Journal of Hydraulic Engineering

A mathematical model is developed for the fluid and sediment interaction in an erodible channel. The model is based on the conservation of mass and momentum for the fluid and sediment. The interaction between the fluid and sediment, as well as the interaction of sediment particles moving in the vicinity of the bed is described in the model. An analysis is performed to derive the vertical distributions of the fluid velocity and sediment concentration over a plane bed in a wide open channel. The analysis yields the friction factor due to the combined effects of grain roughness and sediment movement, as well as the rate of sediment transport. The developed model agrees with existing data for plane beds. The predicted rate of transport of coarse sediment agrees with the Meyer‐Peter and Muller formula. However, detailed measurements of the fluid velocity and sediment concentration over a plane bed are required for a rigorous verification of the developed model.

A boundary‐fitted coordinates method was successfully employed in the evaluation of the discharge coefficients, as well as the free‐surface profiles, for vertical and radial sluice gates for an ideal fluid. The values of the discharge coefficients and the free upstream and downstream surface profiles are in good agreement with the literature. Some details of the flow, such as the velocity profiles and the bed pressure deficit upstream of the gate, can also be predicted accurately. The boundary‐fitted coordinates method was demonstrated to be a viable method in the study of fluid flow with initially unknown discharge and unknown free‐surface profiles.

A method for calculating sediment transport in ice‐covered flows is developed. Laboratory data on bed form, frictional characteristics and sediment transport are obtained for equivalent free‐surface and covered flows. Comparison of the data leads to the conclusion that the lower layer in a covered flow can be treated as a free‐surface flow for the purpose of calculating bed load transport. Using the flow characteristics calculated from the $k‐\epsilon$ turbulence model and a conventional bed load equation, the sediment transport for covered flows can be obtained. The method was verified using measured data.

A theoretical and experimental investigation of the hydraulics of the little‐known Cherepnov water lifter was conducted. It was found that as many as 36 algebraic and differential equations are required to predict the cyclic motion of the flow going through the lifter. With these equations, the behavior of the lifter can be conveniently analyzed on any computer having the Continuous System Modeling Program capability. Results of the computer output were compared with experimental data, and good agreement between theory and experiment was found.

A model called SWRRB (Simulator for Water Resources in Rural Basins) was developed for simulating hydrologic and related processes in rural basins. The objective in model development was to predict the effect of management decisions on water and sediment yields with reasonable accuracy for ungaged rural basins throughout the United States. The three major components of SWRRB are weather, hydrology, and sedimentation. Processes considered include surface runoff, percolation, return flow, evapotranspiration, pond and reservoir storage, and sedimentation. The SWRRB model was developed by modifying the CREAMS (Chemicals, Runoff, and Erosion from Agricultural Management Systems) daily rainfall hydrology model for application to large, complex, rural basins. The major changes were: (1) A return flow component was added; (2) the model was expanded to allow simultaneous computations on several sub‐basins; (3) a reservoir storage component was added for use in determining the effects of farm ponds and other reservoirs on water and sediment yield; (4) a weather simulation model (precipitation, solar radiation, and temperature) was added to provide for longer‐term simulations and more representative weather inputs, both temporally and spatially; (5) a better method was developed for predicting the peak runoff rate; and (6) a simple flood routing component was added. Besides water, SWRRB also simulates sediment yield using the Modified Universal Soil Loss Equation (MUSLE) and a sediment routing model. Tests with data from a $538{\mathrm{km}}^2$ basin in Oklahoma and a $17.7{\mathrm{km}}^2$ basin in Texas indicate that SWRRB is capable of simulating water and sediment yield realistically.

A series of experiments was made in a closed rectangular conduit with bentonite as fine particles and plastic beads as coarse particles. Compared with that in clear water, in bentonite suspensions coarse particles settle more slowly and start moving at a higher flow intensity. Due to the larger threshold velocity and smaller settling velocity, the bed load is smaller and the suspended load is larger. As a result, the total load, consisting of the bed load and the suspended load, is smaller in the low flow intensity region, but larger in the high flow intensity region. The increase of the suspended load favors the transition from dunes to plane bed. So in clay suspension dunes are lower, flatter, and change to plane bed at lower flow intensity. Correspondingly, the form resistance is smaller in clay suspension.

The conservation of buoyancy concept as currently applied to buoyant jets and plumes in water is reviewed with regard to its origin, validity, and accuracy. Although the original buoyant plume model was based on the assumption of a constant thermal coefficient of volumetric expansion, and thus was limited to temperature differences of a few degrees, the original model has been widely applied to cases involving temperature differences as high as 17°C (30.6°F). Such application results in buoyancy forces which are significantly larger than the more accurate values based on models using conservation of energy instead of buoyancy. In the case of the computed trajectories the errors are most noticeable for lower ambient temperatures and lower jet exit velocities. The basic point is that conservation of buoyancy is an approximation and not a fundamental conservation principle. Because of the current use of numerical solutions to the governing equations there is no real justification for its use in place of the more rigorous conservation of energy equation.

The Muskingum flood routing method was developed in studies made for the Muskingum Conservancy District Flood-Control Project during the mid-1930s. Since its development, investigations into the nature of the method have experienced surges of activity. Application of linear system theory led to one form of interpretation. Development of the routing equation from kinematic wave theory provided an additional interpretation. Many investigators have transformed the Muskingum hypothesis into a continuous equivalent. The resulting differential equation was then investigated. The inevitability of negative discharges in the routed outflow using the continuous equivalent has drawn comment from these investigators and is a cause for concern among practicing engineers. A definitive solution to this anomalous result is still unavailable. In practice, however, the continuous approach is seldom practical. The inflow is given as discrete values occurring at discrete times. The result of the routing is a table of discrete outflows at discrete times. For this reason, discrete system methods are used in this study and it is shown that the classical limits on routing parameters ensure nonnegative outflows.

Hydraulic flow characteristics for vortex shafts are investigated for subcritical approach conditions. The analysis is based on Pica's approach by simplifying considerably his procedure. Using appropriate scalings the head-discharge relation may be expressed as a unique function. Using the stability condition that the air core along the shaft axis is not below a certain minimum, explicit expressions for the maximum upstream flow depth and the maximum discharge in terms of the shaft radius, the upstream channel width and the distance of the channel axis from the shaft center are derived. These relations permit a simple and rapid determination of the vortex shaft capacity. Analytical results are compared with observations on model and prototype evaluations. Agreement is favorable in the complete range of the respective parameters. Also, no scale effects could be detected. The present approach, therefore, can be regarded as a universal head-discharge relation for arbitrary, subcritical inflow conditions. Moreover, a graphical evaluation of the relation in question enables a simple and rapid application to cases in practice.