Linear Solution for Hydraulic Analysis of Tapered Microirrigation Laterals

A simplified analytical solution that takes into account the effect of the emitter discharge exponent on the hydraulic computations of tapered microirrigation laterals, is presented. The hydraulic analysis is evaluated based on the spatially variable discharge function approach. A simple power equation was used to express distribution of the variable outflow delivered from the each emitter along the lateral. An analytical solution is developed for the case of a linear relationship between the emitter discharge and pressure head, namely, the emitter discharge exponent equals to unique, y = 1.0. In this procedure, the analytical derivations can be applied for uphill, downhill, and zero slope conditions. Results are comparable to those obtained from the literature.     

Analytical Equation for Variation of Discharge in Drip Irrigation Laterals

Statistical uniformity of discharge variation is an important parameter in designing drip irrigation laterals. A simple analytical equation is derived to determine the coefficient of variation of discharge. This equation is used to determine the coefficient of variation of discharge for a numerical problem. The result is compared with the energy gradient line approach. Both the methods give the same result. For any required coefficient of variation of discharge, the diameter of a lateral can be designed directly for a known lateral length, slope, emitter discharge exponent, pressure head at the start of the lateral, and discharge rate through the lateral, by writing the analytical equation in quadratic form.     

Simple Method for the Design of Microirrigation Paired Laterals on Sloped Fields

In this study, a method for designing paired laterals that meet with required water application uniformity on sloped fields was developed using the energy gradient line approach based on the definition of the best submain position locations in which the same minimum pressure exists in uphill and downhill laterals. The best equation form of best submain position was determined. Also, the solution procedure was introduced to get the final solution to avoid the phenomena of no convergence or slow convergence. In this method, the required water application uniformity was used directly as a computational parameter in designing. When the designed emitter discharge, required water application uniformity and one parameter (either length or diameter) of a paired lateral are provided; the system developed here enables another parameter and the best submain position to be determined for any field slope conditions. Taken together, the results of this study show that final solutions can be obtained quickly and reasonably.     

Accuracy of Global Microirrigation Distribution Uniformity Estimates

Emitter pressures and flow rates were systematically and extensively sampled in one drip and one microspray field. The data distributions are presented. The accuracy of rapid (limited samples) evaluation pressure sampling procedures was found to be quite good if the pressure distribution was systematic, but erroneous if the pressure distribution throughout a field was random. A simple mathematical combination of two nonuniformity components (due to pressure differences, and other causes of flow variation) provided a better estimate of overall system distribution uniformity than more complex mathematics.     

Explicit Hydraulic Design of Microirrigation Submain Units with Tapered Manifold and Laterals

The optimum hydraulic design problem for microirrigation submain units of specified dimensions is solved analytically. New algebraic equations were derived to calculate explicitly the optimum values of the design variables. The design variables are the lengths of two given pipe sizes for the laterals as well as the appropriate lengths of the available pipe sizes for the manifold. Tapered laterals and manifold are selected in such a way that the sum of the costs of the laterals and the manifold is minimized, while the hydraulic design criterion is ensured. The case of a single-diameter lateral with tapered manifold pipeline is also examined. The design procedure can be also applied in sprinkle irrigation tapered laterals. The explicit optimum design solution is demonstrated in two cases studied.     

Optimum Design of Microirrigation Systems in Sloping Lands

When an area to be irrigated has a high slope gradient in the manifold line direction, an option is to use a tapered pipeline to economize on pipe costs and to keep pressure head variations within desired limits. The objective of this paper is to develop a linear optimization model to design a microirrigation system with tapered, downhill manifold lines, minimizing the equivalent annual cost of the hydraulic network and the annual pumping cost, and maximizing the emission uniformity previously established to the subunit. The input data are irrigation system layout, cost of all hydraulic network components, and electricity price. The output data are equivalent annual cost, pipeline diameter in each line of the system, pressure head in each node, and total operating pressure head. To illustrate its capability, the model is applied in a citrus orchard in S?o Paulo State, Brazil, considering slopes of 3, 6, and 9%. The model proved to be efficient in the design of the irrigation system in terms of the emission uniformity desired.     

