MIXING INDUCED BY AN INTERNAL HYDRAULIC JUMP1

ABSTRACT The efficiency of an inverted internal hydraulic jump as a mixing and dispersion mechanism in an aquatic environment was examined. The flow considered was a two-dimensional buoyant flow from a shallow channel over a sloping bottom into a deep reservoir. It could be seen that a rapidly varied flow associated with violent turbulent mixing occurred near the point of discharge if specific discharge conditions and downstream controls were met. Downstream from the mixing zone the flow was stably stratified. The main object of the study was to find the conditions under which a turbulent mixing zone occurred and the rate of turbulent entrainment. Energy loss and length of the mixing zone were also investigated. The independent variables were the outlet densimetric Froude number, the density differential between outfall water and receiving water, the relative depths of the upper and lower layers in the stratified flow portion, the total depth, and the slope of the transition. Theoretical calculations had to be confined to a step increase in depth, but experiments in a laboratory flume showed that results obtained with slopes of 23° and 90° were quite similar. Both theory and experiments showed, for example, that dilution (entrainment rates) up to 2:1 (2 parts heated water to one part cold water) can be achieved at very little energy expense and with downstream depths approximately 8 times the outlet depth. Theoretically, any amount of dilution can be obtained, but large depths may be required. Experimental results also indicate that the length of the mixing zone was frequently ten times the value of the outlet densimetric Froude number.     

ALTERNATIVE APPROACH TO THE FORMULATION OF BASIN HYDRAULIC GEOMETRY EQUATIONS1

ABSTRACT: Along a drainage network, there is a systematic variation of average flow parameters (width, depth, and velocity) at flows having the same flow duration. Hydraulic geometry equations mathematically express this interdependent relationship of stream-flow characteristics for a basin for annual flow durations varying from 10 to 90 percent. However, the equations proposed so far have had rather poor predictive performance for low flows. An independent investigation of the variation of discharge with drainage area and annual flow duration demonstrates a consistent relationship between these parameters. The relationship for the high to median-flow range differs, however, from that for the median— to low-flow range. The proposed equations provide a better predictive performance for low flows than previous formulations and a versatile means of estimating flow parameters for streams throughout a basin. The improved basin hydraulic geometry equations have a wide range of applications in areas such as stream habitat assessment, water quality modeling, channel design, and stream restoration projects.     

ESTIMATING TRANSMISSIVITY AND HYDRAULIC CONDUCTIVITY OF CHICOT AQUIFER FROM SPECIFIC CAPACITY DATA1

ABSTRACT: Specific capacity data obtained from Well Construction reports which are available from USGS offices, can provide useful estimates of tranamissivity (T), and hydraulic conductivity (K), of an aquifer. The Chicot Aquifer in Louisiana is one of the largest sources of fresh ground water in North America. Hydrologic data collected for the Chicot Aquifer indicate that specific capacity tests can be used in estimating local and regional values for T and K, if the Cooper-Jacob equation for transient flow is used with proper corrections for well loss and partial penetration. Where full scale pumping test data are scarce, specific capacity test data that are adequately distributed spatially can be used to map changes in T and K values and can be summarized statistically to indicate applicable regional values. A computer program called “TGUESS” which is available from International Ground Water Modeling Center, Holcomb Research Institute, was used in this study. The contour maps for T and K values are prepared for different well depth intervals to avoid wide variation of values.     

INFLUENCES OF A FOREST ON THE HYDRAULIC GEOMETRY OF TWO MOUNTAIN STREAMS1

ABSTRACT The influence of a forest on the formation of steps in two small streams of the Colorado Rocky Mountains was studied. Steps provided by logs fallen across the channel added to flow energy reduction. The streams required additional gravel bars to adjust to slope. Average step length between logs and gravel bars was strongly related to channel gradient and median bed material size. Based on the average number of log steps per 50 feet of channel, an average of 116 percent of gravel bars were added at Fool Creek and 60 percent at Deadhorse Creek. The latter had 52 percent more logs in the channel and therefore required less bed material movement than the former. Although these are “rushing mountain streams,” most flow velocities ranged between 0.5 and 2.5 f.p.s. Exponents of a function relating rate of change of depth or velocity to discharge indicated that dynamic stream equilibrium was attained. Implications for forest management are that sanitation cuts (removal of dead and dying trees) would not be permissible where a stream is in dynamic equilibrium and bed material movement should be minimized.     

