Journal of Hydraulic Engineering

The downstream dispersion of a sediment bed particle is represented by a stationary point process in space and time domains and plausible forms of the probability density functions of the particle step length and rest duration are derived. The space rate parameter proposed in this paper gives step length density functions whose forms vary from the exponential curve to the bell‐shaped configuration. The time rate parameters used were proposed by Vukmirovic and Wilson. Theoretical results agree well with laboratory experimental data obtained for dune bed conditions.

Among the few equations suggested for calculating the discharge or the backwater due to open channel constrictions, the submerged flow method provides a promising approach. In other studies reported earlier, the submerged flow method had been compared to other methods using the same set of data for both calibration and verification of the equation. In this study, two sets of data collected in two independent laboratory studies have been utilized. The first set has been used to calibrate the submerged flow equation, while the second set has been utilized to verify the calibrations. Furthermore, the submerged flow equation was compared with other methods suggested by earlier investigators for the same set of data. The results showed very consistent discharge estimation by the submerged flow method.

A new general rainfall intensity‐duration‐frequency formula is presented, utilizing a method similar to, but more accurate than one previously developed. The previously developed formula was based on the average depth‐duration ratio of about 40 percent and the mean depth‐frequency ratio of 1.48. It is shown that this formula is only a particular form of the writer's more general formulation. The earlier formula, however, requires only the 10‐yr 1‐hr rainfall depth instead of the writer's three rainfall depths (i.e., 10‐yr 1‐hr, 10‐yr 24‐hr, and 100‐yr 1‐hr). The ratios of 1‐hr to corresponding 24‐hr depth and 100‐yr to corresponding 10‐yr depth can be computed from the required three rainfall depths in the writer's method so that geographical variation of rainfall can be evaluated in terms of both ratios.

A mathematical model of sediment laden, density affected turbulent flows is presented. The finite element technique is used in conjunction with the Newton iterative method to solve the resulting partial differential equations. The model satisfactorily predicts velocity and concentration profiles for unidirectional open channel flows. It is concluded that the model can justifiably be extended to multidimensional flows.

A method for the numerical simulation of longitudinal dispersion of pollutants in streams is developed and tested. It is based on the one‐dimensional, linear advection‐dispersion equation and utilizes the concept of numerical dispersion to model the physical dispersion process in a manner similar to the one used in storage routing schemes of the Muskingum‐type. The finite difference scheme used is explicit, second‐order‐in‐space accurate, and stable when used to model physical dispersion phenomena. The validity and reliability of the computations are investigated in three examples.

The physical background and some mathematical aspects of advection‐dispersion models are reviewed. It is shown that flood and pollution routing can be accomplished by the same numerical scheme, derived from the discretization of the purely advective transport equation through exploitation of the scheme's numerical dispersion properties to model the physical dispersion/diffusion behavior of the flow system. Links to traditional storage routing techniques are established. Relation between physical and numerical model parameters are presented, and the numerical properties of the scheme are explored. The paper concludes with a brief survey of fields of application for the numerical advection‐dispersion model.

Analytical solutions to the one‐dimensional advection‐dispersion equation are presented for several cases where the source concentration is either input continuously at a periodically fluctuating level or input as a single pulse of finite duration. The solute of interest can undergo linear equilibrium adsorption. Both semi‐infinite and infinite flow domains are considered. The solutions are utilized to quantify the degree to which the traveling contaminant pulses are attenuated (damped) as they migrate through an aquifer. The degree of damping is shown to be related to two dimensionless parameters and this relationship is conveniently presented in graphical form. The analytical results compare favorably with the behavior of trace organic contaminant pulses observed during injection of advanced‐treated wastewater into a shallow, alluvial aquifer in the Palo Alto Baylands.

