Showing papers in "Journal of Hydraulic Engineering in 1970"

Initial Instability of Fine Bed Sand

Abstract: The initial entrainment characteristics of fine bed sand are objectively defined in terms of the measured distributions of critical instantaneous bed shear stress associated with the observed movement of individual surface grains. Critical flow conditions are then predicted by equating the lower extremes in these characteristic critical shear stress distributions to the upper extremes in the distribution of instantaneous bed shear stress produced by the particular type of background flow under consideration. The method is applied to the case of two-dimensional channel flow over a flat bed and yields sufficiently consistent results to suggest an extension to Shields' curve for small grain Reynolds numbers. The detailed experimental observations clearly illustrate the important role played by bed region turbulence in the interaction process between the fluid and the mobile bed grains constituting the deformable boundary.

Implicit flood routing in natural channels

Abstract: Flood routing in natural channels and many other applications in hydraulic engineering based on the solution of the equations of unsteady flow require fast and accurate numerical methods. Numerical methods which are successful in other applications prove to be inefficient when used for flood routing. An implicit numerical method which is both fast and accurate can be established on the basis of: (1) a centered difference scheme to represent the primary differential equations in finite difference form; and (2) the simultaneous solution of the finite difference equations for each time step. The difference equations constitute a system of nonlinear algebraic equations which can be solved on a digital computer by Newton iteration method. The computational scheme becomes very efficient when advantage is taken of the sparseness of the matrix of coefficients of the linear systems employed in the iteration. Applications of the implicit method show that it can be conveniently used for highly irregular channels.

Vertical Transfer in Open Channel Flow

Abstract: Vertical turbulent mass transfer coefficients for suspended sediment particles and dye, and fall velocities of the sediment particles were determined experimentally in a large laboratory flume. Local values of the turbulent mass transfer coefficient, and turbulent fall velocities for the sand, were determined from an integrated form of the transfer equation. The results of the experiments indicate that: (1) Magnitude and distribution of the vertical turbulent mass transfer coefficient for dye and fine sediment are close to those of the momentum transfer coefficient, which lends added support to Reynolds' analogy for the equivalence of mass and momentum transfer in turbulent shear flow; (2) in comparison with dye, the mass transfer coefficient for medium sand is somewhat less in magnitude and its distribution indicates that the transfer coefficient is larger near the bed; and (3) the fall velocity of sediment particles is larger in turbulent channel flow than in quiescent water.

Efficient Code for Steady-State Flows in Networks

Abstract: A complete algorithm for the computer solution of steady-state fluid flows in networks is given. Particular stress is placed on fast solution, minimal storage requirements and simplicity of the input data. Although the Hardy Cross method is the classical method of solution of this type of problem, convergence is slow for large networks. To overcome this problem, the whole network is considered simultaneous, and this produces a large system of non-linear equations. Newton's method is applied, which results in an iterative solution of a system of linear equations. In order to reduce computer storage requirements and to simplify the data input, a number of algorithms from graph theory are involved. The resulting matrix of coefficients associated with the system of linear equations is banded and symmetric for which efficient (in time and memory requirements) methods of solution exist.

Numerical Solution of Saint-Venant Equations

Abstract: The general, one-dimensional Saint-Venant equations are presented for a rigid open channel of arbitrary form, not necessarily prismatic, containing a flow that may be spatially varied. The theoretical basis for the method of characteristics is reviewed and used to show that, in the general case, the speed of long-wave disturbances is given by the slope of the characteristic curves. Finite-difference schemes on a rectangular net in the x - t plane and based on the characteristic forms of the Saint-Venant equations, as well as on the direct forms, are given and examined for their stability. The von Neumann technique for stability analysis is presented in detail. Explicit numerical schemes, which are simple, but require small steps in time because of stability problems, are contrasted with implicit schemes that permit numerical solution over large time steps but require the solution of large sets of simultaneous algebraic equations at each step. The double-sweep or progonka method, an exact time- and space-saving technique for solving these (locally linearized) equations, is also given in detail.

Performance and Design of Labyrinth Weirs

Abstract: The purpose of the labyrinth weir is to increase the discharge per unit width of channel beyond that usually obtained from a conventional weir under identical head conditions. This is achieved by compressing a large length of crest in concertina form into the space available on site. An increase of discharge ranging up to sixfold or more can be obtained. Described are the results of a program of research on labyrinth weirs that is aimed to provide comprehensive performance and design data. The experimental work covered the effects of all primary parameters affecting performance such as crest length magnification, plan geometry, number of cycles, etc. Parallel with the experimental work a mathematical model was constructed and a computer program developed which will predict performance to ± 4% accuracy or better over a wide range of operating conditions. Finally a simple design method is instilled from the experimental and theoretical results.

