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International Studies in Phenomenology and Philosophy

Series | Book | Chapter

192020

Euler's discovery and resolution of d'Alembert's paradox

William W. Hackborn

pp. 43-57

Abstract

This article makes a case for Euler as the first discoverer of what has come to be known as d"Alembert's paradox. Suppose a body is immersed in an unbounded fluid and moves with constant velocity relative to the fluid, which is otherwise undisturbed: d"Alembert's paradox asserts that, contrary to experimental evidence, the fluid exerts no drag force on the body (in the direction opposite to the body's motion) if the fluid is inviscid and incompressible. Euler demonstrates this, for a two-dimensional body or an axisymmetric body whose axis aligns with its motion, in his extensive 1745 commentary on New Principles of Gunnery, a book published in 1742 by Benjamin Robins. After a rigorous analysis, Euler recognizes that the absence of a drag force conflicts with experience for fluids like air and water, and he uses Robins' experiments with musket balls to explain this anomaly as a consequence of greater fluid pressure fore of the body than aft of it, due to a corresponding fore–aft asymmetry in the density of the fluid. Essentially, he resolves the apparent paradox by removing the assumption of the fluid's incompressibility.

Publication details

Published in:

Zack Maria, Schlimm Dirk (2018) Research in history and philosophy of mathematics: the CSHPM 2017 annual meeting in Toronto, Ontario. Basel, Birkhäuser.

Pages: 43-57

DOI: 10.1007/978-3-319-90983-7_3

Full citation:

Hackborn William W. (2018) „Euler's discovery and resolution of d'Alembert's paradox“, In: M. Zack & D. Schlimm (eds.), Research in history and philosophy of mathematics, Basel, Birkhäuser, 43–57.