Journal of Irrigation and Drainage Engineering

Presently available solutions of the one‐dimensional unsteady‐state ground‐water flow equation (Boussinesq equation) have been obtained by treating the drainable porosity $f$ as a constant. Experimental evidence however, indicates that $f$ is a function of hydraulic head $h$. An experimentally determined $f‐h$ relationship was incorporated in the Boussinesq equation. The equation was solved by using the extrapolated Crank‐Nicholson's difference scheme for predicting the spatial and temporal water‐table behavior. The predicted hydraulic heads were compared with the other available solutions of the Boussinesq equation obtained by treating $f$ as a constant and with the observed data in two different sand tank model studies. The average absolute deviation between the predicted and the observed water‐table depths was reduced by over 70% when the present approach was used as compared to when $f$ was treated as a constant.

A pilot‐scale treatment system, for developing drip‐irrigation pretreatment criteria, was designed, installed, and operated intermittently over 5,300 h using activated sludge secondary effluent. Principal unit processes studied were granular‐medium filtration and screen filters for removal of suspended solids, and chlorination treatment at various injection frequencies and concentrations to prevent biofilm formation in emitters and distribution lines. Two types of 4 L/h (1 gal./h) drip emitters were tested—automatic self‐flushing and tortuous‐path turbulent‐flow emitters. Adequate filtration reduced both the required frequency of chlorination and lateral flushing. Intermittent chlorination with 2 mg/L free residual chlorine during the last hour of an irrigation cycle was found as effective as continuous chlorination with 0.4 mg/L free residual chlorine in preventing biofilm formation in emitters and distribution networks. Pretreatment recommendations for these types of emitter designs are presented.

A type‐curve method to determine aquifer parameters from a constant‐drawdown test at a drain in a finite strip aquifer is described. An available solution in the form of complementary error functions to one‐dimensional, non‐steady flow toward a drain, under constant drawdown condition in a strip aquifer bounded on the other side by an impervious formation, is used to define a drain function. Values of the drain function are calculated by using a polynomial approximation for the complementary error function and are tabulated, and a corresponding family of type curves is constructed for selected values of dimensionless distance along the width of the strip aquifer. The method is demonstrated through an application. The proposed match‐point procedure may be used to determine the aquifer parameters from observed drawdown values in an observation well in the strip aquifer and discharge data measured in the drain during constant drawdown canal pumping tests.

A side weir is a flow diversion device, which is widely used in irrigation as a head regulator of distributaries and escapes. This paper presents a concept for an elementary discharge coefficient that is related to the discharge flowing through an elementary strip along the side‐weir length. Generalized equations for an elementary discharge coefficient for rectangular and triangular side weirs have been proposed. Experimental results show the accuracy of the proposed equations.

Performance of farm irrigation systems may be limited by water delivery system flexibility. A soil water storage simulation model (SWSSM) was developed to calculate daily soil water storage and corresponding evapotranspiration and deep percolation as a function of water delivery flexibility for a vineyard in California. Uniformity was nearly constant for a range of irrigation time and furrow inflow rate, thus, delivery flow rate and duration were coalesced into delivery depth. Evapotranspiration and deep percolation were simulated for rotation, modified‐frequency, modified‐amount, and demand schedules. Growers follow a demand schedule during critical growth stages and thereafter a modified‐amount schedule with a choice of fixed frequencies. Converting from the actual rotation schedule to the suggested schedule increased seasonal relative evapotranspiration from 0.73 to 0.84 and decreased delivered depth from 1.16 to 0.75 m. Adjustment for extremes in weather is not possible. A suggested water allocation policy provides growers with an incentive to optimize scheduling, but it requires reliability in timing and accuracy in amount delivered.

Infiltration into soils is affected by several factors, including the soil‐air pressure. Soil air may become compressed between a confining layer (water table) and a nearly saturated surface soil. Compressed and counterflowing air substantially reduces soil infiltration rates resulting in potential practical problems of excess runoff and erosion. Using results from laboratory column studies, we describe a simple set of infiltration equations to predict infiltration rate and cumulative infiltration. Infiltration rates progressively declined in bounded soil columns until the soil‐air pressure head exceeded the sum of the ponded water depth and the capillary driving head at the wetting front. After a brief transition period during which stable air channels formed in the porous media, the infiltration rate approached a constant value. We demonstrate a simple method to predict this stable infiltration rate based on the permeability‐saturation relationship for the soil. Finally, we illustrate that the reduction in cumulative infiltration in bounded soils is roughly proportional to the water‐table depth, and that this reduction is greater in sands as compared to loamy soils.

Several infiltration‐advance equations are developed for a finite linear source spreading water onto a smooth horizontal surface. These include ones for a noninfiltrating soil, one with a constant infiltration, and three functional forms of time‐variable infiltration. Along with the equations is a discussion of the spatial and temporal characteristics of the applied water slug from such a source. A transformation technique is also presented showing how to transform existing solutions of infitration advance in Cartesian space to the elliptical space of the finite‐line source. A general wetted‐surface‐area advance equation is also developed. The area advance equation is applicable to most physical irrigation situations on roughly horizontal ground using a source of any shape. The Horton cumulative infiltration equation associated with the fit of the wetted‐area advance equation to measured‐area advance values is compared to the infiltration values calculated using a volume‐balance technique for an actual irrigated basin.

The characteristics of flow over side weirs are taken into account to determine the discharge coefficient for subcritical flow conditions under the assumption of constant‐specific energy. The main‐channel discharge, length of the weir crest, and sill height of the weir are treated as the controlled variables. The discharge coefficient $C_d$ is found to depend on the upstream Froude number $F_1$ and, contrary to earlier findings, also on the ratio of sill height to upstream flow depth $s/y_1$. Multiple regression analysis is conducted to establish the relationship of $C_d$ with both $F_1$ and $s/y_1$ taken together. The relationship is of linear form and provides an easy means of estimating $C_d$.

One‐dimensional horizontal flow in a semi‐infinite confined aquifer can be described in terms of mathematical solutions that relate the drawdown to aquifer parameters and the aquifer flow rate. A new solution that considers the effects of storage in a finite‐width sink into which flow occurs from the aquifer was developed for the leaky‐aquifer case. The solution was obtained by inverting the Laplace‐space solution using the Stehfest numerical algorithm, and a drain function $D(u\text{,}x/B\text{,}A/x{)}_q$ was defined based on the solution. Type curves for the drain function were plotted, and aquifer parameters can be determined by matching drawdown data from observation wells to the type curves. This drain function and its type curves could be used to analyze aquifer drawdowns resulting from a canal pumping test in which a significant part of the discharge from the canal was derived from water stored in the canal and from flow from a leaky aquifer into the canal.