Membrane Pervaporation for Wastewater Reuse in Microirrigation

A novel wastewater microirrigation technology for plants to extract reclaimed water from hydrophilic, homogenous dense membrane modules placed directly in the soil was evaluated. A series of tests were conducted in the laboratory to examine the effects of membrane configuration (hollow fiber (HF) and corrugated sheet (CS) membranes), soil texture (a loam and loamy sand soil), soil water content, feed pressure, and contaminant concentration on water permeate flux. The performance was evaluated in terms of soil water content, soil electroconductivity, water permeate flux and enrichment factor using borate, selenate, sodium chloride and glucose as model compounds. The results showed that the water permeate fluxes ranged from 0.21 to 1.04?L/m2/d for CS modules and from 0.10 to 1.00?L/m2/d for HF modules, respectively. Soil water content and feed pressure were identified as the main controlling factors for water flux. The enrichment factors were found to be less than 0.25 for all the tested contaminants. Thus, it was concluded that this membrane technology holds promise either to treat brackish ground water or to reuse wastewater for agricultural micro-irrigation.     

Discharge Rating Equation and Hydraulic Characteristics of Standard Denil Fishways

This paper introduces a new equation to predict discharge capacity in the commonly used Denil fishway using water surface elevation in the upstream reservoir and fishway width and slope as the independent variables. A dimensionless discharge coefficient based only on the physical slope of the fishway is introduced. The discharge equation is based on flow physics, dimensional analysis, and experiments with three full-scale fishways of different sizes. Hydraulic characteristics of flow inside these fishways are discussed. Water velocities decreased by more than 50% and remained relatively unchanged in the fully developed flow downstream of the vena contracta region, near the upstream baffle where fish exit the fishway. Engineers and biologists need to be aware of this fact and ensure that fish can negotiate the vena contracta velocities rather than velocities within the developed flow region only. Discharge capacity was directly proportional to the fishway width and slope. The new equation is a design tool for engineers and field biologists, especially when designing a fishway based on flow availability in conjunction with the swimming capabilities of target fish species.     

Behavior of Submerged Ogee Crest Weir Discharge Coefficients

Weir head-discharge relationships are typically described using the discharge coefficient-dependent standard weir equation. The submerged weir (tailwater exceeds the weir crest elevation) head-discharge relationship can vary from the free-flow head-discharge relationship, particularly at high submergence levels. The accuracy associated with predicting the upstream head or discharge, corresponding to submerged weir flow conditions, is dependent upon the accuracy with which a representative submerged discharge coefficient can be determined. A submerged ogee crest weir discharge coefficient predictive method developed by the U.S. Bureau of Reclamation (USBR) is reviewed and its predictive accuracy compared to laboratory-scale submerged ogee crest weir experimental data associated with a wide range of submerged flow conditions for nine different ogee crest weir geometries. Discussion is presented in an effort to partially explain the relatively poor correlation between the USBR method and the experimental data set. Alternative submerged discharge coefficient relationships are also presented.     

Modeling Water Movement and Flux from Membrane Pervaporation Systems for Wastewater Microirrigation

A mathematical model to predict the performance of a membrane pervaporation unit directly placed in the soil to reuse wastewater for agricultural microirrigation was presented. The model was formulated by combining the solution–diffusion and the resistance-in-series model for mass transport across the membrane thickness, the Richard’s equation for soil water movement and the van Genuchten function for soil hydraulic properties to predict the water permeate flux for different types of test soil over a wide range of process operating conditions. Its applicability was assessed by comparing to the experimental data collected using both hollow fiber (HF) bundles and corrugated sheets (CS) membrane modules made of a hydrophilic dense polymer. A good agreement was observed between the model predictions and the experimental measurements. Further analysis concluded that the water permeate flux were mainly controlled by the porosity, the particle-size distribution, and the residual water of the soil. The overall mass transfer resistances were estimated to be 1.2×1014 and 5.6×1013?s?Pa/m for the HF and CS modules buried in loam soil, respectively, which are different from those measured in sweeping air pervaporation tests. The soil resistance for water transport was 7.1×1013?s?Pa/m. It is believed that the model could be a valuable tool to refine the design and optimize the operation of the proposed membrane pervaporation system.     

