What is the d’Alembert Paradox and What Does It Mean?

What is the d’Alembert Paradox and What Does It Mean?

June 27, 2021 Off By Felso

D’Alembert applied the same principle to fluids in his Traite de l’equilibre et du mouvement des fluides (“Treatise on the Equilibrium and the Motion of Fluids”), published the following year, and furthered the earlier research of Euler and Daniel Bernoulli on this subject. Although D’Alembert treated mechanics as a purely theoretical subject, he thought that the theory of motion of fluids should be based on an empirical basis.

This view stemmed from the fact that d’Alembert had obtained a theoretical result in fluid mechanics that seemed incompatible with reality, known as the “d’Alembert paradox”. While examining the equations of motion of fluids, D’Alembert came to the conclusion that no force acts on an object traveling in a straight line at constant velocity in an incompressible, viscous (zero viscosity) fluid. However, it can be deduced from this principle, in the most exaggerated interpretation, that submarines can move underwater without the need for propellers. This contradiction, which D’Alembert arrived at in fluid mechanics, disappears when one considers that a real fluid is always somewhat viscous. Viscosity is an important factor in some fluids, such as honey, but negligible in most fluids, such as seawater. In many water-related problems, it is unnecessary to take viscosity into account, but it can lead to significant contradictions when not taken into account at all.

In fluids, the importance of viscous is that eddies form near the surface of a moving solid. These eddies also cause the creation of forces that exert a lifting effect on the object, for example aircraft wings.

Prepared by: Sociologist Ömer Yıldırım
Source: Atatürk University Sociology Department 1st Year “Introduction to Philosophy” and 2nd, 3rd, 4th Grade “History of Philosophy” Lecture Notes (Ömer YILDIRIM)