INTERACTIVE COMPUTER-AIDED HYDRAULIC DESIGN: CULVERTS1

ABSTRACT: Regular use of interactive computer programs in hydraulic design can materially increase the productivity of designers without sacrificing accuracy. This article considers the hydraulic design of culverts by interactive use of a computer program; this approach most profitably combines the speed and accuracy of the computer with the experience of the designer.     

USING CURVE NUMBERS TO DETERMINE BASELINE VALUES OF GREEN-AMPT EFFECTIVE HYDRAULIC CONDUCTIVITIES1

ABSTRACT: Since the trend in infiltration modeling is currently toward process-based approaches such as the Green-Ampt equation, more emphasis is being placed on methods of determining appropriate parameters for this approach. The SCS curve number method is an accepted and commonly used empirical approach for estimating surface runoff, and is based on numerous data from a variety of sources. The time and expense of calibrating process-based infiltration parameters to measured data are often prohibitive. This study uses curve number predictions of runoff to develop equations to estimate the “baseline” hydraulic conductivities (K_b) for use in the Green-Ampt equation. Curve number predictions of runoff were made for 43 soils. K_b values in the Water Erosion Prediction Project (WEPP) model were then calibrated so that the annual runoff predicted by WEPP was equal to the curve number predictions. These calibrated values were used to derive an equation that estimated K_b based on the percent sand, percent clay, and cation exchange capacity of the soil. Estimated values of K_b from this equation compared favorably with measured values and values calibrated to measured natural runoff plot data. WEPP predictions of runoff using both optimized and estimated values of K_b were compared to curve number predictions of runoff and the measured values. The WEPP predictions using the optimized values of K_b were the best in terms of both average error and model efficiency. WEPP predictions using estimated values of K_b were shown to be superior to predictions obtained from the curve number method. The runoff predictions all tended to be biased high for small events and low for larger events when compared to the measured data. Confidence intervals for runoff predictions on both an annual and event basis were also developed for the WEPP model.     

A HYDRAULIC TRANSIENT MODEL OF THE UPPER ST. LAWRENCE RIVER FOR WATER RESOURCES STUDIES1

ABSTRACT: A one-dimensional hydraulic transient model has been designed for water resource studies of Lake Ontario and the Upper St. Lawrence River. The model simulates water surface profiles and flows in the St. Lawrence River between Lake Ontario and the Moses-Saunders Power Dam under both open water and ice-covered conditions. Errors in water surface elevations were found to be less than 0.2 feet during quasi-steady conditions on the river. Comparable errors occurred during the ice-covered conditions. A sensitivity analysis found the model to be most sensitive to the roughness coefficients and the flow through the power dam.     

HYDRAULIC FRICTION LOSS IN SMALL DIAMETER PLASTIC PIPELINES1

ABSTRACT: Although estimation of hydraulic friction loss in pipelines is one of the most frequent routine computations made by water supply engineers, almost no post-construction analysis of the accuracy of these calculations exists in the literature. This paper reports the field measured friction losses in three one-mile sections of small diameter pvc pipe which had been in service for 10 years. Hazen-Williams and Darcy-Weisbach equations are examined to provide a framework for comparing Hazen-Williams coefficients recommended by pipe manufacturers to those obtained by the field measurements. The conclusion is that the C_HW factor of 150 recommended by most pvc pipe manufacturers is too high for the diameter-velocity combinations encountered in rural dead-end small diameter lines. The measured coefficients averaged 133 which is close to that predicted by superimposing Hazen Williams coefficients on the Moody diagram from which the friction factor for the Darcy-Weisbach equation is obtained.     

