Water Flow Parameters on the Symmetry Axis and Extreme Line of Current
https://doi.org/10.22227/1997-0935.2023.8.1262-1271
Abstract
Introduction. An analysis of mathematical models of two-dimensional planned flows was carried out. Such flows are characterized by local depth-averaged velocities and local depths at each point of the flow. The mathematical model formation of the water flow is based on its division into several sections. There is a section where the flow parameters (velocity, depth, width) are kept constant at the stage of flow exit from the pipe — the inertial front. The purpose of the article and its relevance are defined.
Materials and methods. By introducing dimensionless complexes on the basis of π-theorem, the formula for the length of inertial front of the water flow at its spreading from a rectangular pipe into a wide diverting channel is derived. An analogy from gas dynamics is used, namely, the transition to the plane of the velocity hodograph. Using the velocity hodograph,
the distribution of depths and velocities of the flow along its longitudinal axis of symmetry and along the extreme line of current was obtained. The main computation tasks for the flow parameters have been formulated.
Results. Numerical calculations of the formulated main tasks for determining flow parameters are described. Comparison with experimental data is given and the adequacy of the refined mathematical model of a two-dimensional planned flow is confirmed.
Conclusions. The resulting formula for the length of the inertial front makes it possible to achieve the desired error in calculating the parameters of the water flow. With flow expansions up to 5, the relative error of the ordinates and flow velocities does not exceed 7–10 %. Calculation formulas and implemented programs will allow HTS designers to quickly and accurately determine the boundaries, speed and depth of free flow on the culvert.
Keywords
mathematical model,
hydrodynamics analysis,
two-dimensional water flow,
open-channel hydraulics,
analytical solution
Supporting agencies: The authors are grateful to Doctor of Technical Sciences, Professor of the South Russian State Polytechnic University (NPI) named after M.I. Platov Viktor Nikolaevich Kokhanenko for a number of remarks, which were subsequently eliminated. The authors will be grateful to the reviewers for comments and advice that will help improve the paper, thereby raising its level.
About the Authors
O. A. Burtseva
Platov South-Russian State Polytechnic University (NPI)
Russian Federation
Russian Federation
Olga A. Burtseva — Candidate of Technical Sciences, Assistant Professor, Associate Professor of the Department of General Engineering Disciplines
132 Prosveshcheniya st., Novocherkassk, 346428
ID RSCI: 161751, Scopus: 6507800801, ResearcherID: ABG-9531-2020
M. S. Alexandrova
Platov South-Russian State Polytechnic University (NPI)
Russian Federation
Russian Federation
Maria S. Alexandrova — postgraduate student of the Department General Engineering Disciplines
132 Prosveshcheniya st., Novocherkassk, 346428
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Review
For citations:
Burtseva O.A., Alexandrova M.S. Water Flow Parameters on the Symmetry Axis and Extreme Line of Current. Vestnik MGSU. 2023;18(8):1262-1271. (In Russ.) https://doi.org/10.22227/1997-0935.2023.8.1262-1271
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