d’Alembert’s paradox

D'Alembert's paradox, also known as the paradox of fluid resistance, is a concept in physics that highlights a contradiction in the behavior of fluids. In the 18th century, mathematician Jean Le Rond d'Alembert applied principles of solid body mechanics to fluids, suggesting that resistance is related to a loss of momentum on impact. This led to the surprising conclusion that the resistance of particles in a fluid should be zero.1

This result, however, is not accepted by modern physicists and is considered a paradox because it contradicts real-world observations where objects moving through fluids clearly experience resistance. The paradox arises from treating fluids as ideal, inviscid substances, which simplifies calculations but doesn't accurately reflect how real fluids behave. D'Alembert's work on fluid dynamics also contributed to the development of partial differential equations and the concept of limits in mathematics.213