The Electronic-Hydraulic Analogy

I studied Chemical and Biological engineering in undergrad, not electrical, so I spent much more time learning about fluid flow and pressure drops than I did electronic circuits. Though our curriculum did include electronics as part of our control systems class, our exposure to circuits was far more limited than the other engineering majors.

I've always been fascinated by electronics though: playing with simple circuits and microcontroller projects in high school and making guitar effect pedals and audio circuits now.

We develop an intuition around fluid flow because of how ubiquitously we physically experience it in real life. Just about everyone has used a hand pump for a bike or a ball, splashed around in a pool/tub, felt water flowing around their feet when you step into a stream. Fluid mechanics felt pretty natural when I took the course, it was just assigning mathematical rules to what I already physically experienced. But electricity is invisible. You can't see electrons moving through a wire, and the concepts can feel frustratingly abstract when you're first learning.

As I dug deeper into electronics, I noticed that many formulae had structural equivalents in domains I'd already encountered. The governing equations (e.g. Fourier's Law from heat transfer, Poiseuille's law from fluid mechanics) create relationships between quantities analogous to what Ohm's law does for electricity.

This analogy holds up so well that it's been given its own name: the electronic-hydraulic analogy. It maps electrical concepts onto a system of pipes and water tanks. As I was starting out learning analog electronics to make guitar pedals, I found these conceptual comparisons extremely useful for building a basis for circuit intuition.

Charge → Volume

The most fundamental mapping: electrical charge (\(Q\), measured in coulombs) corresponds to a volume of water (\(V\), measured in cubic meters). Just as you can have a certain amount of water stored in a tank, you can have a certain amount of charge in a region in a circuit.

A single electron carries a tiny, fixed charge, about \(1.6 \times 10^{-19}\) coulombs. Think of this as a single water molecule: a discrete, indivisible unit of "stuff" that makes up what flows through the system. In practice you deal with bulk quantities and emergent behavior—you rarely think about individual electrons or individual water molecules.

Wires → Pipes

Pipes are how we move our volumes of water around, and a conductor is simply a pipe for electrons. An ideal wire with zero resistance is like a perfectly smooth, frictionless pipe—water (charge) flows through with no pressure (voltage) drop. Real wires have some resistance, just as real pipes have friction losses.

The analogy extends to wire gauge: thicker wires have lower resistance, just as wider pipes allow more flow for the same pressure difference. This is why high-current applications require thick cables.

Current → Flow Rate

Current (\(I\), measured in amperes) is the rate at which charge flows past a point. One amp equals one coulomb per second:

\[ I = \frac{dQ}{dt} \]

The hydraulic equivalent is volumetric flow rate—cubic meters per second passing through a cross-section of pipe. A fat pipe with water rushing through carries a high flow rate; a thin trickle has a low rate. Similarly, a thick copper wire carrying lots of electrons per second has high current; a thin wire with sparse electron flow has low current.

Conservation laws apply in both domains: in a closed hydraulic system, mass is conserved. Water doesn't appear or disappear—what flows in must flow out (assuming no accumulation). The same applies to charge in a circuit, and this is the basis of Kirchhoff's Current Law.

Voltage → Pressure

Voltage (\(V\), measured in volts) represents electrical potential difference between two points. This maps to pressure difference in the hydraulic world.

More precisely, voltage corresponds to hydraulic head—which accounts for both pressure and elevation. If you lay your hydraulic circuit flat so all pipes are at the same height, you can simply think of it as pressure difference.

A battery is like a pump: it does work to maintain a pressure difference between its terminals. Water flows from high pressure to low pressure; conventional current flows from high voltage to low voltage. Without a pressure difference, water sits still; and without a voltage difference, no current flows.

The units reinforce this: a volt is a joule per coulomb (energy per unit charge), while pressure is energy per unit volume (joules per cubic meter). Both describe how much "push" is available to move their respective substances.

Ground → Atmospheric Pressure

Here's something that confused me early on: what exactly is ground? The actual ground? Any piece of metal? The negative terminal on a battery?

