Purpose: to apply the variation principle of least action to create a theory for calculating the broad-crested weir, to compare the results obtained with the data of various domestic and foreign researchers and to draw conclusions about the accuracy of the solution obtained.
Materials and methods. The minimum flow depth on a broad-crested weir was determined by minimizing the Lagrangian liquid flow. This equation is used to close the equation of specific total flow energy. The verification of the obtained method in determining the minimum depth at the weir crest was carried out by a laboratory experiment and computer simulation of the flow movement through the weir, carried out in the ANSYS 17.0 software package. The results of determining weir capacity were compared with the experimental and theoretical data of domestic and foreign authors.
Results. The comparison of the results of calculations of the broad-crested weir capacity with a wide threshold with the proposed method showed good agreement with the data of various authors, the difference did not exceed 3 %. The comparison of the results of depth calculations at the weir crest showed their agreement with the data of various authors, our own laboratory experiments and computer simulation. The adequacy of the obtained dependence was confirmed on the basis of determination coefficient and the Fisher variance ratio.
Conclusions. A new theoretical method for hydraulic calculation of a broad-crested weir has been obtained, which made it possible to determine the liquid flow depth at the weir crest and its capacity. An analysis of the applicability of the method showed that the depth by the principle of least action is realized only in cases where the flow has no obstacles for free discharge. The limitation of the proposed method is the mandatory presence of a section with a relatively streamline flow and hydrostatic pressure distribution on the weir crest, as well as the absence of flooding of the structure.
doi: 10.31774/2712-9357-2022-12-2-192-208
broad-crested weir, variation principle, principle of least action, discharge coefficient, minimum depth
Shalanin V. А. Principle of least action in broad-crested weir calculation. Land Reclamation and Hydraulic Engineering. 2022;12(2):192–208. (In Russ.). https://doi.org/10.31774/2712-9357-2022-12-2-192-208.
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