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Resonance

, Volume 11, Issue 10, pp 78–92 | Cite as

Archimedes: Bathtub academicpar excellence

  • K. R. Y Simha
  • Usha Srinivasan
Classroom
  • 72 Downloads

Abstract

Stability and control of floating bodies is a major aspect of navigation from ancient to modern times. It is indeed remarkable that Archimedean concepts continue to guide watercraft designers even after 2200 years! Extending Euclidean concept to solids, Archimedes solved the problem of a paraboloid floating stably but with its base inclined to the water surface. Here, we revisit Archimedes and present stability maps (A-maps) for paraboloid, solid cone and a prism. For a specific combination of geometry and specific gravity, these A-maps predict whether a solid floats vertically or in a tilted fashion; or, whether it is partially submerged.

Keywords

Hydrostatics stability of floating bodies metacentre centre of buoyancy paraboloid Archimedean map (A-map) moment of inertia 

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Suggested Reading

  1. [1]
    SW Yuan,Foundations of Fluid Mechanics, Prentice Hall of India, 1969.Google Scholar
  2. [2]
    R K Bansal,Fluid Mechanics and Hydraulic Machines, Laxmi Publications Ltd., October, 2000.Google Scholar
  3. [3]
    C Rorres,The Mathematical Intelligencer, Vol. 26, No. 3, pp. 32–42, 2004.CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2006

Authors and Affiliations

  • K. R. Y Simha
    • 1
  • Usha Srinivasan
    • 1
  1. 1.Department of Mechanical EngineeringIndian Institute of ScienceBangaloreIndia

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