Dispersion in Homogeneous Estuary Flow

Abstract: The effects of the transverse variations of velocity on dispersion in oscillatory, estuary flow are investigated. The dispersion coefficient (\iE) is found to depend on a parameter \iT′ = \IT/T\dc\N, in which \iT is the tidal period and \IT\dc\N is a characteristic time for turbulent diffusion. Applying the relationship between \iE and \iT′ to some estuaries, it is concluded that the effects of the transverse variations of velocity may cause \iE to be as much as 10 times greater than it would be if only the vertical variations were considered. However, for continuous injection conditions, this possible increase in \iE appears to cause calculated concentrations to change by only 10% to 15% of the maximum concentration. Thus, under the conditions and assumptions stated in the paper, equations such as Elder’s or Taylor’s may be used to estimate \iE for continuous injections into estuaries. In other cases, it may be desirable to know the transverse distribution of velocity in order to estimate \iE.

River Channel Patterns

Abstract: River channel patterns of various types are described and defined. Data for 42 rivers are collected in respect to meander and channel characteristics. Relationships are statistically determined between tortuosity ratio and important channel characteristics. Similar equations are evolved for the ratio of meander belt to channel width. These two ratios define shape and size of a meander. Conditions when channels become straight or meandering are described and it is shown that meandering helps the channel to reach final stability.

Wave-Induced Pressures in Beds of Sand

Abstract: Measurements of the variation of the fluctuating component of pressure have been made in two different beds of sand in a wave channel. The sand was laid from an overhead hopper, and it is shown that the stratification of the bed produced by this method causes the permeability to be different in the vertical and horizontal directions. It is suggested that a similar situation exists in the sea bed. Analytical relationships for the pressure and velocity distributions in such a situation are developed, and the agreement between theory and experiment is found to be quite good. As far as is known, this is the first time that the applicability of traditional porous-media analytical methods to wave-induced flow in beds of sand has been verified experimentally.

Boundary Shear Distribution in Open Channel Flow

Abstract: BOUNDARY SHEAR DISTRIBUTION IN BOTH ROUGH AND SMOOTH OPEN CHANNELS OF RECTANGULAR AND TRAPEZOIDAL SECTIONS IS OBTAINED BY DIRECT MEASUREMENT OF SHEAR DRAG ON AN ISOLATED LENGTH OF THE TEST CHANNEL UTILIZING THE TECHNIQUE OF THREE POINT SUSPENSION SYSTEM SUGGESTED BY BAGNOLD. EXISTING SHEAR MEASUREMENT TECHNIQUES HAVE BEEN REVIEWED CRITICALLY. COMPARISON OF THE MEASURED DISTRIBUTION HAS BEEN MADE WITH OTHER INDIRECT ESTIMATES, FROM ISOVELS, AND PRESTON TUBE MEASUREMENTS, BASED ON KEULEGAN'S RESISTANCE LAWS. THE DISCREPANCIES BETWEEN THE DIRECT AND INDIRECT ESTIMATES ARE EXPLAINED. OF THE TWO INDIRECT ESTIMATES THE SURFACE PITOT TUBE TECHNIQUE IS FOUND TO BE MORE RELIABLE. THE INFLUENCE OF SECONDARY FLOW ON THE BOUNDARY SHEAR DISTRIBUTION COULD NOT BE ACCURATELY DEFINED IN THE ABSENCE OF A DEPENDABLE THEORY ON SECONDARY FLOW. /ASCE/

Erodibility of Channels with Cohesive Boundary

Abstract: Results of laboratory investigations on the erodibility of cohesive soils by water were critically reviewed, summarized and compared with similar field results and with older empirical information. There is strong experimental evidence, substantiated by physical reasoning, that the bed shear stress strongly controls both the erosion and the deposition of cohesive sediments. The net attractive physicochemical interparticle forces in the soil provide the main resistance to erosion. For low values the soil shear strength itself does not have any measurable effect on soil erodibility, while for medium to high strength clays, the resistance to erosion seems in general to increase with the macroscopic strength. Under certain conditions erosion may stop completely after some scouring. The depth of this scouring and the final bed roughness increase with increasing shear stress and decreasing shear strength of the bed. A mechanistic model about the interaction between the surface of the bed and the flow is described which explains the observed phenomena. A set of tentative rules is suggested for design of stable channels with cohesive boundaries.

