Hero's Fountain is a sealed three-vessel hydraulic device that drives a jet of water upward without any moving parts, using only the pressure of trapped air pushed by a falling column of water. A typical bench demonstrator throws a jet 0.6 to 1.2 m high for 30 to 90 seconds before the supply chamber empties. Hero of Alexandria documented it around 60 AD as a temple curiosity, and the same configuration still runs daily in science museums like the Deutsches Museum in Munich.
Hero's Fountain Interactive Calculator
Vary hydrostatic head and nozzle bore to estimate the jet-height range and nominal flow from a Hero's Fountain.
Equation Used
The article states that a Hero's Fountain jet height is set by hydrostatic head minus losses. This calculator uses the worked-example range where 800 mm of head produces a 600 to 700 mm jet, equivalent to eta = 0.75 to 0.875. Nominal flow is estimated from the midpoint jet height and the selected nozzle bore.
- Fresh water at room temperature.
- Jet-height efficiency range is based on the article example: 800 mm head gives a 600 to 700 mm jet.
- Nozzle is clean and discharges vertically.
- Air leaks, unsteady chamber volume, and tube friction details are lumped into eta.
How the Hero's Fountain Works
The Hero's Fountain — also called Hiero's fountain in older English texts — runs on one idea: a falling column of water in one sealed vessel pressurises trapped air, and that pressurised air pushes water up out of a separate sealed vessel through a nozzle. There are three chambers stacked or arranged in line. The top is an open basin. Below it sits a sealed middle vessel filled with water and a trapped air column. Below that sits a sealed lower vessel, partly empty, also with trapped air. Two tubes do the work — one carries water down from the top basin into the lower vessel, and the second carries water up from the middle vessel through a nozzle into the open basin. When you prime the system and pour a small amount of water into the top basin, that water drains down into the lower vessel, compresses the air in it, and that compressed air pushes through a third connecting tube into the middle vessel. The middle vessel's air pressure now exceeds atmospheric, and that pushes the middle vessel's water up the jet tube and out into the basin.
The jet height is set by hydrostatic head — specifically the vertical distance between the water surface in the top basin and the water surface in the lower vessel. That head, minus losses, is what's available to lift the jet. If you build the unit with only 200 mm of head you'll get a 150 to 180 mm jet. Build it with 800 mm of head and you'll see 600 to 700 mm of jet. The fountain is not perpetual — it is a battery. Each cycle transfers a fixed mass of water from middle to top basin, and once the middle vessel empties or pressure equalises, the jet dies. To run it again you tip it, refill, and reseal.
The failure modes are mostly about seals and tube placement. If the lower vessel leaks air past a gasket, pressure bleeds off and the jet collapses within seconds. If the down-tube from the top basin terminates above the water line inside the lower vessel, the falling water aerates instead of compressing — the jet sputters. The up-tube from the middle vessel must reach near the bottom of that vessel, otherwise the jet stops as soon as the water level drops past the tube inlet, even though plenty of water remains. Build it sloppy and you'll get 10 seconds of jet instead of 60.
Key Components
- Top basin (open): Catches the jet and feeds the down-tube. Sized for 1.5× to 2× the working volume of the middle vessel so it doesn't overflow during a run. Open to atmosphere — this is the only vent in the system.
- Middle vessel (sealed): Holds the water that becomes the jet. Sealed completely. Internal air space typically 20 to 40% of vessel volume — too little air and the jet pressure fluctuates wildly, too much and you waste working volume.
- Lower vessel (sealed): Receives water from the top basin and converts that falling head into compressed air. Must be sealed to within a few mbar leakage. A worn cork or o-ring here is the most common reason a built fountain runs for 10 seconds instead of a full minute.
- Down-tube (basin to lower vessel): Carries water from the top basin down into the lower vessel. Inlet must be submerged below the lower vessel's water surface — typically extending to within 10 mm of the bottom — to prevent air from blowing back up the tube.
- Air-transfer tube (lower to middle): Connects the air space at the top of the lower vessel to the air space at the top of the middle vessel. This is the pressure-coupling line. It must terminate above the water line in both vessels or it will siphon water instead of transferring pressure.
- Jet tube (middle vessel to basin): Carries pressurised water up out of the middle vessel and through a nozzle into the top basin. Inlet sits within 5 to 10 mm of the middle vessel floor. Nozzle bore typically 1.5 to 3 mm for a clean jet at hand-built scales.
Where the Hero's Fountain Is Used
The Hero's Fountain has no commercial pumping role today — a 12 V Linear Actuator-driven piston pump moves water more reliably and indefinitely. The Hiero's fountain survives as a teaching tool, a museum exhibit, and an ornamental demonstrator. It teaches hydrostatic head, trapped-air pressure, and conservation of energy in a single glance, which is why physics departments and science centres still build them.
