Sedimentation motion of sand particles in moving water (I): The resistance on a small sphere moving in non-uniform flow
In hydraulics, when we deal with the problem of sand particles moving relative to the surrounding water, Stokes’ formula of resistance has usually been used to render the velocity of sedimentation of the particles. But such an approach has not been proved rigorously, and its accuracy must be careful...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-11-01
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| Series: | Theoretical and Applied Mechanics Letters |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2095034922000721 |
| _version_ | 1798004510125195264 |
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| author | Shu-Tang Tsai |
| author_facet | Shu-Tang Tsai |
| author_sort | Shu-Tang Tsai |
| collection | DOAJ |
| description | In hydraulics, when we deal with the problem of sand particles moving relative to the surrounding water, Stokes’ formula of resistance has usually been used to render the velocity of sedimentation of the particles. But such an approach has not been proved rigorously, and its accuracy must be carefully considered. In this paper, we discuss the problem of a sphere moving in a non-uniform flow field, on the basis of the fundamental theory of hydrodynamics. We introduce two assumptions: i) the diameter of the sphere is much smaller than the linear dimension of the flow field, and ii) the velocity of the sphere relative to the surrounding water is very small. Using these two assumptions, we solve the linearized Navier-Stokes equations and equations of continuity by the method of Laplace transform, and finally we obtain a formula for the resistance acting on a sphere moving in a non-uniform flow field. |
| first_indexed | 2024-04-11T12:24:52Z |
| format | Article |
| id | doaj.art-81861defc5ad4a2388f73a4d2ebc0236 |
| institution | Directory Open Access Journal |
| issn | 2095-0349 |
| language | English |
| last_indexed | 2024-04-11T12:24:52Z |
| publishDate | 2022-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Theoretical and Applied Mechanics Letters |
| spelling | doaj.art-81861defc5ad4a2388f73a4d2ebc02362022-12-22T04:23:59ZengElsevierTheoretical and Applied Mechanics Letters2095-03492022-11-01126100392Sedimentation motion of sand particles in moving water (I): The resistance on a small sphere moving in non-uniform flowShu-Tang Tsai0Institute of Mechanics, Academia Sinica (Chinese Academy of Sciences), Beijing 100190, ChinaIn hydraulics, when we deal with the problem of sand particles moving relative to the surrounding water, Stokes’ formula of resistance has usually been used to render the velocity of sedimentation of the particles. But such an approach has not been proved rigorously, and its accuracy must be carefully considered. In this paper, we discuss the problem of a sphere moving in a non-uniform flow field, on the basis of the fundamental theory of hydrodynamics. We introduce two assumptions: i) the diameter of the sphere is much smaller than the linear dimension of the flow field, and ii) the velocity of the sphere relative to the surrounding water is very small. Using these two assumptions, we solve the linearized Navier-Stokes equations and equations of continuity by the method of Laplace transform, and finally we obtain a formula for the resistance acting on a sphere moving in a non-uniform flow field.http://www.sciencedirect.com/science/article/pii/S2095034922000721 |
| spellingShingle | Shu-Tang Tsai Sedimentation motion of sand particles in moving water (I): The resistance on a small sphere moving in non-uniform flow Theoretical and Applied Mechanics Letters |
| title | Sedimentation motion of sand particles in moving water (I): The resistance on a small sphere moving in non-uniform flow |
| title_full | Sedimentation motion of sand particles in moving water (I): The resistance on a small sphere moving in non-uniform flow |
| title_fullStr | Sedimentation motion of sand particles in moving water (I): The resistance on a small sphere moving in non-uniform flow |
| title_full_unstemmed | Sedimentation motion of sand particles in moving water (I): The resistance on a small sphere moving in non-uniform flow |
| title_short | Sedimentation motion of sand particles in moving water (I): The resistance on a small sphere moving in non-uniform flow |
| title_sort | sedimentation motion of sand particles in moving water i the resistance on a small sphere moving in non uniform flow |
| url | http://www.sciencedirect.com/science/article/pii/S2095034922000721 |
| work_keys_str_mv | AT shutangtsai sedimentationmotionofsandparticlesinmovingwateritheresistanceonasmallspheremovinginnonuniformflow |