In this note I will attempt to identify the main events in the history of thought about irrotational flow of viscous fluids. I am of the opinion that when considering irrotational solutions of the Navier-Stokes equations it is never necessary and typically not useful to put the viscosity to zero. This observation runs counter to the idea frequently expressed that potential flow is a topic which is useful only for inviscid fluids; many people think that the notion of a viscous potential flow is an oxymoron. Incorrect statements like “… irrotational flow implies inviscid flow but not the other way around” can be found in popular textbooks.
Though convenient, phrases like “inviscid potential flow” or “viscous potential flow” confuse properties of the flow (potential or irrotational) with properties of the material (inviscid, viscous or viscoelastic); it is better and more accurate to speak of the irrotational flow of an inviscid or viscous fluid.