The mathematical parallels between electrostatics and laminar fluid flow are exploited to develop a set of exercises that allow introductory physics students to discover Gauss’s Law. The primary fluid experiment involves investigating the continuity equation in two dimensions by examining the flow between two closely spaced plates. Extrapolation of the resulting two-dimensional velocity field to three dimensions reveals a radial dependence to the velocity field that is analogous to Coulomb’s Law. This analogy allows the student to predict an electric version of the continuity equation that is Gauss’s Law.