Journal of Hydraulic Engineering

In 1930, Lacey formulated Lindley's ideas on regime canals employing three sets of data, none of which were complete. In the next 55 years, the formulas have undergone scrutiny but are used today in a form quite similar to the original. We have compared Lacey's and subsequent regime equations to the equations of conservation of mass and Newton's laws for water and sediment. The conclusions are that: $f_{\mathrm{VR}}\ne f_{\mathrm{RS}}$ for almost all canals in regime; $f_{\mathrm{VR}}$ is a measure of the concentration of sand being transported provided the transport is vanishingly small; $f_{\mathrm{VR}}$ and $f_{\mathrm{RS}}$ are uniquely related in all channels, rigid and alluvial, in which the kinematic wave number, is one; and Lacey's roughness factor is heavily biased towards gravel and boulder channels. These findings do not detract from the geomorphic value of Lacey's regime. For engineering, however, a reformulation employing the conservation laws and Newton's laws is in order.

In connection with the mechanics of ripples and dunes, the governing equations of convection‐diffusion of suspended sediment in two‐dimensional flow fields over ripples or dunes are solved by the finite‐element method. The role of suspended sediment in determining the steady bedform length is theoretically investigated. The postulate that, in the case of steady bedforms, the diffusive flux vector at any point on the stoss must point into the interior of the flow region divides mathematically acceptable solutions into two categories: (1) Physically acceptable solutions; and (2) physically unacceptable solutions. The marginal solutions, which lie on the common boundary between the two classes in the solution space, are of special interest. They represent steady bedforms with minimum length under the prevailing flow conditions, and they are conjectured to correspond to the steady bedforms occurring in nature. Finally, the theory is compared with the physical observations made in flumes, canals, and rivers. The comparison shows a fair agreement.

The relative merits of different measures of flow intensity as predictors of bed‐load transport rates are assessed. Tractive stress, when based on depth and slope, is a poor predictor, especially in narrow channels. Correct application requires elimination of wall and bedform roughness, leaving only that stress acting on the bed grains. When this is done, excellent correspondence with bed‐load rates is found in the experiments of Gilbert, Meyer‐Peter, and G. P. Williams, analyzed here. Vertically averaged velocity requires a correction for depth and particle size; then, it is directly comparable with grain tractive stress. Stream power has limitations as a predictor because it is the product of vertically averaged velocity and bed tractive stress, and hence subject to the problems that those variables individually experience. Unit stream power is a good predictor of concentration in some circumstances. It performs poorly, however, in the data set of Williams, and reasons for this are given.

The diffusion equation is a simplification of the two‐dimensional continuity and momentum equations. This simpler dynamic model of two‐dimensional hydraulics affords the hydrologist a means to quickly estimate floodflow effects for overland flow. A numerical model using the diffusion approach (DHM) is applied to a set of idealized catchments in order to develop synthetic unit hydrograph S‐graph equivalents. The model is based on an explicit, integrated finite‐difference scheme, and the catchment is represented by topographic elevation and geometric data. Synthetic unit hydrographs (S‐graphs) developed from use of the DHM are used to advance interesting relationships between the unit hydrograph lag factor and the constant effective rainfall intensity used to generate the S‐graphs. Sensitivity of the synthetic S‐graphs to variations in idealized catchment size, slope, shape, friction parameters, and effective rainfall intensity are examined. Comparisons between linear and nonlinear unit hydrograph models, and a diffusion (DHM) and kinematic wave simplification of DHM are made for various time distributions of effective rainfall. Use of the standard SCS unit hydrograph is shown to provide a reasonable approximation of two‐dimensional overland flow as predicted by a DHM or kinematic routing technique.

A common problem in engineering hydrology is estimating the attenuation effects of storage reservoirs on peak inflow rates. While this may always be accomplished by a detailed hydrologic or hydraulic routing of the inflow hydrograph, approximate solutions are often desirable. A simple graphic procedure is developed to permit a direct determination of peak outflow as a function of parameters describing the inflow hydrograph, storage, and outlet characteristics. This procedure is based on the use of a dimensionless two‐parameter inflow hydrograph and the solution of a nonlinear differential routing equation with reservoir storage expressed as an exponential function of outflow. Curves obtained from the results of the complete hydrograph routing indicate that the attenuation can be related to a dimensionless routing number, which in turn is defined by the reservoir and inflow parameters. The approach is judged to provide an accurate solution for routing problems that satisfy the methodology assumptions and permits a rapid evaluation of the effects of parameter changes on attenuation.

As a modification of the currently recommended U.S. Army Corps of Engineers Waterways Experiment Station (W.E.S.) standard spillway crest profile, a crest geometry of which the curvature is continuous is proposed. Such a crest shape is particularly useful to predict the bottom pressure distribution. Moreover, negative pressure peaks might be reduced significantly from those as encountered in the present design.