Analysis Of Varied Flow Research Articles

Gradually Varied Flow Computation in Structured Irrigation Networks

In this paper an algorithm for analysis and design of a structured irrigation network and a traditional irrigation network are developed on the basis of the gradually varied flow analysis of the flow in the entire network. The model developed brings advantages of the structured irrigation network concept and also allows the user to analyses and design the flow distribution in the entire network. Model built around the gradually varied flow analysis model with a tree network is divided into a group based on network consisting of an initial value problem and also a boundary value problem with junctions as the reconciled boundaries. The essence of the model is that it can handle several types of structures such as head regulators, duckbill weirs in the main canal, an open flume, a pipe semi module, a pipe outlet with and without a sleeve, proportional distributors and tail clusters in the offtakes. These structures are very important from the standpoint of analysis and design for successful implementation of a structured irrigation network on an existing system and also for analysis and design of a traditional irrigation system consisting of many gates and other structures. The focus of this paper is the efficacy of the water management in ensuring equitable distribution of flow at different discharges released at the head works.

Study of Flow Characteristics Over a Rounded Edge Drop Structure in Open Channel

Flow over a drop structure is a form of free overfall called hydraulic drop. Hydraulic drop changes the nature of flow abruptly from sub-critical to super-critical condition. Rapidly varied flow analysis is a complex phenomenon and involves remarkable characteristics. Some of the drop structures constructed in Sindh and Punjab provinces of Pakistan had gone through diverse failures, consequential in interruption of water supply to irrigation fields encountering substantial economic loss. In the present study experiments were carried out in the hydraulic laboratory of Mehran University of Engineering and Technology on round edged drop structure fitted in a horizontal rectangular flume (channel model). Data regarding hydraulic drop and hydraulic jump characteristics were collected during the experiment. The observed data included: flow discharge (Q), radius of rounded edge drop structure (r), height of the structure (h), hydraulic drop length (Ld), hydraulic jump length (Lj), depth of flow at toe of the jump (Y1) and tailwater depth (Y2). Applying dimensional analysis, the non-dimensional parameters of the observed data were calculated. Using statistical analysis, empirical relationships among the non-dimensional parameters were established for the appropriate design of the drop structure. The research results showed that the length and depth indices are functions of D=q2gh3 and r/h values. It was also found that for rounded-edge drop structure, the length of the stilling basin (LSB) reduces as r/h ratio increases

만곡 및 세굴 영향에 의한 유속변화를 고려한 호안설계방법 적용성 검토

호안은 하천제방의 비탈면이 침식되지 않도록 보호하는 기능을 갖는다. 호안의 설계가 적정하지 않을 경우 강한 유속과 소류력에 의해 제방이 세굴되어 붕괴에 이를 수도 있다. 따라서 호안의 설계시 필요한 대표유속을 산정하는 것은 매우 중요하나 대부분 1차원 부등류해석에서 얻어진 수위와 평균유속자료를 적용한다. 이 경우 만곡 수로에서 발생하는 자유소용돌이와 강제소용돌이에 의한 유속증가는 반영되지 않으므로 만곡부 호안의 안정성을 확보하기 위해서는 대표유속에 대한 보정이 필요하다. 본 연구에서는 수치모의를 통해 단면의 최대유속과 평균유속을 산정하여 만곡 및 세굴영향을 고려한 대표유속 산정방법의 적용성에 대해 검토하였다. 그 결과 단면평균유속에 만곡의 영향과 세굴의 영향을 고려하여 적용한 대표유속과 수치모의결과에 추출된 최대유속을 비교한 결과가 거의 일치하는 것으로 나타났다. 또한, 호안재로로써 돌망태를 사용하는 경우에 대해서 만곡하도와 직선하도 일때의 사석크기를 기존 설계식에 적용하여 비교하였다. 향후, 우리나라의 특성에 맞는 호안설계방법을 제시하기 위하여 하천특성이 다른 대표적인 하천에 대한 추가적인 수치모의 및 분석이 필요하며, 이때 본 연구결과가 기초자료로 활용될 수 있을 것으로 기대된다. Revetments help protect levee slopes from erosion. If the design of the revetment is not appropriate, the levee may collapse as a result of scouring due to the strong flow velocity and tractive force. Therefore, when designing a revetment, it is very important to calculate the representative velocity. However, the average velocity and depth calculated by 1-D varied flow analysis are generally applied to the design, which do not reflect the increase in velocity caused by the free and force vortex. Therefore, it is necessary to correct the representative velocity in order to ensure the stability of the revetment in a meandering channel. In this study, the applicability of the method of calculating the representative velocity considering the curve and scour was studied (by comparing it with) the average and maximum velocities determined by numerical simulation. The representative velocity corrected for the effect of the curve and scour and the maximum velocity calculated by the numerical simulation were found to match quite well. In addition, the riprap size of the gabion in the meandering and straight channels were compared by applying them to the conventional design formulas. In the future, it is necessary to perform additional numerical simulations for various rivers with different characteristics, in order to propose a method of designing a suitable revetment for Korean characteristics. At this time, the results of this study are expected to be able to be used as basic data.

