Stokes drag on axially symmetric bodies: A new approach
type: Item
instance of: scholarly article
title: Stokes drag on axially symmetric bodies: A new approach
zbMATH Open document ID: 0962.76024
DOI: 10.1007/BF02838005
author: Sunil Datta
author: Kumar Srivastava
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2001-05-29T00:00:00Z
review text: The paper deals with the problem of external steady Stokes flow past axisymmetric impermeable rigid bodies. Using an elementary, but refined, analysis of the drag force formula for a sphere in uniform far-field flow, the authors obtain a simple formula, the evaluation of which renders correct values for the drag force not only on a sphere, but also on a spheroidal body in a uniform far-field flow parallel to its axis of symmetry. In the same way of reasoning, similar and correct formulas are also found for the drag force in the case of uniform transverse far-field flow and for the moment in the case of rotation about the axis of symmetry of a spherical or spheroidal body. These formulas, so far, are very interesting, but, unfortunately, of no practical use, since the final exact solutions for these body shapes and flow situations are already well known. However, the authors conjecture, and that is the main point of the paper, that the same formulas are also valid in general for every axisymmetric body with continuously varying tangent. The validity of such a conjecture would be, of course, of considerable practical importance, since we are interested, in the first place, in the drag force and the moment acting on a body in Stokes flow, and so we would not have to solve the problem as a whole for every new body form of the aforementioned kind. However, knowing the complexity of the final Stokes flow integral equation system for determining axial and radial stress distributions along the meridional contour of a strictly convex axisymmetric body in a uniform far-field flow parallel to the symmetry axis of the body, one must first doubt the general validity of such a conjecture. The two integral equations of the said system are of the first kind and involve complete elliptical integrals of the first and second kind which makes the problem quite difficult for an analytical treatment. For the cases of a spherical or spheroidal (prolate or oblate) body (and this reviewer c…
Mathematics Subject Classification ID: 76D07
zbMATH DE Number: 1394551
zbMATH Keywords: Stokes drag
zbMATH Keywords: spheroidal body
zbMATH Keywords: external steady Stokes flow
zbMATH Keywords: moment
zbMATH Keywords: cycloidal body
reviewed by: Tomislav Zlatanovski
MaRDI profile type: Publication
cites work: Hydromechanics of low-Reynolds-number flow. Part 1. Rotation of axisymmetric prolate bodies
cites work: Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows
cites work: The self-propulsion of microscopic organisms through liquids
cites work: Q3753663
cites work: Q4144962
full work available at URL: https://doi.org/10.1007/bf02838005
OpenAlex ID: W2082123506
description: scientific article; zbMATH DE number 1394551