Journal of Irrigation and Drainage Engineering

The flow features of a side weir in a prismatic circular‐shaped channel as used in sewage and irrigation systems are considered. The complex cross‐sectional channel geometry is simplified, and a generalized de Marchi equation is presented for the free‐surface profile. The general solution is further modified to obtain a similarity plot of normalized flow depth as a function of normalized location for arbitrary weir height. The solution for supercritical approach flow is compared to experimental data for one‐ and two‐sided lateral outflow. Although the agreement between theory and experiment is only fair, the normalized parameters yield all data on a single curve. Eq. (15) may be regarded as the generalized free‐surface profile, provided no hydraulic jump occurs. The hydraulic jump is studied with a modified momentum approach, and a simple relation comparable to that for rectangular channels is obtained. No indications on the length or the velocity distribution in jumps with spatially decreasing discharge can be made with the existing data, however.

The flow features over the broad‐crested weir with vertical upstream wall and sharp‐crested corner are analyzed experimentally. Only the long‐crested weir is considered, for which the discharge coefficient remains practically constant. For a relative overflow depth between 10% and 40%, the surface profile, the bottom pressure profile, the boundary separation profile, and the velocity profiles close to the upper corner are self‐similar, provided effects of scale may be dropped. For extremely long‐crested weirs, undular flow occurs. The first wave profile is shown to be identical with the solitary wave profile. The main properties of the undular hydraulic jump are explored. The broad‐crested weir is characterized by insensitivity to tailwater submergence. The modular limit is found practically constant at 75% of the tailwater level, independent of the relative head on the weir. The discharge‐head relation for submerged flow is analyzed under a novel approach. Finally, recommendations are specified under which a broad‐crested weir may be used as a discharge measurement structure.

The best hydraulic channel section is determined by using Lagrange's method of undetermined multipliers. For a given flow, roughness coefficient, and longitudinal slope, this method optimizes the channel section by minimizing the wetted perimeter (or the cross‐sectional area) subject to a constraint. Any flow equation, e.g. Manning, can be used as the constraint. The channel section could contain any number of variables; e.g., two variables (rectangular and triangular sections), three variables (trapezoidal and round‐bottom triangular sections) and so forth. The approach presented is more general than the conventional methods given in the textbooks. It is shown that minimization of the wetted perimeter and minimization of the cross‐sectional area are mathematically equivalent. The method is applied to the standard sections as well as the round‐bottom triangular section. The best hydraulic round‐bottom triangular section, the determination of which is made possible by this approach, is slightly more efficient than the similar and more widely used trapezoidal section. The geometric properties of the best hydraulic round‐bottom triangular section are of great interest. Its depth is equal to the round‐bottom radius and is twice its hydraulic radius. The proposed method can be applied to other complicated sections that cannot be solved by the traditional method.

A tunnel‐type sediment excluder is commonly used at the headwork of a canal for preventing excess sediment from entering the off‐taking canal. In such excluders, the sediment‐laden water, which flows mainly near the bed, is made to flow through the tunnels provided at the canal bed. It may be then discharged back into the river downstream through the undersluice bays. Comparatively sediment‐free water in the top layers is allowed to enter the canal. Presently, the only hydraulic principle utilized in its design is that energy loss is kept to a minimum and a minimum velocity of flow is ensured through the tunnel for the nondeposition of the coarse material. In the present paper, established concepts of sediment transport are used to outline a procedure for the design of a tunnel‐type sediment exluder when the river bed material is nonuniform in nature. The procedure suggested herein is illustrated with examples using the field data and the results obtained are compared with the available observations from the prototypes.

An automated side weir irrigation system is designed using the concept of constant specific energy. The characteristics of the spatially varied flow along a main channel with multiple side weir outlets are analyzed to determine the roughness coefficient of the channel pertinent to spatially varied flow. A computer program is developed to obtain the geometric parameters of the uniformly discharging weir outlets in a side weir irrigation system. The discharge in the main channel, desired discharges over the weir outlets and the hydraulic and geometric characteristics of the main channel are the main inputs to the computer program. The experiments conducted to evaluate the performance of the developed system show that the deviations of observed discharges from desired ones over the side weir outlets are within 5% for majority of the test runs and in no case these are greater than 10%.

Experiments were conducted to find the effects of seepage on flow over a sand bed in a straight rectangular flume under two conditions: (1) When the channel bed is plane, horizontal, and nontransporting; and (2) when the bed is transporting at a constant sediment concentration. Effects of both injection and suction, caused by seepage flow into and out of the channel bed, are studied for condition 1; and only suction effects are studied for condition 2. Three sands, of sizes 0.34 mm, 0.53 mm, and 0.80 mm, are used in the study. It is found that seepage can cause an increase or decrease in the bed shear stress relative to no seepage for the two conditions. The change in bed shear stress depends on the relative magnitudes of the bed shear stress and the critical shear stress of particles under the no‐seepage condition, sediment concentration, and the seepage rate. Quantitative relationships giving the ratio of bed shear stresses with and without seepage are presented for both conditions of the bed. A procedure to estimate the changes in bed shear stress, friction factor, Manning's $n$, and stream power due to seepage for known initial conditions of the channel and the amount of applied seepage is presented.