Formation of dunes and antidunes in open channels

Abstract: The formation of dunes and antidunes on the erodible bed of an open channel is studied analytically as a problem of stability of the erodible bed The phase lag existing between the local sediment-transport rate and the local velocity on the bed plays an essential role in the formation of the sand waves A physical model for the transport of sediment over a wavy bed is presented and a quantitative explanation of this phase lag is developed The regions of occurrence of dunes of those bed configurations are compared with experimental results previously summarized by Kennedy, the comparison showing a good agreement

Clogging of Porous Column of Spheres by Sediment

Abstract: When a sediment suspension moves downward at a constant laminar flow through a vertical porous column packed regularly with uniform spheres and having critical pores which permit passage of spheres smaller than 1/7-diam. of the matrix grain, sediment deposition takes place by a characteristic mechanism known as bridging. The critical parameter which controls the clogging of the matrix is the ratio of the pore size of the matrix to the sediment size. Sediment with diameters equal to or greater than half the critical pore diameter of the matrix will deposit and, in time, totally clog the matrix preventing further motion of sediment particles through the matrix. Sediment with diameters less than half the critical pore diameter will deposit only in the dead space of the matrix by the straining mechanism. Considering sediment deposition in a vertical porous column as a stochastic process of pure birth, the time and space variation of sediment accumulation in the column is described by a second-order partial differential equation which has a closed solution. The hydraulic resistance of a clogging matrix is represented by an equation similar to Kozeny-Carman equation for head loss in flow through porous media and was verified experimentally.

Periodic Permanent Roll Waves

Abstract: Two theories for periodic permanent roll waves are presented which are based on the shallow-water wave equations for the gradually varied portion of the wave profile, and the shock conditions for the rapidly varied portion. In the first theory the channel slope, S 0 , is assumed to be sufficiently small that the weight of the shock can be neglected in the shock condition. Comparison of results from this theory for small S 0 with experimental results reveals good agreement for S 0 = 0.019, but rather large discrepancies for S 0 = 0.050, 0.084, and 0.12. In the second theory the shock weight is included in the shock condition. Using the measured shock profiles to evaluate the weight of the shock yields theoretical predictions which are in substantial agreement with the experimental results.

Indeterminate Hydraulics of Alluvial Channels

Abstract: Field and laboratory data indicate that the relations among width, depth, velocity, and slope are indeterminate unless the constraints on the development of the bed forms are known. A knowledge of the rate of sediment transport will satisfy this deficiency most of the time but not always. Only a full knowledge of the response of one variable to changes in other variables will permit an evaluation and description of the relation of all the variables to each other. It is possible to predict general patterns of stream behavior. Actual stream behavior deviates about these general patterns in two ways. One is a statistical deviation expected when dealing in probabilities. The second results from a change in the general or usual relation between discharges of water and sediment and size of transported sediment. Because it is impossible to have an alluvial channel that will remain in equilibrium under a wide range of discharges of water and sediment, problems associated with alluvial channels can and must be resolved only by recognizing and accepting the lesser of a good many evils.

Temperature Variations in Deep Reservoirs

Abstract: A mathematical model is developed to study the thermal behavior of freshwater impoundments. The model is formulated to simulate thermal stratification, turnover, hypolimnetic behavior, and epilimnetic behavior. Inputs to the model include meteorological data so that an energy budget relation is included. Output from the model includes the time-varying temperature distribution for the impoundment. A 315-day simulation is made of the thermal distributions in the TVA's Fontana Reservoir using the model. The results of the simulation show excellent comparison between predicted and measured quantities.

Linear-Momentum Flux to Overbank Sections

Abstract: On the basis of experiments in two joined rectangular channels, transfer of linear momentum from the major (less restricted) channel to the minor (more restricted) channel has been demonstrated. The apparent-shear stress on the junction surface was found to be of the same order of magnitude as the boundary-shear stress in the major channel. Based upon this observation, a method for engineering calculations for mean-flow characteristics in joined channels such as a river at flood stage is proposed. The steps in the proposed separate-channel method of analysis are: (1) considering the major-channel boundary including the junction plane as a solid boundary, compute the mean boundary-shear stress on the major-channel boundary; (2) compute the apparent-shear force on the junction surface using the mean boundary-shear stress of the major channel; and (3) incorporate the apparent-shear force on the junction surface as a propulsive force on the minor-channel flow.