- Science museums: Permanent working exhibit at the Deutsches Museum in Munich and at the Museum of the History of Science in Oxford, where glass-walled Hero's Fountains run scheduled demonstrations to show pneumatic-hydraulic coupling.
- University physics teaching: MIT's classical mechanics demonstration collection includes a brass-and-glass Hero's Fountain used in fluid statics lectures to show how a closed pressure system converts head into jet velocity.
- Heritage replicas: Reconstructions of Hero of Alexandria's pneumatica devices at the Kotsanas Museum of Ancient Greek Technology in Athens, including a working Hero's Fountain built from documented drawings in Pneumatica Book I.
- School STEM kits: Eisco Labs and Arbor Scientific sell desktop Hero's Fountain kits in acrylic, typically 300 mm tall, producing a 200 to 250 mm jet for 30 to 45 seconds — used in middle-school physics units on air pressure.
- Ornamental garden features: Bespoke decorative fountains built by traditional metalworkers in Italy and Greece, where the device runs during a dinner service then resets between courses — a quiet alternative to a mains-powered pump.
- Hobbyist maker projects: Glassblower-built Hero's Fountains sold at maker fairs and on Etsy, often using mason jars or laboratory bell jars as the sealed vessels with silicone tubing for the connections.
The Formula Behind the Hero's Fountain
The useful number to predict is jet height — how high the water actually shoots above the nozzle. The formula relates jet height to the hydrostatic head between the top basin and the lower vessel, minus losses. At the low end of typical builds (150 mm head) you'll see jets that barely clear the nozzle and last well over a minute because flow rate is tiny. At the high end (1 m head) you get a tall, satisfying jet that drains the middle vessel in 20 to 30 seconds. The sweet spot for classroom demonstrators sits around 400 to 600 mm of head — tall enough to be visible from the back row, slow enough to last a full explanation.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| hjet | Height of the water jet above the nozzle exit | m | ft |
| htop | Elevation of the water surface in the top open basin | m | ft |
| hlow | Elevation of the water surface in the sealed lower vessel | m | ft |
| η | Efficiency factor accounting for nozzle, tube, and air-transfer losses (typically 0.75 to 0.90) | dimensionless | dimensionless |
Worked Example: Hero's Fountain in a glass-and-brass classroom demonstrator
You are building a glass-and-brass Hero's Fountain for a year 11 physics classroom in Edinburgh. The top basin sits 600 mm above the lower vessel water line at the start of the run. The middle vessel is mounted alongside the lower vessel. Nozzle bore is 2 mm, jet tube is 6 mm internal bore, total tubing length is 800 mm. You expect η around 0.85 for a clean build with silicone gaskets and a polished brass nozzle.
Given
- htop → hlow = 0.600 m
- η (clean build) = 0.85 —
- Nozzle bore = 2.0 mm
- Jet tube ID = 6.0 mm
Solution
Step 1 — at the nominal 600 mm head, compute the theoretical jet height with no losses:
Step 2 — apply the efficiency factor for a clean build to get the nominal jet height:
That's a 510 mm jet — visible from the back of a 30-seat classroom, lasting roughly 40 to 50 seconds before the middle vessel empties. The jet stays coherent for the first 70% of the run, then breaks up into droplets as pressure drops near the end.
Step 3 — at the low end of the typical build range, 200 mm of head:
A 170 mm jet is short — it'll clear the rim of the basin but it won't impress anyone past the front row. The flow rate is also low, so the run lasts 90+ seconds, which is actually useful if you want a long demonstration window with minimal water.
Step 4 — at the high end, 1000 mm of head:
An 850 mm jet looks dramatic but the run is short — the middle vessel drains in 20 to 25 seconds because the jet velocity is much higher. Above about 1.2 m of head the 2 mm nozzle starts to atomise rather than throw a coherent column, and you'll need to step nozzle bore up to 3 mm to keep a clean jet.
Result
The nominal build throws a 0. 51 m (510 mm) jet — a clean, vertical column visible across a classroom and lasting roughly 45 seconds before the middle vessel runs dry. The 200 mm low-end build gives a stubby 170 mm jet but lasts over 90 seconds; the 1000 mm high-end build throws an 850 mm jet for only about 22 seconds, so the sweet spot for teaching is exactly where the nominal sits — 500 to 600 mm of head. If your measured jet falls 30% short of the predicted 510 mm, suspect: (1) a leaking lower-vessel gasket bleeding air pressure during the run — test by sealing it under water and watching for bubbles, (2) the down-tube terminating above the water line inside the lower vessel, which lets the falling water aerate instead of compressing the trapped air, or (3) a burr inside the 2 mm nozzle bore disrupting the jet — a 0.05 mm burr is enough to cut visible height by 20%.