Equations for critical and normal depths of city-gate sections

Critical and normal depths are two important parameters in the design of open channels and the analysis of varied flow. For many practical sections, the governing equations for critical and normal depths are implicit and no analytical solutions exist. Various explicit equations have been developed for common open-channel sections. However, there are very limited studies on calculations of critical and normal depths for the city-gate section (CGS), which is one of the frequently used cross-sections for free-water conveyance tunnels. This paper presents equations for the geometric elements of standard CGSs used in water conveyance systems such as for irrigation, drainage and water supply projects. Based on the principle of gradual optimisation fitting, explicit equations for normal and critical depths of standard CGSs were developed for manual calculations with maximum relative errors of less than 1%. The proposed equations have a high accuracy for use in hydraulic design.

Explicit equations for critical depth in open channels with complex compound cross sections

Critical depth is an important parameter in the analysis of varied flow in open channels. For many practical sections, the governing equations for critical depth are implicit and no analytical solutions exist. Much work has been done to develop explicit equations for critical depth with various degrees of error in open channels with different shapes, especially in trapezoidal, circular, and horseshoe channels. However, for many other complex compound channel sections, such as quasi-trapezoidal, city-gate, and rounded-bottom trapezoidal sections, there are few studies on explicit equations for critical depth with both simple forms and satisfactory accuracy. This paper presents equations for the geometric elements of these complex cross sections. Based on the principle of gradual optimization fitting and iteration theory, explicit equations were developed for direct computation of critical depth for these three types of compound cross sections. The accuracy of the proposed equations was also evaluated. The proposed equations are suitable for manual calculations with high accuracy.

Head ditch hydraulics and the variability of inflows to irrigation furrows

AbstractThe spatial variability and temporal variation of furrow inflows have a major impact on the performance of furrow irrigation, as indicated by the usual measures of application efficiency and uniformity. They also cause difficulties in determining the soil infiltration characteristic through inverse solution techniques and in selecting preferred values for the operational variables of flow rate and time to cut‐off to give maximum performance at the field scale.In this paper a steady spatially varied flow analysis is performed to predict the steady water surface profiles in a typical head ditch and the subsequent spatial variability of the furrow inflows, for both pipe or siphon and sill or bankless‐type water application systems. The resulting patterns were very similar to those seen in the spatially varied pipe flow in gated pipe, with depths and outflows increasing toward the downstream end of the channel. It is shown that it is feasible to design head ditches to minimise the variability in outflows. An unsteady analysis of the same head ditch illustrated the variation of outflows with time caused by the time taken to fill the channel. Copyright © 2009 John Wiley & Sons, Ltd.

부등류 해석을 기반으로 한 노면배수시설 설계

노면배수시설의 설계방법을 임계지속시간의 고려 여부와 등류 및 부등류의 해석 방법에 따라 4가지로 구분하고, 각 방법에 따른 설계결과를 비교·검토하였다. 임계지속시간을 고려하지 않는 방법에서 설계강우는 10분 지속시간의 강우강도로 정하나, 임계지속시간을 고려할 경우 설계강우는 강우의 지속시간과 유출의 도달시간이 유사해지는 경우를 시산적으로 찾아 결정한다. 4가지 설계방법으로 수립된 설계모형을 다양한 수로의 종단경사 및 길어깨 횡단경사를 가지는 노면배수시설에 적용하고, 그 설계결과를 비교 검토하였다. 10분 지속시간의 강우강도를 이용하는 경우, 부등류 해석을 기반으로 설계한 유출구 간격은 종단경사와 길어깨 횡단경사가 작은 경우에만 등류 해석보다 크게 산정되었다. 반면 도달시간을 산정하여 임계지속시간을 결정하는 경우에는 본 연구에서 고려된 모든 조건에서 부등류 해석을 기반으로 설계한 유출구 간격이 등류 해석보다 크게 산정되었다. 그러나 도달시간을 산정하여 임계지속시간을 결정하고 부등류 해석을 기반으로 설계한 유출구 간격은 10분 지속시간의 강우강도를 적용하고 등류 해석을 기반으로 설계한 값보다 항상 작은 것으로 조사되었다. The design methods of the road surface drainage facilities were compared for the improvement of design method. We have developed four computational design models classified by the methods to determine the duration of design rainfall and to analyze the flow of a linear drainage channel. The critical duration was determined by assuming the critical duration to be 10 minutes or by finding the duration of design storm being similar to the travel time of flow by trial and error. The flow of a linear drainage channel was analyzed as the uniform flow or the varied flow. The design models were applied to the artificial road surface drainage facilities with various channel slopes and road shoulder slopes. If the rainfall intensity of the 10 minutes duration was applied, the outlet spacing obtained from the design based on the varied flow analysis was larger than the uniform flow analysis only when the channel slope and the road shoulder slope was small. On the other hands, if the duration of design rainfall was determined by calculating the travel time, the varied flow analysis brought about larger outlet spacing than the uniform analysis for all conditions. However, the model of the critical duration concept and the varied flow analysis resulted in smaller outlet spacing than the current design method employing the rainfall of 10 minutes duration and the uniform flow analysis.