Dynamic Equations for Steady Spatially Varied Flow

Abstract: Dynamic equations for steady spatially varied flow in uniform channels are derived separately based on momentum and energy principles. It is shown that the momentum equation is inherently different from the energy equation. In general, six different gradients are involved in steady spatially varied flow: the friction slope in the momentum equation, the dissipated energy gradient in the energy equation, the total head gradient, the gradient of the piezometric head, the free surface slope, and the channel slope. Conventional practice of using the Manning, Chezy, or Weisbach formulas to evaluate the friction slope or the dissipated energy gradient is only an approximation.

Water Wave Pressure on Horizontal Plate

Abstract: Simple rules are developed to estimate the maximum uplift pressures induced on the underside of a flat plate by various types of incident waves. Theoretical prediction techniques are provided for both the slow-rise pressure component and the fast-rise pressure component (impact) for different incident waves: standing waves, regular progressive waves, and dispersive waves, all in constant water depth. Laboratory experiments were conducted in a dispersive wave basin partially to check the validity of prediction techniques and partially to provide additional information so that the prediction techniques can be extended empirically to cover the more complicated but more practical situation of a plate in shoaling water. The fast-rise pressure should be of engineering concern not only because the magnitude of its peak is enormous but also because the magnitude of the corresponding impulse is significant. The slow-rise pressure component was found to range from one to two times the hydrostatic pressure.

Markov Models for Flow Regulation

Abstract: The problem of defining alternative operating policies for a single multipurpose reservoir was examined through the use of several pairs of discrete stochastic linear- and dynamic-programming models. The net flows into the reservoir were assumed to be serially correlated, their probabilistic sequence defined by first-order Markov chains. Each linear programming model was shown to correspond to a dynamic programming model. The solutions and computational efficiencies of each of the models were compared using a simplified numerical example based on an actual reservoir operating problem. Although the policies obtained from each pair of corresponding models were identical, the time required to solve the dynamic programming models was less than that required for the linear programming models.

Effect of Flume Width on Bed-Form Characteristics

Abstract: The dimensions of bed-forms developed in laboratory channels are found to be a function of channel width. A 10-30% reduction is observed in the size of irregularities, (wavelength ~ 4 ft; height ~ 0.2 ft) displayed by a self-formed bed of 0.6 mm diameter sand in a channel of 1.5 ft width, compared to that in a 5.0 ft-wide channel, under closely similar water and sediment discharge conditions. Emphasis is placed on the need to standardize parameters for the dimensional description of bed-form profile, and the adoption of significant form height and the average distance between alternate zero-crossings is advised. The distribution of bed elevations conforms reasonably well with accepted theoretical distributions for water waves provided allowance is made for the greater spectral width values that characterize the bed-form profiles. Because sediment movement occurs as surface creep in this case, the transport, calculated from bed-form celerity and a form height parameter proposed by Mercer, is in close agreement with the measured total transport.

Free Surface, Velocity Gradient Flow Past Hemisphere

Abstract: The drag on a hemisphere in a finite-flow field with free surface effects is evaluated by successively studying six flow fields, which allows the study of one new variable at a time. These flow fields are: the semi-infinite uniform and nonuniform flow fields, the finite uniform and nonuniform flow fields without free surface effects, and the finite uniform and nonuniform flow fields with free surface effects. Three regimes of flow are defined for the hemisphere which are: (1) A regime of pronounced free surface effects, (2) a regime of moderate free surface effects, and (3) a regime of negligible free surface effects. The effect of these variables and range of conditions under which they are effective is considered.

Unconfined Aquifer Seepage by Capillary Flow Theory

Abstract: A numerical scheme is presented to analyze a two-dimensional unconfined aquifer of rectangular cross-section to determine the fall of the water table, the water content and the rate of outflow into an adjoining water body which fully penetrates the aquifer. The capillary or unsaturated flow above the water table is considered through the use of Richards' equation. It was found that the problem can be solved by an alternating explicit-implicit finite difference scheme. It has the advantage of being efficient and of being suitable even when the fully saturated flow zone is very small. The unknown position of the seepage surface and the unknown boundary between the saturated and the unsaturated zone constitute a very critical aspect of the calculations.

Risks in Hydrologic Design of Engineering Projects

Abstract: By using the probability theory it has been shown that for any hydrologic design with a certain return period and expected life of a project there is always a calculated risk of failure involved. For a time invariant hydrologic system this simple risk can be computed. Conversely, if the expected project life and the simple risk are known, the corresponding design return period can be determined. Such a determination of the return period is independent of the type of distribution and the plotting position of the hydrologic data. Furthermore, there are additional risks and uncertainties involved which should be considered in hydrologic design of engineering projects such as those due to limited record of data available, using rainfall records to synthesize runoff information, stochastic nature of the hydrologic system, and the techniques utilized in the mathematical processing of the data.