When to Use a Hero's Fountain and When Not To
Hero's Fountain is one of several ways to move water without an electric motor. The honest comparison is against a hand-pumped piston, a gravity siphon, and a small mains-powered submersible — because those are the alternatives a teacher, museum curator, or hobbyist actually picks between when planning a build.
| Property | Hero's Fountain | Hand-pumped piston | Gravity siphon | Small submersible pump |
|---|---|---|---|---|
| Run duration per prime | 20 to 90 seconds | Indefinite while pumped | Until source empties | Indefinite while powered |
| Jet height | 50 to 80% of head height | Up to 3 m with effort | Cannot jet — drains only | 1 to 5 m typical |
| Power source | Stored hydrostatic head | Human muscle | Gravity only | Mains or battery |
| Reset/recharge | Tip and refill manually | Continuous pumping | Re-prime tube | None |
| Maintenance | Replace gaskets every few years | Piston seal annually | Effectively none | Impeller cleaning, motor wear |
| Educational value | Excellent — visible physics | Moderate | Moderate | Low — black box |
| Build complexity | Moderate (3 sealed vessels) | Moderate | Trivial | Buy off the shelf |
| Typical cost | £40 to £200 hobbyist build | £60 to £150 | £5 of tubing | £15 to £80 |
Frequently Asked Questions About Hero's Fountain
This is almost always the air-transfer tube routing — the short tube that couples the air space in the lower vessel to the air space in the middle vessel. If either end of that tube dips below the water line inside its vessel, water siphons through it instead of pressure transferring. You lose the pneumatic coupling within seconds and the jet dies even though both vessels still have plenty of water.
Pull the unit apart and confirm both ends of that tube terminate well above the working water line — at least 20 mm of clearance at the highest expected level. A common build mistake is mounting the tube ports too low on the vessel sidewalls.
A 30% shortfall this large usually means the efficiency factor η in your build is closer to 0.55 than 0.85. The two biggest contributors at this scale are nozzle quality and tube friction. A drilled rather than reamed 2 mm nozzle has internal burrs that disrupt the jet — under a loupe you can see the water exit as a fan rather than a column. Replace it with a brass nozzle finished to 0.4 µm or better Ra and you'll usually recover 80 to 100 mm of height.
The second contributor is jet-tube ID. If you used 4 mm tubing instead of 6 mm, friction loss across 800 mm of tube length at the flow rates involved costs you another 40 to 60 mm of jet height. Step up the bore.
For a permanent classroom or museum demonstrator, use rigid tubing — copper, brass, or borosilicate glass — sealed into the vessels with proper compression fittings or ground-glass joints. Silicone tubing works fine initially but slowly permeates air over weeks, which means a unit that sat over a school holiday will need re-priming and may have lost up to half its trapped-air charge.
For a one-off science fair build that runs for a single afternoon, silicone is faster, cheaper, and forgiving of small alignment errors. Just don't expect it to hold a charge if you build it Friday and present it Monday.
No — and this is the most common misunderstanding about the device. The fountain is energy-limited, not flow-limited. The energy that drives the jet comes from the falling water in the down-tube giving up its hydrostatic head. Once the lower vessel fills and the middle vessel empties, all the head is gone and no amount of recirculation puts it back, because to lift water from the bottom back up to the top you need exactly as much energy as the fountain just released — plus losses.
People have proposed every imaginable plumbing variation since Hero's time. They all violate the first law of thermodynamics. If you want continuous operation, add an external pump or accept that you're tipping the unit between runs.
You want a jet of at least 700 to 800 mm to read clearly from 15 m away under typical lecture lighting. That means 900 to 1000 mm of head and an efficiency around 0.80 to 0.85, so the lower vessel needs to sit roughly 1 m below the top basin water line.
The middle vessel volume sets your run duration — at this scale, plan for 2 to 3 litres of working volume, which gives roughly 25 to 35 seconds of jet. Build the vessels in clear borosilicate so the audience can also see the water levels changing in both sealed chambers — that's the part of the demonstration that actually teaches the physics, not the jet itself.
Pulsing means the air column in one of the sealed vessels is too small relative to the water volume, so as water level changes by even a few mm the pressure swings noticeably. The fix is to increase the dead-air space in the middle vessel to at least 30% of vessel volume — that gives you a larger pneumatic capacitance and smooths out the pressure delivery.
A second cause is a partially blocked nozzle — debris, mineral scale, or a flake of gasket material lodged in the bore. The flow alternately builds pressure and breaks through, which produces visible pulsing. Pull the nozzle and inspect it under magnification.
References & Further Reading
- Wikipedia contributors. Heron's fountain. Wikipedia
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