Twenty‐one drainage lysimeters were installed in 1988 to measure water balance parameters for citrus trees. The lysimeters were designed to simulate the high water‐table conditions that exist for the more than 150,000 ha of citrus grown in the Florida Flatwoods. The lysimeters were constructed from 3.5‐m diameter by 1.0‐m deep polyethylene tanks. Young trees were transplanted into the lysimeters in 1988. Four experimental treatments consisting of constant water tables at depths of 0.61 m, 0.76 m, and 0.91 m plus a fluctuating water‐table treatment were included in the study. Trees were watered with a microirrigation system and all irrigation and drainage water was metered. Water‐table levels were maintained by float‐controlled pumps. Annual evapotranspiration (ET) averaged 16,030 L tree⁻¹ for March 1989 to March 1990 and 11,733 L tree⁻¹ for March 1990 to March 1991. ET rates were not significantly different among water‐table treatments. Tree growth, yield, and juice quality were not affected $(p=0.05)$ by the water‐table treatments.

Among various toxic substances that contaminate plants and enter the food chain, thereby posing health problems to human beings, heavy metals are particularly severe in their action. The behavior of heavy metals present in sewage sludge and industrial wastes that are used in agricultural practices has been the center of much attention during the last decade. Among these heavy metals, cadmium has been identified as the most critical metal due to its human toxicity. The presence of cadmium and its accumulation in the plant root zone also results in decreased crop yield. This study develops a methodology to simulate the transport of cadmium in soil water and its uptake by plant roots. The transient unsaturated water flow equation with a root extraction term is coupled with mass transport equation and mass balance of solute concentration. The model takes into account the root growth with time. The macroscopic root‐soil water flow and solute (cadmium) movement model yields a set of partial differential equations that can be solved using numerical techniques for a given set of initial and boundary conditions.

The problem of seepage from an unlined earthen canal is considered. The phreatic surface generated on the two sides of the canal is characterized by the nonlinear Boussinesq equation incorporating the slope element. A closed‐form analytical solution to the linearized Boussinesq equation was derived. A finite‐difference solution to the nonlinear Boussinesq equation was also obtained using the unconditionally stable Du Fort‐Frankel explicit method for the seepage problem in the semiinfinite flow problem. The numerical solution in general predicted a higher phreatic surface than the analytical solution.

Several types of flow‐measurement structures are used in rivers. One of the more common flow‐measurement structures is the critical‐depth flume. By definition, the velocity increases through the contracted section of the flume, which, in turn, minimizes deposition of sediment in the structure. Critical‐depth flumes are preferred in rivers where sediment transport through the structure is substantial. Dimensioning of these flumes for sediment‐free flow conditions over the structure has not yet been studied. In this paper, theoretical and experimental studies carried out on critical‐depth flumes of symmetrical compound cross sections are presented. Design criteria based on hydraulic model studies conducted with sedimentary materials having various properties are given. Following the procedure for dimensioning a proper flow‐measurement structure, a design example is presented for application. This procedure can easily be applied to a river of known hydraulic and geometric properties to determine the appropriate dimensions of the flow‐measurement structure along which there will be no sediment deposition under any flow condition. Consequently, a fixed rating curve that is unaffected by sediment deposition can be obtained for the flow‐measurement structure.

We develop an approximation of the Green‐Ampt infiltration equation by using the first two terms of a Taylor‐series expansion of the equation. The resulting approximate equation is in the form of the Philip's equation, with an added term to account for the error in the approximation. The Taylor‐series approximation is compared with Li et al.'s 1976 quadratic approximation for the case of constant rainfall with variable time to ponding. The maximum error for the new approximation is about 3.5%; and the maximum error for the quadratic approximation is about 8%. For a range of values of the ratio of infiltrated depth to capillary potential of 0.1 to 150 the approximation of the Taylor series fits the Green‐Ampt infiltrated depth more closely than the quadratic approximation. It is shown that the approximation of the Taylor series gives less error than the quadratic approximation for coarser textured soils.

Unit hydrographs for a gaged site can be determined from observed events. If several events are used for the derivation, several unit hydrographs result. An averaging procedure must be used to achieve a single representative unit hydrograph. The variability is due to inherent uncertainty in the rainfall processes and to inadequacies in the basic model. It is appropriate to consider the unit hydrograph itself a random function. This paper develops a stochastic expression for the instantaneous unit hydrograph (IUH) based upon the Nash cascade. This conceptual model holds the number of reservoirs constant, while treating the reservoir constant as a random variable. Records of 24 storm events, observed on a 12.2‐km² watershed located in north central Missouri, were studied. The results of the study indicate that the stochastic model can be used to estimate the hydrograph.