The plane, free overfall is treated by using extended energy and momentum equations taking account of the streamline inclination and curvature. The end‐depth‐ratio is estimated by momentum considerations in the brink and the upstream sections. Distinction is made between pressure head and flow depth which coincide only for parallel, horizontal streamlines. The surface profiles for the up‐ and downstream zones of the brink section are investigated. Compared with known, laborious calculation procedures, the present computations allow fair and simple determination of all flow quantities.

The kinematic‐wave approximation is used to obtain a closed‐form solution for the catastrophic failure of a dam upon a wet, sloping channel. The solution shows that increasing the initial water depth upon the channel increases both the time and distance required for the resulting shock to approach any given depth downstream. It is also shown that the kinematic‐wave solution becomes valid only after the shock travels a certain distance downstream and that increasing the initial water depth upon the channel increases this distance.

The paper presents a three‐dimensional numerical mathematical model for calculating the near field of side discharges into open channel flow. The method employs the standard $k‐\epsilon$ turbulence model for determining the turbulent stresses. Two discretization schemes are considered, namely, the hybrid central/upwind differencing scheme and the quadratic, upstream‐weighted differencing scheme. The latter has been shown by previous investigators to produce improved numerical solutions for a number or recirculating flows. This finding is confirmed by the present investigation. The predictions are compared with experimental observations of earlier investigators of isothermal side discharges into both rough‐ and smooth‐bed open channel flows; each at discharge to cross flow velocity ratios of 0.3 and 4.0. The agreement is in the main, satisfactory for all the different cases considered.

A number of concepts related to computer studies of transient flow in pipeline systems are addressed. The topics are directed to applications on microcomputers, but are not limited to that special purpose. The topics include organizational concepts for system data handling, and ideas to realize certain storage and computational efficiencies when using the method of characteristics as the computational procedure. Alternatives to the method of specified time intervals, namely a staggered grid and an algebraic treatment, are discussed. A simple improved modification in the friction term is also emphasized. Two common elements in hydraulic systems that influence the form of pressure waves, series connections and lossy elements, are focused upon with a view to providing an improved visualization of their response characteristics. Equations and graphs are presented for cases with and without initial through flow. Finally, an example of the failure of a physical system is presented to emphasize the importance of unsteady flow visualization in hydraulic system design.

The numerical simulation of a sedimentation tank involves determining the velocity field and the sediment concentration distribution for the tank. In this study, the vertical velocity field is established by a finite difference model of the vorticity‐transport stream function equations with a constant eddy viscosity. The eddy viscosity is obtained with the aid of a physical model. The numerical model is verified experimentally. The vorticity transport is treated by the Alternating Direction Implicit (ADI) method. A variable grid is used to maximize the effectiveness of the computational nodes. A weighted centereddifference‐upwind scheme is used for the convective terms. The two‐dimensional sediment transport (convective‐diffusion) equation is solved by the same numerical approach used for the vorticity transport equation. The bottom boundary condition permitted re‐entrainment of settled solids. The model can be used for steady or unsteady solids transport. The model is applied to study the effect of reaction baffle submergence on solid removal. The model output is also compared with the Camp‐Dobbins method of determining solids removed in turbulent flow. The removal predicted by the numerical model is consistently less than that predicted by the Camp‐Dobbins approach.

Experiments in a large test channel defined friction factors for equilibrium flows up to 150 cfs over a sand bed. Although the friction factors were generally higher than those predicted by either of the three most cited published procedures, they were consistent with published data from smaller flumes with similar sand as the bed material. The Froude number seemed to unify the data into a single average trend. Correlations between the friction factor for flat bed flows and the Reynolds number and relative sand‐grain roughness were also shown to embody a strong Froude number dependency with only minor Reynolds number effect. Division of the total friction factors into components associated with the channel walls, sand grain resistance, and bed form resistance did not improve correlations with the Froude number. The apparent absence of Reynolds number effect in correlation of the friction factor with Froude number may not be general for finer sediments and an extended range of Reynolds numbers. A transformation of the Alam/Kennedy friction diagram for bed forms suggests a decrease in friction factor for finer sands or larger Reynolds numbers or both.