The key insight is that voltage, like pressure, is always relative. When we talk about a 9V battery, we're saying there's a 9V difference between its terminals. We have to define some reference point to call zero.

In fluid mechanics, gauge pressure does exactly this. We define atmospheric pressure (about 14.7 psi) as zero and measure everything relative to it. A tire inflated to "30 psi" is actually at 30 psi above atmospheric. A vacuum pump pulling -10 psi is below atmospheric. The atmosphere itself is our reference: that's "ground."

Electrical ground works the same way. We pick a point in our circuit, call it 0V, and measure everything else relative to that. Ground isn't "no electricity", it's just a chosen reference. This is why you can have negative voltages: they're simply below whatever we defined as zero, just as negative gauge pressure means below atmospheric.

Ground as a massive reservoir at atmospheric pressure, like a lake. It's so large that you can dump water into it or pull water out without meaningfully changing its pressure. In circuits, ground is often connected to an actual physical ground (the Earth) or a large copper plane precisely because these act as effectively infinite reservoirs for charge.

Resistance → Pipe Friction

Some pipes are easier to push water through than others, depending on frictional resistance. A short, wide pipe with smooth walls lets water flow easily. A long, narrow pipe with rough walls? You need a lot more pressure to get the same flow.

Electrical resistance (\(R\), measured in ohms) works the same way. A resistor is like a constriction in a pipe—it makes it harder for current to flow, and you need more voltage to push the same amount of charge through.

This is where the analogy gets satisfying: the governing equations have identical structure. All transport phenomena follow the same pattern:

\[ \text{Flux} = \text{Conductance} \times \text{Gradient of Potential} \]

For electricity, this is Ohm's law in its microscopic form:

\[ \mathbf{J} = \sigma \mathbf{E} \]

where \(\mathbf{J}\) is current density, \(\sigma\) is electrical conductivity, and \(\mathbf{E}\) is the electric field (the gradient of voltage).

For laminar flow in pipes, Poiseuille's law has the same shape:

\[ Q = \frac{\pi r^4}{8 \mu L} \Delta P \]

Rearranging to match the macroscopic form of Ohm's law (\(\Delta V = IR\)):

\[ \Delta P = \underbrace{\frac{8 \mu L}{\pi r^4}}_{R_{\text{hydraulic}}} Q \]

That middle term is hydraulic resistance. It depends on viscosity \(\mu\), pipe length \(L\), and radius \(r\). Note the brutal fourth-power dependence on radius: halve the pipe diameter and resistance increases sixteenfold.

Capacitors → A Balloon in a Pipe

A capacitor stores electrical energy. In the hydraulic analogy, think of it as a balloon you've stuck somewhere within your pipe system.

Here's the picture: you have a rigid pipe, and at some point there's an elastic balloon attached to it. The pipe continues on the other side of the balloon, but no water can actually pass through the balloon membrane, it just stretches.

When you apply pressure to one side, the balloon expands into the pipe on the other side, displacing water there. Water's flowing, so it looks like water is "flowing through" the capacitor, but really it's just the balloon stretching and pushing water on the other side. This is basically what happens with charge in a capacitor, and seeing current flow through. There isn't really any flow through the capacitor, charge accumulates on one plate, and an equal charge gets pushed off the other plate.

The balloon's stiffness is analogous to capacitance. A large, stretchy balloon (high capacitance) can stretch to fit a lot of water for a given pressure than a small, stiff balloon.

What happens when you first start to pump up a balloon? The balloon offers no resistance when it's slack, pumping is a breeze. But as it fills, it pushes back harder and harder (great arm workout) until the pressure equalizes and flow stops. As soon as the pressure drops when you disconnect the pump, if you haven't tied the balloon off, all the air you pumped in will be released: rapidly at first, and then petering off as it loses air.

Analogously in electronics, a capacitor looks like just a piece of wire at first; like a short circuit (when the voltage across it is changing rapidly) but looks like an open circuit (a gap in the wire) at DC (once voltage is constant). When facing a voltage drop, a capacitor will discharge with an inverse exponential curve: the rate of discharge slows down over time. In electronics, this behavior helps capacitors smooth out voltage fluctuations by absorbing energy when voltage rises and releasing it when voltage falls.

