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Reasoning by analogy is powerful in physics for students and researchers alike, a case in point being electronics and hydraulics as analogous studies of electric currents and fluid flows. Around 100 years ago, Nikola Tesla proposed a flow control device intended to operate similarly to an electronic diode, allowing fluid to pass easily in one direction but providing high resistance in reverse. Here we use experimental tests of Tesla's diode to illustrate principles of the electronic-hydraulic analogy. We design and construct a differential pressure chamber (akin to a battery) that is used to measure flow rate (current) and thus resistance of a given pipe or channel (circuit element). Our results prove the validity of Tesla's device, whose anisotropic resistance derives from its asymmetric internal geometry interacting with high-inertia flows, as quantified by the Reynolds number (here, Re ~ 1e3). Through the design and testing of new fluidic diodes, we explore the limitations of the analogy and the challenges of shape optimization in fluid mechanics. We also provide materials that may be incorporated into lesson plans for fluid dynamics courses, laboratory modules and further research projects., Comment: 23 pages (double spaces), 8 figures