Friction Factors for Spatially Varied Flow with Increasing Discharge

This paper describes an experimental investigation of how friction factors change for spatially varied flow in sloping channels receiving lateral inflow. The results are compared with those of Beij in 1934, and it is concluded that uniform flow resistance coefficients are not always appropriate for spatially varied flow. Moreover, the common technique of assuming a constant friction factor over the entire length of the channel has been found to have little theoretical justification. The method of Keulegan in 1952 for calculating friction factors in spatially varied flow gives a better estimate, but does not explicitly take account of the lateral inflow rate or velocity. Beij’s 1934 experimental data, which was used by Keulegan does not show a systematic variation of friction factor with lateral inflow rate for a constant Reynolds number although this may be due to the low flowrates used. The results of the present study indicate that the friction factor increases with lateral inflow rate for a constant Reynolds number in the experiments that included subcritical and supercritical flow conditions. A method for calculating friction factors which allows for lateral inflow is presented as a precursor to the development of a general method of evaluating friction factors for spatially varied flow with increasing discharge.     

Quick Method for Open-Channel Discharge Measurements Using Air Bubbles

An economical methodology is proposed by which distinct air bubbles released at the bottom of a channel may be utilized for determining the local flow discharge q per unit width. Simple theoretical analysis shows that q is linearly dependent on the rise length L of bubbles released at the bottom. This length is the horizontal displacement of the bubbles between the release cross section and the cross section where they emerge. The theoretical findings were compared with measurements in three laboratory flumes and in an irrigation canal. Based on the above, a relationship between L and q has been established. The empirically proposed relationship is very useful for fast discharge measurements in channels and natural streams.     

End Depth–Discharge Relation at Free Overfall of Trapezoidal Channels

For steady flow near the free overfall (end section) of a horizontal trapezoidal channel, the velocity distribution is nonuniform and the streamlines are curved. An accurate relation between discharge rate and end depth was formulated including these effects. To determine these effects, the streamline pattern in the vertical plane of channel symmetry was determined using measured velocity components and the water surface profile. At the end section, the streamline pattern yielded the streamline curvature, which in turn provided the curvature correction required to predict the true static pressure head profile. The measured static pressure head distribution agreed well with the predicted static pressure head distribution for the end section. The pressure force at the end section was obtained on the basis of the measured static pressure distribution at the end section, and this information yielded a reliable relation between the end depth and the channel discharge rate. Analysis of present and past experimental data indicated that, the pressure head coefficient was the dominant parameter that influences the relationship between discharge rate and end depth in trapezoidal channels. Near the end depth, in the region above the maximum velocity point, the total energy determined from the measured velocity and pressure fields was essentially constant.     

Hydraulic Analysis and Optimum Design of Multidiameter Irrigation Laterals

A new analytical continuous-uniform outflow approach that takes into account the effect of the number of outlets on the multidiameter lateral hydraulics is presented. The pressure head profile along the multidiameter pipeline is described by a simple analytical function providing direct calculation of the outlet pressure head along the pipeline. The method is significantly improved by introducing an adjusted spatially variable outflow equation—of power function form—for the errors caused by the assumption of equal outlet discharge. The effect of ground slope on hydraulic computation is also considered. Simple equations are derived for the direct calculation of the maximum, minimum, and inlet pressure head along the multidiameter pipeline. The optimum design problem for two-diameter laterals is also solved analytically. For specified total length of a two-diameter pipeline, a simple algebraic equation is derived to calculate directly the appropriate lengths of the reaches of different diameters in such a way that the total cost of the pipeline is minimized. Comparison tests with an accurate numerical stepwise method indicate that the proposed analytical approach is sufficiently accurate.     

