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CRITICAL SURFACE CONING DUE TO A LINE SINK IN A VERTICAL DRAIN CONTAINING A POROUS MEDIUM

Published online by Cambridge University Press:  19 July 2019

S. AL-ALI Open the ORCID record for S. AL-ALI [Opens in a new window] ,
G. C. HOCKING Open the ORCID record for G. C. HOCKING [Opens in a new window]  and
D. E. FARROW Open the ORCID record for D. E. FARROW [Opens in a new window]
S. AL-ALI
Affiliation:
Mathematics and Statistics, Murdoch University, Perth, WA, Australia email [email protected], [email protected], [email protected] Mathematics Department, College of Sciences and Mathematics, Tikrit University, Saladin, Iraq
G. C. HOCKING*
Affiliation:
Mathematics and Statistics, Murdoch University, Perth, WA, Australia email [email protected], [email protected], [email protected]
D. E. FARROW
Affiliation:
Mathematics and Statistics, Murdoch University, Perth, WA, Australia email [email protected], [email protected], [email protected]
*
✉[email protected]
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Abstract

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The withdrawal of water with a free surface through a line sink from a two-dimensional, vertical sand column is considered using the hodograph method and a novel spectral method. Hodograph solutions are presented for slow flow and for critical, limiting steady flows, and these are compared with spectral solutions to the steady problem. The spectral method is then extended to obtain unsteady solutions and hence the evolution of the phreatic surface to the steady solutions when they exist. It is found that for each height of the interface there is a unique critical coning value of flow rate, but also that the value obtained is dependent on the flow history.

Keywords

coningline sinkporous mediafree surface
Type
Research Article
Information
The ANZIAM Journal , Volume 61 , Issue 3 , July 2019 , pp. 249 - 269
Copyright
© 2019 Australian Mathematical Society 

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