d'Alembert's Paradox is the result of assuming that a fluid flow is inviscid: a body in the flow can experience a lift force without a drag force. This was a problem because it conflicted with experimental evidence, which shows that there is some drag associated with a body in a flow. Mathematically, it follows from the calculation of lift from the Kutta-Joukowski lift theorem, which is positive, and the evaluation of the drag per unit span (in this case, for a cylinder):

d=-0p cos θ R
p=p + 0.5ρU2 - 2ρU2 sin2θ

Which, after substitution, yields:


Of course, the Kutta-Joukowski theorem and the above equation for drag both depend on a flow with no viscosity, which does not exist in the reality we all share. Thus, in any real world situation, some profile drag will be exerted on a solid body in a fluid flow.