Mathematical Formulations of Lumped Parameter Models for Unsteady Flow and Comparison of the Models Derived From Womersley's Solution and Paraboloid Velocity Profile.
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| Title: | Mathematical Formulations of Lumped Parameter Models for Unsteady Flow and Comparison of the Models Derived From Womersley's Solution and Paraboloid Velocity Profile. |
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| Authors: | Bosu, Kushal1 (AUTHOR), Guha, Abhijit1 (AUTHOR) a.guha@mech.iitkgp.ac.in |
| Source: | ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. Apr2026, Vol. 106 Issue 4, p1-23. 23p. |
| Subjects: | Unsteady flow, Lumped parameter systems, Electric inductance, Equivalent electric circuits, Pulsatile flow |
| Abstract: | Mathematical expressions for resistance and inductance that correspond to Womersley's well‐known solution for periodic unsteady flow in a cylindrical tube are rigorously formulated. A formal mathematical analysis is also formulated for periodic unsteady flow by assuming the paraboloid velocity profile. The volumetric flow rate given by such unsteady analysis is compared here with Womersley's solution; Womersley himself had compared his solution with Poiseuille's steady solution (without mathematical justification). Analytical expressions for the phase difference between the flow rate and pressure are derived, both for the paraboloid velocity profile and Womersley's solution. The formulations of the equivalent electrical circuits are mathematically exact. The equivalent electrical circuit corresponding to Womersley's solution and that for paraboloid velocity are shown to be different at an arbitrary Womersley number. When the Womersley number approaches zero, the resistances in the two analyses are the same, but the inductances are not. When the Womersley number approaches infinity, the inductances in the two analyses are the same, but the resistances are not. The validity (or inappropriateness) of the expressions for the resistance and the inductance that are routinely used, on a rather ad hoc basis, in the vast literature on the lumped parameter analysis of pulsatile physiological flows is thus rigorously assessed. [ABSTRACT FROM AUTHOR] |
| Copyright of ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193323506 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Mathematical Formulations of Lumped Parameter Models for Unsteady Flow and Comparison of the Models Derived From Womersley's Solution and Paraboloid Velocity Profile. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Bosu%2C+Kushal%22">Bosu, Kushal</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Guha%2C+Abhijit%22">Guha, Abhijit</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> a.guha@mech.iitkgp.ac.in</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22ZAMM+--+Journal+of+Applied+Mathematics+%26+Mechanics+%2F+Zeitschrift+für+Angewandte+Mathematik+und+Mechanik%22">ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik</searchLink>. Apr2026, Vol. 106 Issue 4, p1-23. 23p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Unsteady+flow%22">Unsteady flow</searchLink><br /><searchLink fieldCode="DE" term="%22Lumped+parameter+systems%22">Lumped parameter systems</searchLink><br /><searchLink fieldCode="DE" term="%22Electric+inductance%22">Electric inductance</searchLink><br /><searchLink fieldCode="DE" term="%22Equivalent+electric+circuits%22">Equivalent electric circuits</searchLink><br /><searchLink fieldCode="DE" term="%22Pulsatile+flow%22">Pulsatile flow</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Mathematical expressions for resistance and inductance that correspond to Womersley's well‐known solution for periodic unsteady flow in a cylindrical tube are rigorously formulated. A formal mathematical analysis is also formulated for periodic unsteady flow by assuming the paraboloid velocity profile. The volumetric flow rate given by such unsteady analysis is compared here with Womersley's solution; Womersley himself had compared his solution with Poiseuille's steady solution (without mathematical justification). Analytical expressions for the phase difference between the flow rate and pressure are derived, both for the paraboloid velocity profile and Womersley's solution. The formulations of the equivalent electrical circuits are mathematically exact. The equivalent electrical circuit corresponding to Womersley's solution and that for paraboloid velocity are shown to be different at an arbitrary Womersley number. When the Womersley number approaches zero, the resistances in the two analyses are the same, but the inductances are not. When the Womersley number approaches infinity, the inductances in the two analyses are the same, but the resistances are not. The validity (or inappropriateness) of the expressions for the resistance and the inductance that are routinely used, on a rather ad hoc basis, in the vast literature on the lumped parameter analysis of pulsatile physiological flows is thus rigorously assessed. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/zamm.70402 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 23 StartPage: 1 Subjects: – SubjectFull: Unsteady flow Type: general – SubjectFull: Lumped parameter systems Type: general – SubjectFull: Electric inductance Type: general – SubjectFull: Equivalent electric circuits Type: general – SubjectFull: Pulsatile flow Type: general Titles: – TitleFull: Mathematical Formulations of Lumped Parameter Models for Unsteady Flow and Comparison of the Models Derived From Womersley's Solution and Paraboloid Velocity Profile. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Bosu, Kushal – PersonEntity: Name: NameFull: Guha, Abhijit IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00442267 Numbering: – Type: volume Value: 106 – Type: issue Value: 4 Titles: – TitleFull: ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik Type: main |
| ResultId | 1 |
