See here for a preprint of this new article, which will appear as part of the *Synthese* topical collection Explanatory and Heuristic Power of Mathematics, edited by Sorin Bangu, Emiliano Ippoliti and Marianna Antonutti.

Abstract: This paper illustrates how an experimental discovery can prompt the search for a theoretical explanation and also how obtaining such an explanation can provide heuristic benefits for further experimental discoveries. The case considered begins with the discovery of Poiseuille’s law for steady fluid flow through pipes. The law was originally supported by careful experiments, and was only later explained through a derivation from the more basic Navier-Stokes equations. However, this derivation employed a controversial boundary condition and also relied on a contentious approach to viscosity. By comparing two editions of Lamb’s famous *Hydrodynamics* textbook, I argue that explanatory considerations were central to Lamb’s claims about this sort of fluid flow. In addition, I argue that this treatment of Poiseuille’s law played a heuristic role in Reynolds’ treatment of turbulent flows, where Poiseuille’s law fails to apply.