Journal of Irrigation and Drainage Engineering

The v‐shaped short‐crested weir with a semicircular cross section is used to measure discharges in open channels. Its truncated triangular shape provides a rather wide measuring range. Data obtained from laboratory experiments provide information on the head‐discharge relations for the bottom angle, $\alpha =150°\text{,}$ under free‐flow conditions. Drowned flow starts at a submergence ratio of 20‐30%. The maximum discharge depends on the dimensions chosen, but may reach a rate of $1.5m^3/s\text{,}$ making the structure suitable for small and moderate discharges. The lightweight weir is portable, and can be fixed at the front side of an existing structure or in vertical slots. If required, the weir can be constructed with a movable crest to act as a vertical gate with overflow. Results of investigations, design rules and limits of application are given. The dimensions and rating curves are presented for a typical weir designed for a capacity of $1m^3/s\text{.}$

The two‐dimensional nonlinear partial differential equation that describes the transient movement of water in an unsaturated porous medium is investigated by using the zero‐order continuous linear finite element method. The governing equation is transformed logarithmically to smooth the abrupt changes in the soil‐water characteristic relations. The Newton‐Raphson method is used to iterate toward the “exact” solution of the original nonlinear equations. In addition, a modified implicit finite difference scheme is used to approximate the time derivatives. Predictions of the finite element model are verified with a one‐dimensional example. The model is then used to investigate two‐dimensional infiltration from a trickle irrigation source. The numerical results compare well with those obtained from laboratory and field experiments. The advantage of the present model is its capability to simulate water movement through very dry soil environments, which causes a steep moisture front, as well as its potential applicability in irregularly shaped flow regions, which are commonly encountered in the field and are difficult to model with finite difference or other numerical methods.

The factors related to potential yields of crops are briefly described. The most important are water, fertility, and available energy as measured by the evaporative potential. Mathematical yield models are presented relating crop evapotranspiration and total water available to relative yields. Data relative to irrigation amounts, rainfall, type of irrigation, water costs, costs of applying water, total crop production expenditures, and the range of crop incomes for various California crops are used to determine how various factors relate to the economics of deficit irrigation. The principal considerations in evaluating profit include whether land or water are limiting resources, the value of crop production based on yield and price, the contribution of rainfall to the crop water supply, the costs of irrigation water and its relationship to total crop production costs. Other considerations, such as leaching requirements and the need to promote uniform maturing of a crop, are briefly described. A minimum data set recommended for evaluating crop water requirements consists of rainfall and maximum and minimum temperatures. When water is cheap, rainfall is scarce, and yields and prices are favorable, the farmer should usually irrigate for approximately the maximum possible yield.

Good irrigation management requires the ability to predict the outcome of any given combination of field and management parameters—soil infiltration characteristics, border length, slope and roughness, and inflow rate and cut‐off time in the case of simple border irrigation. While accurate mathematical models of the border‐irrigation process have been available for some time, their use requires high‐speed digital computing equipment. To eliminate the need for such complicated numerical solutions every time a given combination is to be tested, a set of generalized ultimate‐outcome solutions have been generated and the results presented in a series of dimensionless normalized graphs. These allow determination, with a pocket calculator, of the ultimate distribution of infiltrated water in the field after recession is complete and of the total volume of runoff, which result from any given set of field and management parameters. A numerical example illustrating the procedure is included.

In contrast to borders, water depth in furrows has a primary influence on infiltration. If flow depth remains relatively constant everywhere and infiltration parameters are measured at that depth, volume infiltrated per unit length computed in a mathematical model of furrow flow depends only on the time of stream arrival. But, a significant depth gradient results in error unless the variable depth is incorporated into the infiltration computation. Six different schemes are considered. The most complicated assumes that infiltration into every element of wetted perimeter at a section depends on the time that element has been wetted. Less complex schemes assume that volume infiltrated per unit length at a station depends on time of stream arrival there and, in order of increasing crudeness, local wetted perimeter, local top width, upstream wetted perimeter, upstream top width, top width at normal depth for the give inflow. Comparisons of computed results with field measurements of upstream depth, advance, and cumulative volume infiltrated with time lead to the tentative conclusion that use of current local wetted perimeter is the most satisfactory approach.

A new approach for the analysis of aquifer test data for confined nonleaky aquifers is presented. An implicit function theorem is used to estimate the transmissivity and storage coefficient from intersecting graphs, which are drawn for different drawdown observations. The proposed method eliminates the subjectivity involved in the conventional curve‐matching techniques and can work even with a small number of observations. The method has been successfully applied to actual aquifer test data from a confined nonleaky aquifer.

A present capability exists for analysis of a border irrigation by the use of mathematical models of the process or by the use of curves representing generalized dimensionless results thereof. The corresponding synthesis, design of appropriate inflow rates and cutoff times for a given border, currently not so well‐established, is treated herein. A management‐design chart is proposed for free‐flowing (open‐ended) borders. This is a plot of average low‐quarter infiltration depth resulting from any combination of inflow rate and cutoff time in a border with given infiltration characteristics and of given length, slope, and roughness. To minimize deep percolation losses while ensuring that the field receives sufficient water everywhere, only those irrigations in which the requirement just equals the average low‐quarter depth are considered in the design. The chart is thus a plot of requirement contours on axes of inflow rate and cutoff time. Superimposed on the plots are values of water‐application efficiency to assist in determining the optimum combination of required depth, inflow rate, and cutoff time.

Using one dimensional flow analysis, curves are calculated for designing channel transitions so as to avoid choke. The prevention of choke is achieved by insuring that the flow in the channel below the imposed transition is in the same regime as that existing above the transition. This places certain limits on the amount of change in channel width and depth that can be included in a transition. These limits are defined by the design curves presented.