Analogy between a hydraulic circuit (left) and an electronic circuit (right).

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) ^[1] 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.^[2]

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.^[2] 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.^[3][4] 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.^[5]

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.^[6]

Hydraulic analogy with horizontal water flow

Principal equivalents

EM wave speed (velocity of propagation) is equivalent to the speed of sound in water. When a light switch is flipped, the electric wave travels very quickly through the wires.

Charge flow speed (drift velocity) is equivalent to the particle speed of water. The moving charges themselves move rather slowly.

DC is equivalent to a constant flow of water in a circuit of pipes.

Low frequency AC is equivalent to water oscillating back and forth in a pipe

Higher-frequency AC and transmission lines is somewhat equivalent to sound being transmitted through the water pipes, though this does not properly mirror the cyclical reversal of alternating electric current. As described, the fluid flow conveys pressure fluctuations, but fluids do not reverse at high rates in hydraulic systems, which the above "low frequency" entry does accurately describe. A better concept (if sound waves are to be the phenomenon) is that of direct current with high-frequency "ripple" superimposed.

Inductive spark used in induction coils is similar to water hammer, caused by the inertia of water.

Equation examples

type	hydraulic	electric	thermal	mechanical
quantity	volume ${\displaystyle V}$ [m3]	charge ${\displaystyle q}$ [C]	heat ${\displaystyle Q}$ [J]	momentum ${\displaystyle P}$ [Ns]
quantity flux	Volumetric flow rate ${\displaystyle \Phi _{V}}$ [m3/s]	current ${\displaystyle I}$ [A=C/s]	heat transfer rate ${\displaystyle {\dot {Q}}}$ [J/s]	velocity ${\displaystyle v}$ [m/s=J/Ns]
flux density	velocity ${\displaystyle v}$ [m/s]	current density ${\displaystyle j}$ [C/(m2·s) = A/m2]	heat flux ${\displaystyle {\dot {Q}}''}$ [W/m2]	stress ${\displaystyle \sigma }$ [N/m2 = Pa]
potential	pressure ${\displaystyle p}$ [Pa=J/m3=N/m2]	potential ${\displaystyle \phi }$ [V=J/C=W/A]	temperature ${\displaystyle T}$ [K]	force ${\displaystyle F}$ [N]
linear model	Poiseuille's law ${\displaystyle \Phi _{V}={\frac {\pi r^{4}}{8\eta }}{\frac {\Delta p^{\star }}{\ell }}}$	Ohm's law ${\displaystyle j=-\sigma \nabla \phi }$	Fourier's law ${\displaystyle {\dot {Q}}''=\kappa \nabla T}$	dashpot ${\displaystyle \sigma =c\Delta v}$

If the differential equations are equivalent in form, the dynamics of the systems they describe will be related. The example hydraulic equations approximately describe the relationship between a constant, laminar flow in a cylindrical pipe and the difference in pressure at each end, as long as the flow is not analyzed near the ends of the pipe. The example electric equations approximately describe the relationship between a current in a straight wire and the difference in electric potential (voltage). In these two cases, the states of both systems are well-approximated by the differential equations above, and so the states are related. The assumptions that make these differential equations good approximates are needed for this relationship. Any deviations from the assumptions (e.g. pipe or wire is not straight, flow or current is changing over time, other factors are influencing potential) can make the relationship fail to hold. The differential equations for hydraulics and electronics above are special cases of the Navier–Stokes equations and Maxwell's equations, respectively, and the two are not equivalent in form.

Limits to the analogy

If taken too far, the water analogy can create misconceptions. Negative transfer can occur when there is a mismatch between phenomena in the source (hydraulics) and the corresponding phenomena in the target (electronics).^[2] For the analogy to be useful, one must remain aware of the regions where electricity and water behave very differently.

Fields (Maxwell equations, inductance): Electrons can push or pull other distant electrons via their fields, while water molecules experience forces only from direct contact with other molecules. For this reason, waves in water travel at the speed of sound, but waves in a sea of charge will travel much faster as the forces from one electron are applied to many distant electrons and not to only the neighbors in direct contact. In a hydraulic transmission line, the energy flows as mechanical waves through the water, but in an electric transmission line the energy flows as fields in the space surrounding the wires, and does not flow inside the metal. Also, an accelerating electron will drag its neighbors along while attracting them, both because of magnetic forces.

Charge: Unlike water, movable charge carriers can be positive or negative, and conductors can exhibit an overall positive or negative net charge. The mobile carriers in electric currents are usually electrons, but sometimes they are charged positively, such as the positive ions in an electrolyte, the H⁺ ions in proton conductors or holes in p-type semiconductors and some (very rare) conductors.

Leaking pipes: The electric charge of an electrical circuit and its elements is usually almost equal to zero, hence it is (almost) constant. This is formalized in Kirchhoff's current law, which does not have an analogy to hydraulic systems, where the amount of the liquid is not usually constant. Even with incompressible liquid the system may contain such elements as pistons and open pools, so the volume of liquid contained in a part of the system can change. For this reason, continuing electric currents require closed loops rather than hydraulics' open source/sink resembling spigots and buckets.

Fluid velocity and resistance of metals: As with water hoses, the carrier drift velocity in conductors is directly proportional to current. However, water only experiences drag via the pipes' inner surface, while charges are slowed at all points within a metal, as with water forced through a filter. Also, typical velocity of charge carriers within a conductor is less than centimeters per minute, and the "electrical friction" is extremely high. If charges ever flowed as fast as water can flow in pipes, the electric current would be immense, and the conductors would become incandescently hot and perhaps vaporize. To model the resistance and the charge-velocity of metals, perhaps a pipe packed with sponge, or a narrow straw filled with syrup, would be a better analogy than a large-diameter water pipe.

Quantum mechanics: Solid conductors and insulators contain charges at more than one discrete level of atomic orbit energy, while the water in one region of a pipe can only have a single value of pressure. For this reason there is no hydraulic explanation for such things as a battery's charge pumping ability, a diode's depletion layer and voltage drop, solar cell functions, Peltier effect, etc., however equivalent devices can be designed which exhibit similar responses, although some of the mechanisms would only serve to regulate the flow curves rather than to contribute to the component's primary function.

In order for the model to be useful, the reader or student must have a substantial understanding of the model (hydraulic) system's principles. It also requires that the principles can be transferred to the target (electrical) system. Hydraulic systems are deceptively simple: the phenomenon of pump cavitation is a known, complex problem that few people outside of the fluid power or irrigation industries would understand. For those who do, the hydraulic analogy is amusing, as no "cavitation" equivalent exists in electrical engineering. The hydraulic analogy can give a mistaken sense of understanding that will be exposed once a detailed description of electrical circuit theory is required.

One must also consider the difficulties in trying to make an analogy match reality completely. The above "electrical friction" example, where the hydraulic analog is a pipe filled with sponge material, illustrates the problem: the model must be increased in complexity beyond any realistic scenario.

See also

• Bond graph
• Fluidics
• Hydraulic circuit
• Hydraulic conductivity
• Mechanical–electrical analogies

Notes

External links

Wikimedia Commons has media related to Hydraulic analogy.

• Animation
• Hydraulic Analogy for Inductive Electric Elements