Journal of Hydraulic Engineering

Characteristics of a buoyant surface jet discharged on a sloping bottom are reviewed and a numerical experiment is performed to evaluate the depth at the point where the jet detaches from the bottom. This calculation is important in the context of predicting dilution and spreading characteristics of buoyant discharges, for example, associated with heated discharges from power plants. The experiment is based on a direct numerical solution of the longitudinally integrated momentum equation, which takes into account entrainment and bottom friction. Results are compared with laboratory and field data reported in the literature, as well as previous empirical relations for calculating this depth. It is found that the appropriately scaled detachment depth varies with the inverse of the discharge densimetric Froude number. The scaled depth decreases with increases in either the entrainment or bottom friction coefficient, but increases with increasing slope. A minor effect of discharge aspect ratio is also shown. An equation is developed for predicting detachment depth and the results help to resolve differences seen in previous relations.

The propagation of waves in ice‐covered channels is analyzed using linearized forms of the three equations governing one‐dimensional unsteady flow in rectangular ice‐covered channels. The equations describe fluid continuity, momentum, and the ice‐cover response. The ice cover is assumed to be a relatively thin, continuous elastic plate. Five well‐defined bands of wave celerity are found in the wave‐number spectrum. Three bands exist at wavelengths longer than about 20 characteristic lengths of the ice and define the range of quasi‐open‐channel wave propagation over which the wave celerities are analogous to open‐channel wave celerities. Two bands exist at shorter wavelengths: an ice‐coupled band (in which the wave celerity increases sharply with wave number and is a function of the wavelength and the ice‐cover properties) and, at even shorter wavelengths, an acoustic band. The attenuation of ice‐coupled and acoustic waves is found to be small. The group velocity over the dispersive ice‐coupled band is found to always exceed the wave celerities.

To obtain the relationship between the hydraulic characteristics and the breach shape, a new method is developed for calculation of the hydraulic characteristics of dam‐break waves in an arbitrary channel, whose perimeter can be described by a number of line segments. By a mathematical transformation, the shape parameters of a breach cross section are separated from the integral equation and become a coefficient that can be calculated. The original integral equation of dam‐break flood is transformed into a model equation. This model equation can be treated as a pure mathematical problem. By this model, the hydraulic characteristics of the dam‐break waves with complicated outlet shape can be calculated directly and the accuracy of the method is the same as that of Ritter's solution of a rectangular cross section. In addition to the solving process for an arbitrary section, an example of a complex cross section and the data for a trapezoidal cross section are presented.

Bed‐load transport capacity in braided gravel‐bed rivers varies as hydraulic geometry changes downstream. Differences in capacity lead to variations in bed‐material storage as a consequence of bed‐load transport during floods. In turn, storage changes produce irregular fluctuations in bed‐level or sediment translation waves in the bed material. These waves are the mechanism by which bed load is transported in braided and, in fact, all alluvial rivers with variable downstream hydraulic geometry. An approximate expression for wave velocity indicates that annual wave travel distance can be hundreds of meters or more per year for waves up to 0.5 m high. Although sediment waves cause shifts in bed‐load rating at a cross section, bed‐load yield may still be estimated using bed‐load ratings based on depth‐discharge relations defined for periods between rating changes. A procedure is given for stable channel design in the presence of sediment waves based on equivalence of yield for some period in the design reach and a stable reference reach. The condition that the bed‐load ratings for the two reaches must intersect either aids or allows solutions of the design problem.

A study of the effect of the location of the toe of a B‐jump (relative to the break in the channel slope) on its characteristics was designed and implemented. The experimental results were used to introduce new expressions for the hydraulic quantities that govern a B‐jump. Three slopes were investigated: 1:3, 1:4, and 1:5 (vertical:horizontal). Measurements of the length of the roller and the tail‐water depth were also made. Analysis of the experimental data showed the importance of introducing a new parameter representing the effect of the relative location of the toe of the jump along the sloping channel. The proposed expressions were developed for flows with the approach Froude numbers ranging from 2.4 to 7.4.

The transfer of energy and irreversible energy losses at junctions may dominate flow distribution in pipe networks comprised of connected large‐diameter pipes of short lengths. Neglecting the junction effects when calculating network hydraulics is unacceptable and the use of constant loss coefficients to represent these effects in such networks may not be adequate. In the present study, precise relationships based on experimental data are used to represent the junction‐loss coefficients. These relations, which depend on flow conditions, are incorporated into a computer network analysis model. Significant deviations in flow rates calculated using constant junction loss coefficients and the semiempirical relationships based on experimental data are obtained using an example network characterized by short pipe sections. It is also shown that although there is always a net energy loss at a junction, there may be significant exchange of specific energy from one flow stream to the other. The use of constant loss coefficients is inadequate to account for this phenomenon.