선형 배수로에 대한 부등류 해석

본 연구는 노면배수시설에 이용될 수로 양단에 유출구를 가지며 유량이 연속적으로 증가하는 선형 배수로의 부등류 흐름의 해석 방법을 정립하기 위하여 수행되었다. 지배 방정식으로서 유한 차분 형태의 대수방정식을 사용하여 지배단면에서의 수심 값을 경계조건으로 Newton-Raphson 방법에 의하여 수면곡선을 계산하였다. 하류단에 유출구를 갖는 수로와 수로 양단에 유출구를 갖는 수로를 고려하고, 다양한 종단경사에 대하여 흐름 해석을 수행하였다. 단, 양단에 유출구를 갖는 수로의 경우 양단을 지배단면으로 만드는 임계 종단경사를 조사하여 이보다 작은 종단경사에 대한 흐름 해석을 수행하였으며, 임계경사는 지배단면의 위치와 종단경사의 관계로부터 결정하였다. 하류단에 하나의 유출구를 갖는 수로의 경우 수로 상에 존재하는 지배단면의 위치를 조사하여 그 지점을 기준으로 상류 및 하류 방향으로 수심을 계산한다. 반면 양단에 유출구를 갖는 수로의 경우 지배단면이 수로 양단이라면 분수계를 가정하여 분수계를 기점으로 구분되어지는 상류측 및 하류측 수로에 대한 흐름 해석을 수행하고, 상류단에서 분수계 방향으로 그리고 하류단에서 분수계 방향으로 계산된 분수계 지점의 두 수심이 동일할 때까지 흐름 계산을 반복한다. 흐름 계산 결과 양단에 유출구를 갖는 수로가 임계경사보다 큰 경사로 설치된 경우에는 하류단에 유출구를 갖는 수로의 흐름 거동과 유사지는 것으로 판단되었다. 노면배수시설 설계의 중요한 요소인 최대수심은 종단경사가 작을 때 등류 해석으로 계산된 값이 부등류 해석보다 크게 산정되었으며, 이는 종단경사가 작을 때 등류 해석을 기반으로 한설계가 과대설계가 되기 쉽다는 것을 의미한다. The present study was carried out to examine flow properties in linear drainage channels such as road surface drainage facilities. The finite difference formulation for the varied flow analysis was solved for flow profiles in the channels. Starting the first step at the control section, the Newton-Raphson method was applied for producing numerical solutions of the equation. We considered two types of linear drainage channels, a channel with one outlet at downstream end and a channel with two outlets at both ends. Moreover, the flow analysis for various channel slopes was performed. However, we considered channels with the two outlets of slopes satisfying the condition that the both ends are the control section. The maximum of those slopes was decided from the relation between the channel slope and the location of control section. The flow of a channel with one outlet was calculated upward and downward from the control section existing in channel or upward from the control section at downstream end. The flow of a channel with two outlets at both ends were calculated for upstream and downstream channel segments divided by the water dividend, respectively and the flow analysis was completed when the water depth at the water dividend calculated from upstream end was equal to that calculated from downstream end. If the slope was larger than the critical slope, the channel with two outlets was likely to behave like the channel with one outlet. The maximum water depth was investigated and compared with that calculated additionally from the uniform flow analysis. The uniform flow analysis was likely to lead a excessive design of a drainage channel with mild slope.

Exact Equations for Critical Depth in a Trapezoidal Canal

Critical depth is an important parameter in the analysis of varied flow in canals and natural streams. For triangular, rectangular, and parabolic channel sections it is possible to express critical depth analytically. However, for many practical sections, including the trapezoidal section, the governing equations are implicit in the critical depth. For these sections the critical depth is presently obtained either by trial and error procedure, or by using empirical equations based on curve fitting. In this Technical Note exact analytical solutions of critical depth for the trapezoidal open channel section have been obtained in the form of fast converging infinite series.

