Why did d’Alembert’s paradox conflict with modern physics?

D’Alembert’s paradox arises from his 1752 work, Essai d’une nouvelle théorie de la résistance des fluides, in which he applied principles of solid-body mechanics to fluid dynamics. By treating air as an incompressible, inviscid fluid, he calculated that the resistance (drag) exerted on a body moving through the fluid is zero.1

This conclusion conflicts with modern physics because it contradicts the reality that objects moving through fluids experience drag. The paradox exists because d’Alembert’s model relied on potential theory, which neglects the effects of viscosity and the formation of boundary layers and eddies. In actual fluid flow, viscosity causes the fluid to adhere to the surface of an object, leading to the separation of the boundary layer and the creation of pressure differences that result in drag. D’Alembert himself was dissatisfied with his result, and it remains a classic example of the limitations of ignoring viscous forces in hydrodynamics.123