Linear Free Surface of Steady and Unsteady Flow Theoretical Study
This study investigates the relationship between the crucial cone point in limiting steady and unsteady simulation flows inside a simple two-dimensional, vertical sand column subjected to water withdrawal. The analysis employs a versatile technique applicable to both linear steady and linear unstea...
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| Format: | Article |
| Language: | English |
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Tikrit University
2024-02-01
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| Series: | Tikrit Journal of Pure Science |
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| Online Access: | https://tjpsj.org/index.php/tjps/article/view/1365 |
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| _version_ | 1849319634511069184 |
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| author | Suha Ibrahim AL-Ali Nihad Jalal AL-Awsi |
| author_facet | Suha Ibrahim AL-Ali Nihad Jalal AL-Awsi |
| author_sort | Suha Ibrahim AL-Ali |
| collection | DOAJ |
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This study investigates the relationship between the crucial cone point in limiting steady and unsteady simulation flows inside a simple two-dimensional, vertical sand column subjected to water withdrawal. The analysis employs a versatile technique applicable to both linear steady and linear unsteady problems. By utilizing Fourier series techniques, the method finds the solution for a line sink in a vertical duct and extends the steady technique to achieve unsteady solutions. The evolution of the beneath-the-water table surface towards steady states is monitored when they exist. The key findings highlight that as the impermeable base moves further away, the distance between the interface and the sink increases. With increasing flow rates, the critical depth elevates; however, a minor decrease in the critical flow rate is observed when the sink approaches the base. The prior behaviour of the flow impacts the critical flow rate value for each interface height. The study provides steady and unsteady solutions, employing linearized formulations, which demonstrate good agreement with observed phenomena. The length scale of the spatial separation between the interface and the sink emerges as a critical factor in determining cone. These findings contribute to a better understanding of cone phenomena and emphasize the significance of considering specific dimensions in the analysis of flow dynamics within porous media.
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| format | Article |
| id | doaj-art-d115daea6d8b464d95a53c5e3ef1d803 |
| institution | Kabale University |
| issn | 1813-1662 2415-1726 |
| language | English |
| publishDate | 2024-02-01 |
| publisher | Tikrit University |
| record_format | Article |
| series | Tikrit Journal of Pure Science |
| spelling | doaj-art-d115daea6d8b464d95a53c5e3ef1d8032025-08-20T03:50:21ZengTikrit UniversityTikrit Journal of Pure Science1813-16622415-17262024-02-0129110.25130/tjps.v29i1.1365Linear Free Surface of Steady and Unsteady Flow Theoretical StudySuha Ibrahim AL-Ali0Nihad Jalal AL-Awsi1Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, IraqDepartment of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq This study investigates the relationship between the crucial cone point in limiting steady and unsteady simulation flows inside a simple two-dimensional, vertical sand column subjected to water withdrawal. The analysis employs a versatile technique applicable to both linear steady and linear unsteady problems. By utilizing Fourier series techniques, the method finds the solution for a line sink in a vertical duct and extends the steady technique to achieve unsteady solutions. The evolution of the beneath-the-water table surface towards steady states is monitored when they exist. The key findings highlight that as the impermeable base moves further away, the distance between the interface and the sink increases. With increasing flow rates, the critical depth elevates; however, a minor decrease in the critical flow rate is observed when the sink approaches the base. The prior behaviour of the flow impacts the critical flow rate value for each interface height. The study provides steady and unsteady solutions, employing linearized formulations, which demonstrate good agreement with observed phenomena. The length scale of the spatial separation between the interface and the sink emerges as a critical factor in determining cone. These findings contribute to a better understanding of cone phenomena and emphasize the significance of considering specific dimensions in the analysis of flow dynamics within porous media. https://tjpsj.org/index.php/tjps/article/view/1365free surfacesteadytime-dependentporous mediumfreshwaterTropical Island |
| spellingShingle | Suha Ibrahim AL-Ali Nihad Jalal AL-Awsi Linear Free Surface of Steady and Unsteady Flow Theoretical Study Tikrit Journal of Pure Science free surface steady time-dependent porous medium freshwater Tropical Island |
| title | Linear Free Surface of Steady and Unsteady Flow Theoretical Study |
| title_full | Linear Free Surface of Steady and Unsteady Flow Theoretical Study |
| title_fullStr | Linear Free Surface of Steady and Unsteady Flow Theoretical Study |
| title_full_unstemmed | Linear Free Surface of Steady and Unsteady Flow Theoretical Study |
| title_short | Linear Free Surface of Steady and Unsteady Flow Theoretical Study |
| title_sort | linear free surface of steady and unsteady flow theoretical study |
| topic | free surface steady time-dependent porous medium freshwater Tropical Island |
| url | https://tjpsj.org/index.php/tjps/article/view/1365 |
| work_keys_str_mv | AT suhaibrahimalali linearfreesurfaceofsteadyandunsteadyflowtheoreticalstudy AT nihadjalalalawsi linearfreesurfaceofsteadyandunsteadyflowtheoreticalstudy |