Electronic–hydraulic analogies are the representation of electronic circuits by hydraulic circuits. 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. 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. 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. The analogy may also be reversed to explain or model hydraulic systems in terms of electronic circuits, as in expositions of the Windkessel effect.
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 is analogous to a capacitor that stores compressional energy when the time-dependent pressure deviates from atmospheric pressure. A hole (or long tube) is analogous to an inductor that stores kinetic energy associated with the flow of air.
Hydraulic analogy with horizontal water flow
Voltage, current, and charge In general, electric potential is equivalent to hydraulic head. This model assumes that the water is flowing horizontally, so that the force of gravity can be ignored. In this case, electric potential is equivalent to pressure. The voltage (or voltage drop or potential difference) is a difference in pressure between two points. Electric potential is usually measured in volts. Electric current is equivalent to a hydraulic volume flow rate; that is, the volumetric quantity of flowing water over time. Usually measured in amperes. A unit of electric charge is analogous to a unit volume of water.
Basic circuit elements
A relatively wide hose completely filled with water is equivalent to a conducting wire. A rigidly mounted pipe is equivalent to a trace on a circuit board. When comparing to a trace or wire, the hose or pipe should be thought of as having semi-permanent caps on the ends. Connecting one end of a wire to a circuit is equivalent to un-capping one end of the hose and attaching it to another. With few exceptions (such as a high-voltage power source), a wire with only one end attached to a circuit will do nothing; the hose remains capped on the free end, and thus adds nothing to the circuit. A resistor is equivalent to a constriction in the bore of a pipe which requires more pressure to pass the same amount of water. All pipes have some resistance to flow, just as all wires and traces have some resistance to current. A node (or junction) in Kirchhoff's junction rule is equivalent to a pipe tee. The net flow of water into a piping tee (filled with water) must equal the net flow out.
A capacitor is equivalent to a tank with one connection at each end and a rubber sheet dividing the tank in two lengthwise (a hydraulic accumulator). When water is forced into one pipe, equal water is simultaneously forced out of the other pipe, yet no water can penetrate the rubber diaphragm. Energy is stored by the stretching of the rubber. As more current flows "through" the capacitor, the back-pressure (voltage) becomes greater, thus current "leads" voltage in a capacitor. As the back-pressure from the stretched rubber approaches the applied pressure, the current becomes less and less. Thus capacitors "filter out" constant pressure differences and slowly varying, low-frequency pressure differences, while allowing rapid changes in pressure to pass through.
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