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1

Comparison of Average Energy Slope Estimation Formulas for One-dimensional Steady Gradually Varied Flow

Artichowicz W., Mikos-Studnicka P.

Archives of Hydro-Engineering and Environmental Mechanics

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2014

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Vol. 61, nr 3-4

89–-109

EN

To find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is a discrete form of the differential energy equation. Such an approach requires the average energy slope between cross-sections to be estimated. In the literature, many methods are proposed for estimating the average energy slope in this case, such as the arithmetic mean, resulting in the standard step method, the harmonic mean and the geometric mean. Also hydraulic averaging by means of conveyance is commonly used. In this study, water surface profiles numerically computed using different formulas for expressing the average slope were compared with exact analytical solutions of the differential energy equation. Maximum relative and mean square errors between numerical and analytical solutions were used as measures of the quality of numerical models. Experiments showed that all methods gave solutions useful for practical engineering purposes. For every method, the numerical solution was very close to the analytical one. However, from the numerical viewpoint, the differences between the methods were significant, as the errors differed up to two orders of magnitude.

2

Two-dimensional shallow water model for rapidly and gradually varied flow

Szydłowski M.

Archives of Hydro-Engineering and Environmental Mechanics

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2001

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Vol. 48, nr 1

35-61

EN

The numerical solution of full shallow water equation (SWE) including the eddy viscosity terms is presented. In the first part of the paper the solution of the homogeneous part of SWE for discontinuous, rapidly varied flow is reported. The method presented here is based on Roe idea of numerical fluxes of mass and momentum. The numerical solution of SWE on unstructured, triangular mesh is reported and the influence of geometry approximation is examined. The imposing of the boundary condition on a triangular numerical mesh is described in detail. The consistent with finite volume method (FVM) approximation of the viscous part of SWE is presented. The procedure similar to the finite element method (FEM) is used to calculate the function derivatives inside the finite volumes. The specific difficulties of source terms numerical integration are studied and some methods to avoid these problems are presented. To integrate the bottom friction term the splitting technique is implemented. The computed results are compared to analytical solution of Saint-Venant equations, experimental data and results available in the literature. Good agreement between these results is observed.

3

Hydraulic investigation of venturi flumes

Sawicki J.

Archives of Hydro-Engineering and Environmental Mechanics

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2001

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Vol. 48, nr 1

115-130

EN

Venturi flume is a very popular measuring device. A particularly attractive version of such a device is a standing-wave-flume, as this enables determination of liquid discharge by one-point depth measurement only. However, it is necessary to underline, that some essential simplifications must be introduced into the theoretical description of this case. The paper contains the results of the control investigations of six existing Venturi flumes, installed in three functioning sewage-disposal-plants in Poland. It was shown, that some important mistakes can be committed, when somebody plans such a flume. These mistakes worsen the flow measurement accuracy. In conclusion it was stated that the standing-wave-flume must be designed very carefully, with the use of gradually-varied flow equations. An alternative, which is worth using, is a Venturi flume with two-point depth measurement.

4

Boundary problem for equations of steady gradually varied flow in open channels

Szymkiewicz R.

Archives of Hydro-Engineering and Environmental Mechanics

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2001

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Vol. 48, nr 4

23-37

EN

In this paper the problem of solution of ordinary differential equations describing a steady, gradually varied flow is discussed. It is shown that, apart from the initial problem usually solved for open channels, the formulation of the boundary problem is necessary when water levels are imposed at ends of channel. This approach is the mathematically correct formulation of the solution problem for steady, gradually varied flow equations. It enables us to determine directly the water profile and discharge for a single channel, as well as for channel network, instead of the trial and error method usually used. Moreover the formulation of boundary problem with respect to the Manning coefficient and lateral inflow is presented. To solve the listed problems the finite differences method is used.

5

Gradually varied flow of unloaded mud in open channel

Nsom B., Debiane K., Piau J. M., Ayadi A.

Applied Mechanics and Engineering

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1999

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Vol. 4, no 3

443-470

EN

We present a theoretical and experimental study of unloaded free surface mudflow in gradually varied conditions. First of all, a polymer gel following the same rheological law as the natural mud was identified, and its severe rheometric characterization was performed. Then the flow of this synthetic mud was generated in a 1-D open channel. The velocity and depth profiles were then systematically investigated. The theoretical study consisted in determining the velocity profiles in terms of the rheological parameters in uniform conditions as well as in determining the form parameter characterizing the gradually varied flow of yield stress fluids in open channels.