HYDRAULIC GEOMETRY AND STREAM CHANNEL BEHAVIOR: A UNCERTAIN LINK1

ABSTRACT: The at-a-station hydraulic geometry of stream channels can serve as a predictor of alluvial stream channel behavior. This geometry is the empirical relations describing changes in water surface width, mean depth, and mean velocity with changing discharge. The exponent values are correlated with channel morphology and behavior such as scour and fill, flow resistance, bank resistance, and competence. Channel behavior and morphology are apparently related, but some causes for effects are uncertain. Several studies, using empirical and theoretical bases, are reviewed here to illustrate the relation between hydraulic geometry and channel behavior, but the relations are not always consistent. Hydraulic geometry variables are easy to measure and readily available, but they do not always reflect what may be more important ones such as turbulence, the velocity distribution profile, and distribution and cohesion of sediment particles. This paper illustrates some of these problems, provides some solutions, and addresses need for more work to better predict stream channel behavior from hydraulic geometry     

MODELING INFILTRATION WITH VARYING HYDRAULIC CONDUCTWITY UNDER SIMULATED RAINFALL CONDITIONS1

ABSTRACT: Physically-based models are extensively used to simulate the infiltration process under varied field conditions. Most models are based on the deterministic nature of input parameters related to the flow process (such as hydraulic conductivity). These models yield poor predictions of infiltration rates because they do not include the field-scale variations of flow parameters. The paper presents an approach for integrating the field-scale variability of hydraulic conductivity with an infiltration model to simulate infiltration under the rainfall conditions. A model describing the spatial structure of hydraulic conductivity has been developed using stochastic techniques. The stochastic structure of hydraulic conductivity was then incorporated in the Green-Ampt and Mein-Larson infiltration model. The model outputs on the instantaneous infiltration rates and cumulative infiltration were evaluated using the field infiltration data measured under simulated rainfall conditions. The results show that the combined model is capable of rep. resenting the instantaneous infiltration rates and cumulative infiltration of the study soils. The model may, therefore, be used to simulate the rainfall infiltration process for spatially-variable soils under the field conditions.     

HYDRAULIC AND ECONOMIC BENEFITS OF DOWNSPOUT DWERSION1

ABSTRACT: A downspout diversion program in an urban area is evaluated to assess the impacts on sanitary sewer flow volumes and cost effectiveness. Sanitary sewer flows and wastewater treatment cost data are compared for the five years before and 1.25 years after the downspout diversion was completed. In order to establish a cause and effect relationship between flow volumes and downspout diversion, measurements of precipitation, consumption patterns, and system loss (maintenance, fire flows, main ruptures) for the before and after time periods were obtained. The results indicate the downspout diversion contributed to a reduction of over 25 percent in the mean flow volumes within the sanitary sewer collection network during all rainfall events, with flow reductions ranging from 25 percent to 62 percent for rainfall depths between 6 mm (0.25 inches) and 25.4 mm (1.0 inches). Costs incurred for wastewater treatment were also reduced significantly, as overtime for overflow maintenance was eliminated. Downspout diversion is a viable nonstructural alternative for sthrmwater flow reduction in highly urbanized communities which may lack available space for large scale detention facilities.     

OPTIMAL MANAGEMENT AND DESIGN OF HYDRAULIC SYSTEMS1

ABSTRACT: A possible methodology is developed to deal with the problem of designing complex pipeline systems, when they are subject to different rates of demand, and when a hypothesis of the flow distribution in different branches is not allowed. The mathematical algorithm used in linear programming. The problem, which is not linear, is dealt with by means of an iterative method; that is, by starting with a possible solution and inserting at each iteration the solution found in the preceding iteration. By taking as variables of the problem the piezometric heads of the ends for each branch of the network, the piezometric gradients and flows, and by thus considering the diameter as a derived variable, it is possible to isolate the nonlinearity in the cost function of the network. The latter is linearized each time close to the solution found in the preceding iteration.     

INTERPRETATION OF THE DUAL PROGRAM FOR OPTIMAL GROUNDWATER HYDRAULIC CONTROL1

ABSTRACT: Optimization formulations for hydraulic control that take the form of linear programs possess a corresponding dual linear program. The economic and physical interpretations of the dual linear program are examined for formulations in which hydraulic head in groundwater systems is constiained. In each case it is shown that the dual linear program has a physically meaningful interpretation. For a hydraulic gradient control formulation used for remedial analysis it is shown that the dual variable can be interpreted as the remedial benefit due to each gradient control constraint. The dual linear program maximizes the remedial benefit. The value of the dual variable can be used to compute such useful properties as the total remedial benefit of pumping at a specific location. For a formulation that optimizes aquifer yield while constraining drawdown the dual variable can be used to measure the total cost of drawdown capacity consumption per unit of pumping at a specific location. The dual program minimizes the cost of drawdown capacity consumption. By examining the meaning of the dual linear program an alternate statement of the problem under study is revealed. Quantities arising from the dual program add to the value of the optimization approach. Significant new information can be derived from existing linear optimization formulations with minimal additional computational effort.     