Pattern of Potential Flow in a Free Overfall

Abstract: A theory is presented to describe the two-dimensional flow of liquid in an open channel which terminates abruptly at a sharp drop A dimensionless diagram expressing constancy of total head on the upper free surface and similar to the conventional specific-head versus depth and discharge versus depth diagrams is used to trace the course of the flow in the overfall Together with the fact that the ratio of free-surface-velocity magnitude to average horizontal component of velocity in the cross-section is a decreasing function of distance in the direction of flow, an observation drawn from a subsequent, detailed examination of the flow, the diagram is used to show that the limiting case of the free overfall is at a Froude number of approach of unity A detailed description of the flow is given by an integral equation derived from conformal mapping and singularity distributions Comparisons are made between the computed profiles and theoretical and experimental results of other investigators

Nonequilibrium Transport of Suspended Sediment

Abstract: The nonequilibrium transport of suspended sediment in an open channel is studied at an abrupt change from a nonerodible to an erodible bed. The convective-diffusion equation is solved for the case of constant velocity distribution and parabolic eddy diffusion coefficient. Diffusion in the direction of flow is neglected. Graphs of the concentration distribution, the channel-depth average concentration and the scour rate are presented.

Distribution of tractive force in open channels

Abstract: The designs of alluvial channels by the tractive force method requires information on the distribution of wall shear stress over the wetted perimeter of the cross-section. The present study was undertaken in order to provide some details on actually measured shear distributions and, hence, to check the validity of currently available design information. The latter is entirely analytical in origin and is based either on the assumption of laminar flow or on over-simplified models of turbulent channel flow. The experiments were carried out in a smooth-walled laboratory flume at various aspect ratios of the rectangular cross-section. Wall shear stress was determined with Preston tubes which were calibrated by a method exploiting the logarithmic form of the inner law of velocity distribution. Results are presented which clearly suggest that none of the present analytical techniques can be counted upon to provide any precise details on tractive force distributions in turbulent channel flow.

Bed Topography Effect on Flow in a Meander

Abstract: Stabilized bed topography in a meandering channel with fixed walls and movable bed was measured at various width-depth ratios and Froude numbers. Velocity and bed-shear distributions were measured in a fixed-bed model whose configuration conformed to the stabilized topography of the movable-bed model. An approximate theoretical analysis of the bed configuration under fully developed flow conditions shows that the transverse bed slope is directly proportional to a parameter characterizing the relative importance of fluid inertia compared with the gravity acting on a particle. Good agreement has been observed between the theoretical and experimental results in the downstream half of the model channel. The effects of formation of the bed topography on the flow characteristics are considered.

Computation of Open-Channel Surges and Shocks

Abstract: Unsteady flows in fixed-bed open channels have been computed for a number of years on the basis of the same assumptions as those which had previously underlain calculation of steady, gradually varied flow, the key one being hydrostatic pressure distribution in every cross-section. The St. Venant equations comprising the equations of motion and continuity for this case commonly are solved either by the method of characteristics or by finite differences in a rectangular network in the x-t plane. Positive waves are characterized by converging characteristics; once these intersect a bore or shock forms, and many customary methods of solution fail. The equations of motion for flow with and without shocks are compared, the generation of bores is analyzed by exact solution of characteristic equations, and several numerical schemes are presented for computation of unsteady flows that may contain shock zones. Comparison is made between computed results and experimental data gathered for a variety of cases; corroboration is generally good, though computation based upon characteristics is inconsistent and generates the largest errors.

Predicting Concentration Profiles in Open Channels

Abstract: A steady state two-dimensional conservation of mass equation is solved numerically in order to describe the process of vertical mass transfer for both neutrally buoyant liquid and suspended sediment particles in an open channel flow. The relevancy of the equation is illustrated by comparing its solution with laboratory data obtained from experiments conducted in a large flume. The solution is then used to graphically illustrate the effects of various hydraulic parameters on mass transfer. Parameters investigated include the velocity distribution, the magnitude and distribution of the turbulent mass transfer coefficient, the particle fall velocity and the boundary conditions at the channel bed. The solutions indicate that the fall velocity controls the rate of descent of the dispersant mass but has little effect on the rate of spread of the dispersant. Conversely, the transfer coefficient controls the rate of spread of the dispersant but has little effect on its rate of descent. The most striking conclusion drawn from this study is that the dispersant distribution is not very sensitive to the distribution of the turbulent mass transfer coefficient.