Comparison of Water Distribution Uniformities between Increased-Discharge and Continuous-Flow Irrigations in Blocked-End Furrows

A comparative analysis of the distribution uniformities of infiltrated water depth in blocked end furrows between three irrigations with increased-discharge (IDI) and three irrigations with constant flow rate (CFI) is presented. The goal is to evaluate IDI irrigation contrasted to CFI irrigation, which is the most commonly used in underdeveloped countries. The average distribution uniformities of IDI irrigation is 9% higher than that of CFI irrigation. Therefore, IDI irrigation is a viable alternative of efficient irrigation in blocked end furrows. Field assays were performed in 290?m?long×0.75?m?wide, 0.6% slope furrows in clay loam.     

Periodic Oscillation Caused by a Flow over a Vertical Drop Pool

The flow patterns of various dropping flows were investigated and classified experimentally for subcritical approach flows passing a vertical drop pool. A wave gauge was used to measure the free surface fluctuations in the pool. A flow visualization technique was employed to reveal the flow structure of the dropping flows qualitatively. It was discovered that, under certain conditions, the dropping flow forms a switching jet that oscillates up and down periodically and impinges on the bed and the downstream pool wall alternately. The switching jet switches between an impinging jet (a napped flow) and a sliding jet (a skimming flow), causing it to oscillate periodically with a unique period. The primary frequency of the periodic oscillation was determined by applying spectral analysis to the time series of the gauge measurements. Since a large number of air bubbles was entrained in the oscillatory flow, particle image velocimetry, and bubble image velocimetry were used for quantitative velocity determination in the liquid region and the aerated region, respectively. The mechanism causing the periodic oscillation in the pool was elucidated, and variables affecting the oscillation frequency were identified. An empirical relation between a weighted Strouhal number and a grouped dimensionless parameter was proposed to predict the primary frequency of the periodic oscillatory flow.     

Discharge Capacity of Labyrinth Side Weir Located on a Straight Channel

Side weirs, also known as lateral weirs, are flow diversion devices widely used in irrigation as a head regulator of distributaries and escapes, land drainage, and urban sewage systems. The studies on the subject have been generally focused on rectangular and triangular side weirs located on a straight channel. However, the same is not true for labyrinth side weirs. The current studies deal with sediment transport and scour problems around side weirs and lateral structures. The investigation of the hydraulic effects of labyrinth side weirs to increase discharge capacity of them has been studied in this particular work. In the study, 2,830 laboratory tests were conducted for determining discharge coefficient of labyrinth side weirs, and results were analyzed to find the influence of the dimensionless weir length L/b, the dimensionless effective length L/?, the dimensionless weir height p/h1, triangular labyrinth side weir included angle θ, and upstream Froude number F1 on the discharge coefficient, water surface profile and velocities in the channel along the side weir. It has been found that discharge coefficient of labyrinth side weirs gives pretty higher coefficient value compare to that of classical side weirs and a reliable equation for discharge coefficient of labyrinth weirs is presented. Discharge coefficient of the labyrinth side weir is 1.5–4.5 times higher than rectangular side weir.     

Discharge Relation for Cutthroat Flume under Free-Flow Condition

A cutthroat flume is commonly used as flow measuring device for open-channel flow due to ease of fabrication and installation. In most of the cases it is difficult to calibrate the flume in the field. Therefore, accurate relation between discharge and upstream head applicable for all sizes of cutthroat flume is needed. Seven different sizes of cutthroat flumes, having different length to throat width ratios, are fabricated and tested in the laboratory under free-flow condition. Selecting groups of different variables describing flow through a cutthroat flume number of dimensionless parameters are formed. Regression analysis of experimental data is carried out between all possible combinations of pairs of dimensionless parameters and the pair giving the best correlation is selected. Using the selected pair, relation between dimensionless parameters of discharge and head is developed. The relation is simple and convenient to use and, at the same time, more accurate compared to methods available in literature for prediction of discharge.     

Head-Discharge Equation for Sharp-Crested Polynomial Weir

Polynomial weirs can be applied in agricultural and municipal engineering to produce a wide range of head-discharge behavior, including the proportional (linear) characteristics of the Sutro weir. This note describes a method to determine the head-discharge equations of sharp-crested weirs with openings defined by polynomials of any order n. Examples of behavior of fourth-order polynomial weirs are discussed.