropy-based methods using experimental data collected from the literature. Therefore, this study derived the analytical expressions for the distribution of sediment concentration and the mean sediment concentration in debris flow based on the general index entropy and Renyi entropy theories together with the principle of maximum entropy and tested the validity of existing conventional deterministic methods as well as four different entropy-based expressions for the limited collected observational data. This study shows the potential of using the Tsallis entropy theory together with the principle of maximum entropy to predict sediment concentration in debris flow over an erodible channel bed.

scholarly journals A Simple Explicit Expression for the Flocculation Dynamics Modeling of Cohesive Sediment Based on Entropy Considerations

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 845 ◽  
Author(s):  
Zhongfan Zhu
Keyword(s):  
Experimental Data ◽  
Explicit Expression ◽  
Shannon Entropy ◽  
Growth Pattern ◽  
Cohesive Sediment ◽  
Tsallis Entropy ◽  
Cumulative Distribution ◽  
Power Relationship ◽  
Floc Size ◽  
Flocculation Time

The flocculation of cohesive sediment plays an important role in affecting morphological changes to coastal areas, to dredging operations in navigational canals, to sediment siltation in reservoirs and lakes, and to the variation of water quality in estuarine waters. Many studies have been conducted recently to formulate a turbulence-induced flocculation model (described by a characteristic floc size with respect to flocculation time) of cohesive sediment by virtue of theoretical analysis, numerical modeling, and/or experimental observation. However, a probability study to formulate the flocculation model is still lacking in the literature. The present study, therefore, aims to derive an explicit expression for the flocculation of cohesive sediment in a turbulent fluid environment based on two common entropy theories: Shannon entropy and Tsallis entropy. This study derives an explicit expression for the characteristic floc size, assumed to be a random variable, as a function of flocculation time by maximizing the entropy function subject to the constraint equation using a hypothesis regarding the cumulative distribution function of floc size. It was found that both the Shannon entropy and the Tsallis entropy theories lead to the same expression. Furthermore, the derived expression was tested with experimental data from the literature and the results were compared with those of existing deterministic models, showing that it has good agreement with the experimental data and that it has a better prediction accuracy for the logarithmic growth pattern of data in comparison to the other models, whereas, for the sigmoid growth pattern of experimental data, the model of Keyvani and Strom or Son and Hsu model could be the better choice for floc size prediction. Finally, the maximum capacity of floc size growth, a key parameter incorporated into this expression, was found to exhibit an empirical power relationship with the flow shear rate.

The Experimental Study of Residential Kitchen Gradually Expanding Oriented Structural Member Exhaust Pipe System Characteristics

2012 ◽  
Vol 610-613 ◽  
pp. 2827-2831
Author(s):  
Yue Ren Wang ◽  
Bo Song ◽  
Zhi Yang Su
Keyword(s):  
Experimental Data ◽  
Cross Section ◽  
Structural Member ◽  
The Other ◽  
Exhaust Pipe ◽  
Pipe System ◽  
Operating Rate ◽  
The Cross ◽  
System Characteristics ◽  
Better Than

The purpose of this paper is to study the residential kitchen exhaust pipe system by introducing a gradually expanding oriented structural member called GEOSM for short and analyze the experimental effects of exhaust volume. With the change of the operating rate, we can obtain the best size of the GEOSM. In order to collate and analyze the experimental data, test the experimental effects of the g GEOSM of different sizes. Not only the pressure of main and branch but also the wind speed of the branch is recorded in this paper. In six floors of 400*250 gradually expanding oriented structural member exhaust pipe system, the fan’s volume can completely meet the basic requirements of everyday life whether its volume is high-end or low-end. The effect of exhaust is obviously better than the other size of the GEOSM when the cross section width of the GEOSM is 150mm and the cross section length of the GEOSM is 250mm, the height of the GEOSM is 350mm.There arises more smoke down when the cross section width of the GEOSM is 150mm and the cross section length of the GEOSM is 300mm, the height of the GEOSM is 350mm

scholarly journals Modelling the Hindered Settling Velocity of a Falling Particle in a Particle-Fluid Mixture by the Tsallis Entropy Theory

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 55 ◽  
Author(s):  
Zhongfan Zhu ◽  
Hongrui Wang ◽  
Dingzhi Peng ◽  
Jie Dou
Keyword(s):  
Experimental Data ◽  
Settling Velocity ◽  
Concentration Function ◽  
Tsallis Entropy ◽  
Entropy Theory ◽  
Clear Fluid ◽  
Deterministic Models ◽  
Fluid Mixture ◽  
Hindered Settling ◽  
Hindered Settling Velocity

The settling velocity of a sediment particle is an important parameter needed for modelling the vertical flux in rivers, estuaries, deltas and the marine environment. It has been observed that a particle settles more slowly in the presence of other particles in the fluid than in a clear fluid, and this phenomenon has been termed ‘hindered settling’. The Richardson and Zaki equation has been a widely used expression for relating the hindered settling velocity of a particle with that in a clear fluid in terms of a concentration function and the power of the concentration function, and the power index is known as the exponent of reduction of the settling velocity. This study attempts to formulate the model for the exponent of reduction of the settling velocity by using the probability method based on the Tsallis entropy theory. The derived expression is a function of the volumetric concentration of the suspended particle, the relative mass density of the particle and the particle’s Reynolds number. This model is tested against experimental data collected from the literature and against five existing deterministic models, and this model shows good agreement with the experimental data and gives better prediction accuracy than the other deterministic models. The derived Tsallis entropy-based model is also compared with the existing Shannon entropy-based model for experimental data, and the Tsallis entropy-based model is comparable to the Shannon entropy-based model for predicting the hindered settling velocity of a falling particle in a particle-fluid mixture. This study shows the potential of using the Tsallis entropy together with the principle of maximum entropy to predict the hindered settling velocity of a falling particle in a particle-fluid mixture.

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