Journal of Hydraulic Engineering

The vortex tube is a device for extracting sediment from canals that consists of a tube laid horizontally across the canal bed with an open slit along its top edge. Flow from near the canal bed is collected in the vortex tube and is extracted from the canal. Its trapping efficiency is defined as the proportion of the canal sediment load that is extracted. The present paper provides a theory for predicting the trapping efficiency of vortex tubes that is based on a theoretical sediment flux profile for the canal upstream from the vortex tube. The theory is compared with field measurements of trapping efficiency at six sediment extractors. The ratio of observed trapping efficiency to predicted trapping efficiency has a mean value of 1.0 and a standard deviation of 0.25 over 120 measurements. The present paper also provides quantitative guidance on locating vortex tubes so that local effects, such as canal bends, do not reduce trapping efficiency. (A design method for vortex tubes, which uses trapping efficiency predictions, is presented in a companion paper.)

The vortex tube is a device for extracting sediment from canals. A companion paper presented methods for assessing the trapping efficiency of vortex tubes. This present paper provides a flow analysis that is based on flow continuity, a momentum balance along the tube axis, and an angular momentum balance as flow enters the tube. The predictions of the analysis are compared with laboratory and field data: the ratio of an observed discharge coefficient to its predicted value had a mean value of 0.97 and a standard deviation of 0.11 over 956 measurements. The analysis is then used to form design guidelines so that the following three criteria are satisfied: the difference in head between the canal and the vortex tube outlet is acceptable; the tube does not block with sediment; and water is near uniformly abstracted along the length of the tube. Finally, a procedure is given for the design of vortex tubes that uses as input the required trapping efficiency, the required head loss, and the canal characteristics.

Layer‐averaged equations describing the characteristics of a two‐dimensional unsteady inclined starting plume, which consists of two parts, i.e. a front part and a body part, are derived. A numerical model is formulated on the basis of an explicit finite‐difference scheme incorporating the characteristic method with a specified‐space grid for the body part and the Runge‐Kutta‐Gill method for the front part. The model is calibrated with existing experimental data and the calculated results are then compared with additional laboratory experimental data. The proposed hybrid model incorporates the major physical principles involved. For a wide range of practical applications, the model is capable of predicting such plume characteristics as velocity, thickness, and density.

Various numerical techniques, such as wave‐speed adjustment or interpolation, are generally required in order to apply the fixed‐grid method of characteristics to multipipe systems or to systems with variable wave speed. However, these techniques introduce into the solution unwanted side effects such as numerical attenuation and dispersion. The present paper develops the concept of an equivalent hyperbolic differential equation to study how discretization errors arise in pipeline applications for the most common interpolation techniques. In particular, it is shown that space‐line interpolation and the Holly‐Preissmann scheme are equivalent to a wave‐diffusion model with an adjusted wave speed, but that the latter method has additional source and sink terms. Further, time‐line interpolation is shown to be equivalent to a superposition of two waves with different wave speeds. In general, the equivalent hyperbolic differential equation concept evaluates the consistency of the numerical scheme, provides a mathematical description of the numerical dissipation and dispersion, gives an independent way of determining the Courant condition, allows the comparison of alternative approaches, finds the wave path, and explains why higher‐order methods should usually be avoided.

The paper examines the problem of prediction of uniform turbulent flow in a compound channel with the nonlinear $k‐\epsilon$ model. This model is capable of predicting the secondary currents, caused by the anisotropy of normal turbulent stresses, that are important features of the flow in compound channels, as they determine the transverse momentum transfer. The model is applied to reproduce experimental runs available in the literature. The comparison shows that the model predicts with accuracy the distribution of the primary velocity component, the secondary circulation, and the discharge distribution. The numerical results are used to search a subdivision surface between main channel and floodplain on the basis of the flow field and to compare different subdivision surfaces on the basis of the discharge distribution by a simple uniform flow formula. The better subdivision surfaces as predicted by the model are the diagonal surface going from the corner between main channel and floodplain to the free surface on the symmetry plane and the bisector of the same corner.

The aggregated‐precipitation input to a catchment is defined in this work as one that minimizes an objective measure of the difference between the calculated and the observed hydrograph. This measure is different from the evaluated mean areal precipitation using, for example, Thiessen polygons. Once the aggregated inputs are derived for a set of storm events over a given basin, the relationships between the mean areal precipitation, the precipitation at a point inside the basin, and the derived aggregated input may be analyzed to detect linkages among them. We represented this linkage by a weighting function, which multiplies single raingage records to obtain the aggregated input. Streamflow measurements and a simple model of the rainfall‐runoff process are used to evaluate this weighting function, which varies during the storm. The ultimate goal of this work is to use this relationship to evaluate the aggregated input for ungaged storm events. In this preliminary phase, only linearly distributed and aggregated‐input models were considered, coupled with rainfall fields generated from a stochastic space‐time precipitation model. Results obtained by considering the distributed rainfall fields generated by a simpler version of the WGR model are presented, with reference to a catchment in Northern Italy.

The possibility of shock‐wave reduction by a wedge‐shaped bottom drop is considered. The results are shown to depend on the so‐called shock number S. Optimum wall deflection is defined as the configuration with horizontal flow surface ahead and beyond the shock front. Off‐design is also discussed and it is found that acceptable flow conditions occur for a limited range. An earlier approach to the generalized wall profile is expanded by accounting for the bottom drop.