Journal of Hydraulic Engineering

This paper summarizes studies conducted for the City of Fort Collins, Colorado, to determine the effects of prolonged droughts on the city's water supplies. As a result of the analysis, various water‐supply strategies were developed to be used by the city for handling the problems associated with extreme droughts. This study utilized stochastic modeling coupled with water‐resource‐system modeling to evaluate drought effects on the water supplies of the city. A stochastic model was developed for the five river basins that account for the city's water supplies. The stochastic model was verified with 400 years of tree‐ring data obtained for the area. Periods of records were then generated to determine potential droughts that could occur. Representative l‐in‐20‐, l‐in‐50‐, l‐in‐100‐, and 1‐in‐500‐year droughts were selected for the analysis.

Using a water‐resource‐system model, the water‐supply system of the City of Fort Collins, Colorado, which consists of five river basins, was simulated for selected drought periods to determine the yield of the city's existing water supplies and for other potential water‐supply sources. The paper outlines approaches for estimating yields of various water‐supply sources from adjacent basins during projected drought conditions. A water‐rights model (MODSIM) is used to simulate allocations of water supplies based on existing and future water‐rights ownership scenarios for the city. Safe demand levels are determined to assure adequate water availability during extreme drought events. The results of the study indicated that although water supplies for the city are adequate at the present time, policies should be adopted to assure that supplies are adequate to meet future demands during drought periods. The study provided a tool to use in evaluating the drought sensitivity of new water sources for meeting future water demands. The approach presented in this study has widespread application to evaluation of droughts on western urban water supplies.

Aerators on spillways may be regarded as an effective protection against cavitational erosion. The air entrainment of aerators is governed by a number of independent parameters, that include the slopes of the spillway and the aerator, the heights of ramp and offset, the approaching flow depth and Froude number, and the stagnation pressure in the nappe cavity. Based on model observations, two approaches are presented for the air entrainment coefficient β. The first, direct approach is based on the analysis of each effect on β. An expression is presented that should be tested for other geometries. The second, indirect approach is based on the length of jet for zero cavity subpressure. The resulting expression for the maximum air entrainment coefficient may then be corrected for the effect of cavity subpressure. The present approach introduces developing and developed aerator flow conditions. Further, the cavity subpressure is accounted for by a difference Euler number. The final system of equations for β is compared to model and prototype data, and a fair agreement is noted.

This paper describes in detail a new two‐dimensional transient model for the prediction of thermally stratified reservoir flows. Unlike many other reservoir models, the present model does not employ the hydrostatic approximation. The full general orthogonal three‐dimensional anelastic equations of motion are laterally averaged to produce a set of two‐dimensional equations in a vertical plane that is oriented along the principal axis of the reservoir. Using an orthogonal boundary fitted mesh, the governing differential equations are rendered discrete by a finite volume technique. The resulting set of coupled difference equations for momentum, mass, and energy are solved by a method that is especially appropriate to reservoirs in which the depth is small compared to the length. Comparisons between the predictions of the model and the flume data of Johnson are presented. These comparisons show that the model is well able to predict the important features of density underflows.

Many previous studies suggest the division of total resistance into skin resistance and form resistance without direct evidence. In this study, the skin resistance, form resistance, and total resistance are independently measured for a series of rigid bed forms in the laboratory. The data show that the sums of skin resistance and form resistance are close to the total resistance for all experimental runs conducted. Furthermore, data collected in this and other studies indicate that form resistance can be predicted from known bed form shapes. The Darcy‐Weisbach form factor and the pressure drag coefficients are related only to the relative height of the dunes and independent of the flow velocities. The variations of form resistance for alluvial bed forms are similar to the expansion losses in pipelines. Skin resistance on the bed form has no significant effect on form resistance of the same bed form. The measured local skin stress increases almost linearly from a zero value at the flow reattachment point to a maximum value at the dune crest. A relationship is derived to predict the skin resistance as a function of flow Reynolds number, relative roughness, and relative height of dunes based on data collected in this and other studies. The skin and form drag for nonuniform bed forms are also measured and analyzed.

A three‐dimensional scale model was designed and built to simulate ground‐water solute transport at the Savannah River Site in east‐central South Carolina. The site is $0.75{\mathrm{km}}^2$ in surface area, and averages 35 m in depth. Liquid wastes have been continuously disposed of on the site for about 30 years. The model was built to an undistorted geometric length scale of 1/500. Model materials of sand, cement, and water, blended in varying proportions to achieve different hydraulic conductivities and effective porosities, allowed simulation of four geologic formations in the prototype. The organic dye Rhodamine 6G was used to represent the prototype solute, tritium. Using scaling laws developed for advection, dispersion, chemical interaction, and making adjustments for the radioactive decay of the tritium, the model plume favorably compared with the carefully mapped plume at the prototype. Capillary forces were not scaled. The writers cautiously recommend more widespread use of scale models in ground‐water research.

Experiments in a grid‐stirred laboratory tank $(0.5m\times 0.5m\times 0.4m)$ have been conducted in an effort to elucidate the details of the surface transfer mechanisms, including the structure of up‐ or down‐welling motions and existence of various boundary layers. In addition to earlier two‐component measurements of the turbulent near‐surface velocity field, a gas microprobe has been constructed and used for measurements of gas fluctuations. The gas probe uses the polarographic principle for the measurement of oxygen and has tip dimensions of the order of a few microns. Measurements are presented that display the conditions in the gas boundary layer (about 400‐microns thickness), including mean and fluctuating conditions.