Exact Solutions for Normal Depth Problem

Normal depth is a key parameter occurring in the design of canals. It also occurs in the analysis of varied flow in canals and natural streams. The open channel resistance equation involves implicit form for all the practical canal sections. The solution of the implicit equation for normal depth involves tedious method of trial and error. Presented herein are the exact equations for normal depth for various open channel sections.

CRITICAL SLOPE EQUATIONS FOR OPEN CHANNELS

ABSTRACT Critical slope is a key parameter occurring in the analysis of varied flow in open channels. The analysis of varied flow under various operating conditions is required for design of canals. The available critical slope equations are based on the Manning's equation, which does not involve meaningful resistance parameters like average roughness height and the kinematic viscosity of water. Furthermore, the Manning's equation is applicable in the restricted range of relative roughness. Reported herein are explicit equations of critical slope for various open channel sections.

Spatially varied flow over rockfill embankments

A procedure for determining the flow conditions through and over a simple, rockfill embankment having a horizontal top surface is presented. In this situation, the free surface flow regime can be characterized as spatially varied and the seepage flow regime as non-Darcian. Included in the paper are a review of spatially varied flow theory and analysis, a brief description of the numerical method used to conduct the non-Darcy seepage analysis, a few comments with respect to the determination of the flow properties of the model rockfill, and a discussion of the application of the analysis procedure to a model rockfill embankment. Two flow conditions were tested. The one flow condition was for partial overtopping of the embankment, while the other involved complete overtopping. The spatially varied flow analysis was carried out using a spreadsheet, and it included the incorportion of Hinds' method for control point location. A modified version of a Darcian finite element seepage program was used for the seepage analysis. The computed results are compared with those obtained from a physical model. As shown in the paper, the results are generally supportive of the proposed modeling procedure. Key words: control point, non-Darcy seepage, numerical model, physical model, porous media, rockfill, spatially varied flow.

Critical Depth Equations for Irrigation Canals

Critical depth is an important parameter assuming the analysis of varied flow in the canals and natural streams. Direct solution of critical depth problems is not possible, as the governing equations for practical canal sections are implicit. The solution requires tedious computations of trial and error. Tabular and graphical methods are also available for solution. These methods are subject to errors of double interpolation or error of judgment in reading the graphs. No method is available for rounded-bottom and rounded-corner canal sections. Reported herein are explicit equations for critical depths in various sections used as irrigation channels.

Rapidly Varied Flow Analysis of Undular Bore

Exact expressions for the integral fluxes of mass, momentum, and energy in a steady wave on a uniform current lead to a consistent set of rapidly varied flow equations for an undular bore. Analysis of an undular bore depends crucially on the wave theory adopted for the estimation of the integral fluxes of mass, momentum, and energy, but it also depends on the residual power dissipation across the bore front. For Airy wave theory and no dissipation, there are no physically viable solutions. The observational evidence depicts finite amplitude waves in transitional water, and higher order wave theory does provide physically appropriate solutions that agree well with experiment. A separate rapidly varied flow analysis of the transition region between the undular and turbulent bore regimes anticipates the upper bound of the undular bore regime that is a feature of experimental observations. The transition region solution asymptotically approaches the classical turbulent bore solution at higher bore strengths.

BOUNDARY CONDITIONS FOR ANALYSIS OF FLOW IN TIDAL INLETS

One-dimensional gradually varied flow analysis of flood routing and inlet flows (Mahmood and Yevjevich, 1975; Amein, 1975 and Hinwood and Wallis, 1975) has been a subject of study in the last few decades and many mathematical models have been developed based on those studies. A common feature in all these models is that the boundary conditions at the ends of the channel reaches are supplied from measured values of stage, discharge or velocity. These boundary conditions form an integral part of the mathematical models. In the case of implicit schemes, without the supply of these boundary conditions there will be more unknowns than equations. Even though in the explicit schemes they are not required in order to supply sufficient equations, it is obvious that the flow will not be properly simulated without imposing proper end conditions of flow. Normally two end conditions will be required, the upstream and downstream conditions, even though in a network of channels there will be more than two end conditions. Of these two the upstream condition is usually the forcing function and the downstream one is the result of the flow due to the forcing function. The downstream condition depends on what happens to the flow outside the system. In other words, it depends on the shallow water wave reflections from the continuation of the channel beyond the downstream end of the system considered. These reflections are characterized by the expansion or contraction of the channel, the rate of change of the side slopes and other channel characteristics. As mentioned earlier, the downstream end condition is supplied from measured values of flow parameters so that the channel features (outside the system) mentioned above are automatically simulated. However, if it is required to know the response for any given forcing function, the corresponding measured downstream values may not be available. This means that the downstream boundary condition cannot be imposed in ,the usual way. This paper describes a method by which the downstream boundary condition can be imposed in the absence of measured downstream response to a given forcing function.