The electronic–hydraulic analogy (derisively referred to as the drain-pipe theory by Oliver Lodge) is the most widely used analogy for "electron fluid" in a metal conductor. Since electric current is invisible and the processes in play in electronics are often difficult to demonstrate, the various electronic components are represented by hydraulic equivalents. Electricity (as well as heat) was originally understood to be a kind of fluid, and the names of certain electric quantities (such as current) are derived from hydraulic equivalents. As with all analogies, it demands an intuitive and competent understanding of the baseline paradigms (electronics and hydraulics), and in the case of the hydraulic analogy for electronics, students often have an inadequate knowledge of hydraulics. Paradigms There is no unique paradigm for establishing this analogy. Different paradigms have different strengths and weaknesses, depending on how and in what ways the intuitive understanding of the source of the analogy matches with phenomena in electronics. Two paradigms can be used to introduce the concept to students using pressure induced by gravity or by pumps. In the version with pressure induced by gravity, large tanks of water are held up high, or are filled to differing water levels, and the potential energy of the water head is the pressure source. This is reminiscent of electrical diagrams with an up arrow pointing to +V, grounded pins that otherwise are not shown connecting to anything, and so on. This has the advantage of associating electric potential with gravitational potential. A second paradigm is a completely enclosed version with pumps providing pressure only and no gravity. This is reminiscent of a circuit diagram with a voltage source shown and the wires actually completing a circuit. This paradigm is further discussed below. Other paradigms highlight the similarities between equations governing the flow of fluid and the flow of charge. Flow and pressure variables can be calculated in both steady and transient fluid flow situations with the use of the hydraulic ohm analogy. Hydraulic ohms are the units of hydraulic impedance, which is defined as the ratio of pressure to volume flow rate. The pressure and volume flow variables are treated as phasors in this definition, so possess a phase as well as magnitude. A slightly different paradigm is used in acoustics, where acoustic impedance is defined as a relationship between acoustic pressure and acoustic particle velocity. In this paradigm, a large cavity with a hole