A new nonpoint source pollution management model is presented and applied to ascertain scenarios of expanding residential/commercial land uses to minimize impacts on ground‐water quality. The model is a linear program (LP), which can relate distributions of regional ground‐water quality to corresponding development scenarios at optimality. This is achieved by including equations from a numerical steady‐state transport model in the LP constraint set. The model is applied to 1980 and projected conditions for a subarea of Cape Cod, Massachusetts. Elemental water quality, elemental housing density, nondegradation water quality standards, the 1980 land‐use pattern, and a projected development population are incorporated as constraints. The analysis elucidates optimal development distributions that produce a minimum ground‐water‐quality impact. The dual variables generated from binding continuity, water quality, and development density constraints are particularly valuable for the information they provide on the impacts of relaxing land‐use and water‐quality limitations.

A simple design aid is presented for quick preliminary sizing of flood‐control detention basins and outlet structures. The design objective is to control the postdevelopment flood volume rather than the peak discharge. Alternatively, the method can be used to control downstream channel erosion caused by post‐development flows. The detention basins considered have a single outlet, which can be of either orifice or weir type. The design aid is based on the predetermined solutions to the reservoir‐routing equation. The hydrologic storage equation is used for this purpose. To evaluate the channel‐erosion tendencies, a generic bed‐load formula is employed. All the equations are written in dimensionless form, and the solutions are obtained in terms of a set of governing dimensionless parameters. The results are generalized using the concept of hydrologic similarity, and they are presented in chart form. These charts can be used to determine the required stage‐storage relationship for a detention basin and the size of the outlet structure. Sample applications are included to illustrate the use of the charts.

This paper describes a new approach to designing field‐scale irrigation and drainage systems in arid irrigated areas. This approach allows for a drainage design that can adjust to irrigation schedules to alleviate waterlogging and salinity problems. This approach has been implemented in a computer model. The computer model contains a feedback loop between the irrigation scheduling and the drainage design components. The modular components of the system are a weather generator, irrigation scheduling, upward flow, salinity of the irrigation water, transient‐state drainage design, and crop production. The model modifies the irrigation schedule taking into consideration the effects on the drainage design. The performance of the system is evaluated using the net benefits, as well as explicitly addressing the stochastic nature of irrigation and drainage. The model is constructed so the irrigation and drainage components may be varied individually to study the impact on the whole system. This capability will allow the user to quantify the cost of minimizing drainage water production by modifying the irrigation schedule.

The Federal Emergency Management Agency (FEMA) method for delineating floodplains on alluvial fans was modified by French in 1992 to estimate design peak flow rates of specified return periods at transportation alignments crossing alluvial fans. The hydraulic engineer can use these estimates to size the drainage facilities required to protect an alignment from flood damage. The focus of this paper is an examination of the validity of the estimates derived from this modified methodology. The strategy adopted in the study was to identify a limited number of existing transportation alignments that cross alluvial fans and use the design methodology to solve for the return periods associated with the maximum capacities of the drainage structures that protect the alignment from damage. The probability that one or more events would exceed the estimated capacity of each structure in the period of time the structure has been in place can then be estimated in accordance with the U.S. Water Resources Council's 1981 guidelines and compared with the recorded history of flood damage to the alignment. This study showed that for a number of reasons the methodology likely yields conservative estimates.

Side weirs are flow‐diversion devices widely used in irrigation, land drainage, urban sewage systems, and so forth. For computation of side‐weir discharge, the de Marchi equation is widely used. Using de Marchi's equation, various investigators have related the weir discharge coefficient with the main channel's upstream Froude number. Thus, the dominant variable ratio of head to weir height has not been considered in previous investigations. Presented herein is a concept of elementary discharge coefficient for the discharge of an elementary rectangular strip along the weir crest. Like that of a normal weir, this elementary discharge coefficient has been related to the head weir height ratio only. Using this relation, a methodology for determination of the weir discharge is described.

In areas of steep terrain, concrete lined channels designed for supercritical flow are often used to convey stormwaters. During dry conditions, concrete channels attract playing animals, children, and adults. These channels are hazardous during storms because of the high water velocities. Even more hazardous, a trash rack placed in the channel has the potential to pin a person to the rack, preventing escape from the waters. A parabolic shaped grate designed to deliver victims to safety is modeled. Results show that the grate can be appropriate for supercritical flow channels. The parabolic shape works with the velocity profile of the water by providing a flatter slope as the velocity of the flow increases. Floating objects sweep up the grate out of the flow of the water. A severe clogging factor has little effect on the grate. If the channel is designed with a hydraulic jump induced on the grate, the jump can aid in pushing a victim up the grate.