DETERMINATION OF HYDRAULIC C.ONDUCTWITY TENSOR USING A NONLINEAR LEAST SQUARES ESTIMATOR1

ABSTRACT: Reliable and consistent estimation of the components of the hydraulic conductivity tensor provides information needed to make proper decisions regarding clean up and restoration of contaminated aquifers. In this study, the nonlinear least-squares estimation technique was applied to drawdown versus time data from three or more observation wells to determine a theoretical ellipse of equal drawdown. The angle of rotation of this ellipse with respect to the working coordinate axes was determined by a procedure based on contouring the drawdowns at a given time. This ellipse, in turn, was used to estimate the directions and magnitudes of the horizontal components of the hydraulic conductivity tensor. The technique is applicable to confined, as well as leaky, aquifers. Sources of error in this technique include nonhomogeneity of the aquifer and partial penetration of the pumping and observation wells into the aquifer. The procedure presented may be used as an additional tool to verify computations of hydraulic conductivity anisotropy based on other techniques.     

MEASUREMENT OF HYDRAULIC CONDUCTIVITY AND DIFFUSIVITY FOR PREDICTING THE PROCESS OF SOIL WATER INFILTRATION FROM A TRICKLE SOURCE1

ABSTRACT: Two soil water functions, hydraulic conductivity K(θ) and diffusivity D(θ), were estimated by two methods In one method D(θ) was estimated according to Bruce and Klute (1956), and K(θ) was calculated from D(θ) and the retention curve. In the second, K(θ) was obtained by field estimation, with D(θ) being calculated from K(θ) and the retention curve. The criterion of reliability for both methods was agreement between experimental and predicted distribution of soil water content. The prediction was made using the functions K(θ) and D(θ) as soil water parameters in both methods. Theoretical and experimental agreement was generally good. The first method, however, was found to be best for high soil water content and the second for low soil water content. In addition, the water content at the end of the monotonic increase of function D(θ) (estimated according to Bruce and Klute 1956) was found to be about the upper limit of field soil water content. It can be used as a boundary condition in the numerical solution of a cylindrical model of infiltration from a trickle source. It was concluded that the best agreement between theory and experiment can be found when the combined values of D(θ) and K(θ) from both methods of estimation are used.     

SELECTED METHODS OF AQUIFER TEST ANALYSIS1

Changes in groundwater levels due to a well discharging at a constant rate are used with various formulas to determine hydraulic properties of aquifers and their confining bed and to detect the presence of aquifer boundaries. These formulas are generally solved by graphical methods.     

THE ROLE OF MINIMUM VARIANCE THEORY IN DEFINING THE REGIME CHARACTERISTICS OF THE LOWER NAMOI-GWYDIR DRAINAGE BASIN1

ABSTRACT: While minimum variance theory appears to offer an explanation for the hydraulic behaviour and regularity among channel systems it is not entirely successful in predicting the regime of a channel system. In the case of the Namoi-Gwydir river system the hydraulic variables velocity, depth, width, slope, friction, and shear appear to govern the behaviour and, hence regime of the channels. The significance of sediment load in determining regime could not be assessed.     

EFFECTS OF NO-FLOW RIVER CONDITIONS ON THE PLATTE RIVER WELL FIELD1

ABSTRACT: Effects of no-flow river conditions on the quantity and quality of water in the Platte River well field of the City of Grand Island, Nebraska, were examined utilizing a finite-difference computer simulation model specifically developed for this well field. Results suggest that the effects of these no-flow periods on water quality may be most important. In particular, the no-flow periods eliminate the hydraulic barrier between the well field and an area north of the River that is contaminated with nitrate (concentrations in the 20 to 40 mg/1 NO₃-N range). They also change the direction and velocity of movement of the contaminated ground water. Simulation results indicate that contaminated ground water moves toward the well field with a velocity of 0.42 ft/d after 30 days of no-flow and 1.43 ft/d after 180 days of no-flow. Limiting no-flow conditions to 10 consecutive days would protect the well field.