Journal of Hydraulic Engineering

This paper discusses the most common types of high-head gates, including slide gates, fixed-wheel gates, radial gates, and jet-flow gates, and their application. Hydraulic design considerations for these gates are discussed. “High-head gates” refers to all gates used in dams, tunnels, penstocks, or outlets that are required to withstand and operate under water heads greater than 25 m. The applicability of each type of gate is considered for high-head situations. The paper addresses the state of the art of high-head gates as it has developed since the 1973 paper by the Task Committee on Outlet Works of the Committee of Hydraulic Structures of the then–Hydraulics Division. This paper was submitted to the then–ASCE Hydraulic Division, as part of the final report to the Task Committee on Design and Operation of Hydraulic Gates.

A model that describes the density-profile evolution in a confined region with a stably stratified fluid, where mixing is induced by a circular, nonswirling turbulent jet discharged vertically down into the fluid is presented here. The interaction between the downward-moving jet and a resulting rising plume is modeled through a coupled system of equations that encompasses integral equations for volume, momentum, and buoyancy conservation for the jet and plume, respectively. A schematized flow pattern in the ambient fluid is employed to determine the effect of the jet/plume mixing on the density-profile evolution, and a diffusion equation is used to describe additional mixing processes in the ambient fluid outside the jet/plume region. The model is validated with experimental data on the density-profile evolution in a rectangular container produced by a mixing jet, and the calculations compare favorably with data for higher values on the densimetric Froude number. The mixing is underestimated for lower values on the Froude number.

Experiments are reported that quantify the effect of channel geometry on local scour at abutments for bridges crossing compound river channels. The data apply to the case of the abutment extending into the main channel. The channel geometry effects are represented by a multiplying factor. This factor, K _G , has the effect of reducing the scour depth from that in the “corresponding” rectangular channel, which is defined as the channel that has the same overall width as the compound channel and the same depth as the main channel of the compound section. Up to threefold reductions in scour depth, from that in the corresponding rectangular channel, were observed. It is shown that K _G , as determined by a simple expression involving the cross-section geometry and roughness of the main and flood channels, is consistent with the experimental data. An expression for the equivalent length of abutment in a compound channel is proposed also.

The three-dimensional quasi-steady vortex flow field around circular piers in a quasi-equilibrium scour hole under a clear water regime has been investigated experimentally. The main characteristic features of the flow, to be modeled, are a relatively large secondary vortex flow within the scour hole and skewed velocity distributions along the circumference of the pier. The flow field has been divided into a number of parts according to the flow characteristics. The components of quasi-steady velocity for different parts have been theoretically expressed in the form of equations satisfying the continuity equation and the requirements of fitting an individual profile of the measured velocity components. Using the suitable functions, the equations of the velocity components derived for different parts have been combined and matched at the junctions of these parts to get a single equation for each velocity component. The measured data have been utilized to determine the coefficients and exponents used in these equations through curve fittings. The proposed flow model, which corresponds closely with the observations, can be utilized to simulate the flow field in prototype.

The first-order flux difference splitting scheme and its second-order extensions are investigated for their applicability to dam-break problems. Roe's first-order explicit scheme is first formulated using an approximate Jacobian. A general entropy-satisfying formula is incorporated, which significantly improves the applicability of the Roe scheme. The Roe scheme is extended to second-order accuracy using the Lax-Wendroff numerical flux, the MUSCL approach, and the modified flux approach. To damp out oscillations resulting from the second order of accuracy, a flux/slope limiter is incorporated in the second-order schemes. Numerical results for dam-break problems demonstrating the effect of the violation of the entropy-inequality condition and effectiveness of the proposed treatment by a general entropy-satisfying formula are presented. The Roe scheme is compared against its second-order extensions as well as with first-order schemes such as the Lax-Friedrichs and modified Beam and Warming schemes. It is demonstrated that although higher-order schemes provide better shock resolution, Roe's first-order scheme may be preferred for practical applications when computation time, overall accuracy, and applicability are considered.

Routing equations for detention reservoir systems are developed from an approximate analytical solution of the nonlinear storage differential equation. The approximate solution is obtained by a two-term perturbation expansion whereby the zeroth-order term is the linear solution and the first-order term is the correction. The first-order approximation, which allows for arbitrary multievent inflow hydrographs, irregular reservoir configuration, and various types and sizes of outlets, is found to be accurate for all practical purposes. The asymptotic solution allowed the derivation of design equations that can apply for arbitrary reservoir configuration and for various types and sizes of outlet.

Data from the Seymour River watershed in southwestern British Columbia were used to develop a 24-h design storm for the coastal region. The study showed that there is only a small variation in the time distribution of the storm with elevation, and comparison with the results of other studies and data from other stations showed that the findings of this work are transferable to other areas of the region. Simulation of the streamflow in a watershed of the region revealed that the developed 10% time probability curve and the Soil Conservation Service Type IA curve reproduce the observed peak flows. Analysis of the spatial distribution of the annual extreme 24-h storms showed that the mean annual precipitation, which increases up to an elevation of 400–800 m, and then levels off or even decreases, can be used as an index for the estimation of the 24-h extreme rainfall. Although the study has been concentrated on the coastal British Columbia, there are indications that the results may be applicable to the greater region of the coastal Pacific Northwest.

In this study, critical submergence for an air-entraining vortex at intakes in a uniform canal flow was investigated. The potential flow solution for the combination of a point sink and a uniform canal flow is available, and is known as Rankine's ovoids or half-bodies. This study was based on Rankine's ovoids. Experiments have shown that the critical submergence occurs when the upper boundary of Rankine's ovoids reaches the water surface directly above the intake center. Theoretical and experimental results have indicated that the critical submergence for an intake in a uniform canal flow is equal to the radius of an imaginary spherical sink surface (assuming no canal flow) where the radial velocity is equal to half of the velocity of the uniform canal flow. The imaginary spherical sink has the same center and discharge as the intake. The agreement between the theoretical critical submergence and experimental results is found to be good.

The paper discusses the rapid damping of pressure peaks in a water-hammer phenomenon after the end of a complete valve-closure maneuver. This effect is due to flow characteristics not considered when one-dimensional models are employed. Such an effect is linked to the cross-sectional velocity profiles, and therefore to the intrinsic two-dimensionality of the flow field. Applying a 2-D model, recently proposed in the literature, to expand the limited experimental data available with numerical results, useful information on the evolution of the velocity profiles during a transient has been obtained. Starting from an in-depth inspection of the terms in the momentum equation, an additional term is introduced to model the effects of the flow-field two-dimensionality in a 1-D formulation. Finally, the adequacy of a relationship previously proposed by the writers to evaluate the additional term is specifically showed for fast transients in the field of low-Reynolds-number flows when no cavitation occurs, even if its validity has been proven elsewhere for rather different conditions.

A simple analytic expression for calculating fine suspended-sediment transport rates is derived by assuming a parabolic distribution of eddy viscosity, which results in a von Kármán–Prandtl–type velocity profile, and Rouse's sediment-concentration profile. The resulting equation for sediment transport rate requires a set of hydraulic conditions and a reference sediment concentration. This expression is easy to use in practical applications, and predicted transport rates compare favorably with rates calculated from field measurements.