A really great parallel intuition here is why capacitors block DC but pass AC. Constant pressure just inflates the balloon to equilibrium and then it stops, there's no sustained flow. But if pressure oscillates, the balloon is constantly inflating and deflating, which keeps water sloshing back and forth on the other side. The faster the oscillation, the less time the balloon has to get filled to a point of significant "push back," so more flow gets through. This is why capacitive reactance decreases with frequency.

Diodes → One-Way Valves

A diode only allows current to flow in one direction. The hydraulic equivalent is a check valve: a flap or ball that opens when pressure pushes one way and seals shut when it pushes the other way.

The direction matters. In a diode, current flows from anode to cathode (in the direction of the arrow in the schematic symbol).

Real check valves need some minimum pressure difference to crack open, typically there's a spring holding the flap shut that needs a certain amount of force to overcome. Diodes have the same behavior: they need about 0.6-0.7V of forward voltage before they start conducting. Below that threshold, there's no flow through. This is called the forward voltage drop, and it's analogous to the "cracking pressure" of a check valve.

The analogy even captures what happens when you push a diode too hard in reverse. If you push a real check valve too hard in the unintended direction, the flap can rupture or the seal can blow out. Similarly, every diode has a reverse breakdown voltage. Exceed it and the diode conducts in reverse (destructively, for most diodes, though Zener diodes exploit this behavior intentionally).

Signal Speed

If you've ever played around in water, flattening your hand like a paddle and pushing to create a wave you've felt the pressure propagate through the water. Or you might have tried making sounds underwater with your friends, tapping around, and seeing how well you could hear them. In water, pressure waves travel at the speed of sound in water (~1500 m/s) but the bulk flow velocity (the actual water molecules moving around) move much slower.

This is analogous to what happens in electrical circuits. Individual electrons drift slowly: millimeters per second in typical wires. But the signal, the electromagnetic wave that carries information, propagates at a significant fraction of the speed of light (typically 50-99% of c, depending on the medium).

That said, there's still a real difference. In water, the signal propagates through the physical mechanical compression of the fluid. In a wire, the signal propagates through electromagnetic fields that extend outside the conductor. This is the basis of how transformers work: you can influence the current in one wire by placing another wire nearby. There's no direct analogy for this in the case of water in pipes, there's no external field interaction.

Limitations

All analogies eventually break down. The electronic-hydraulic analogy helps build basic intuition, but it fails when pushed:

• Compressibility. In these, I imagine water as incompressible (which for most cases, is a close enough approximation). Real fluids compress slightly under pressure; charge doesn't "compress" in wires at all. Current is the same everywhere in a point of equipotential, instantaneously.
• Fields and action at a distance. Electric and magnetic fields can influence charge without physical contact. As we discussed, there's no hydraulic equivalent to electromagnetic induction, you can't make water flow in one pipe by waving a magnet at it.
• More complex semiconductor behavior. As you get into fancier and fancier components, you'll see semiconductor devices have behaviors that depend on quantum mechanics and band structure. At the point that you start dealing with these though, you've probably already developed a very solid intuition around electronics.

For understanding resistors, capacitors, diodes, and basic circuit behavior, the analogy works pretty well. Just know when to let it go.

Reference

Electrical	Hydraulic
Charge \(Q\) [C]	Volume \(V\) [m³]
Current \(I\) [A = C/s]	Flow rate \(\dot{V}\) [m³/s]
Voltage \(V\) [V = J/C]	Gauge pressure \(P\) [Pa = J/m³]
Resistance \(R\) [Ω = V/A]	Flow resistance [Pa·s/m³]
Ground (0V reference)	Atmospheric pressure (0 gauge)
Wire	Pipe
Battery	Pump
Resistor	Constriction / friction
Capacitor	Elastic balloon / membrane
Diode	Check valve (one-way valve)

Further Reading

• Look up Moritz Klein's explainers, his approach to break concepts down is so intuitive and digestible.
• Khan Academy: Introduction to Electrical Engineering