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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Main Authors: Suha Ibrahim AL-Ali, Nihad Jalal AL-Awsi
Format: Article
Language:English
Published: Tikrit University 2024-02-01
Series:Tikrit Journal of Pure Science
Subjects:
Online Access:https://tjpsj.org/index.php/tjps/article/view/1365
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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
description 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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institution Kabale University
issn 1813-1662
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publisher Tikrit University
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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