Hero's fountain transfers pressure between sealed vessels as water falls from an open basin and drives a separate upward jet. This calculator is a fixed-fraction scenario, not a performance prediction for a particular build.
Hero's Fountain Interactive Calculator
Apply fixed 75%, 81.25% and 87.5% fractions to entered head, then calculate an ideal-orifice flow from the midpoint height and nozzle bore.
Equation Used
- Entered head is treated as a static available-head scenario.
- Jet-height ratios are fixed assumed values rather than calculated losses.
- Flow uses ideal Torricelli speed from the midpoint assumed jet height.
- No discharge coefficient, tubing loss, air-volume/pressure evolution, leakage, changing level, priming or duration model.
The height fractions are illustrative choices, not measured efficiencies or values calculated from vessel geometry. The flow omits a discharge coefficient, tube losses, air compression and changing water levels.
Qualitative pressure-transfer cycle
Water falling from the open basin into a sealed receiving vessel compresses trapped air. An air connection transfers that pressure to a separate sealed water vessel, where it drives water up a jet tube into the basin.
The device is not perpetual: water inventories and levels change, pressure falls, and the system must be reset. The animation shows the three flow paths qualitatively.
Use as a teaching scenario
The calculator illustrates head, ideal jet speed and nozzle-area scaling. It does not specify vessel sizes, tubing, seals, pressure limits, run time or a safe construction.
Fixed-fraction scenario used here
The three displayed heights are exactly 0.75h, 0.8125h and 0.875h. These are assumed comparison ratios, not values derived from the two inputs.
The flow tile uses nozzle area A=πd²/4 and ideal speed sqrt(2g hmid). Real flow normally requires a discharge coefficient and a time-dependent pressure/loss model.
Transparent example
At 800 mm entered head, the fixed scenarios are 600, 650 and 700 mm. With a 2 mm nozzle, ideal speed based on 650 mm is about 3.57 m/s and ideal midpoint flow is about 11.2 mL/s.
Those outputs do not predict run duration or the measured jet of a physical fountain.
Scope and limitations
Physical performance depends on vessel air volumes, starting water levels, elevation differences, tube diameters and lengths, nozzle discharge coefficient, seal leakage, friction and minor losses, unsteady air compression and the changing levels during a run.
Frequently asked questions
Are the percentages universal efficiencies?
No. They are illustrative fixed fractions. The tool does not derive them from vessel or tube geometry.
Does nozzle diameter change jet height here?
No. It changes only the ideal flow calculation; the three assumed height fractions stay fixed.
Can this predict how long the fountain runs?
No. Vessel volumes, water inventories and time-dependent pressure are absent.
Is this a perpetual fountain?
No. Water moves from the supply vessel into the receiving vessel. The available supply is finite, and the apparatus eventually needs resetting.
Mechanism reference and calculation basis
Museo Galileo’s Hero’s fountain entry describes the basin, two sealed vessels and three connecting paths. Water entering the receiving vessel transfers air pressure to the supply vessel and drives the jet.
The calculator applies three illustrative fractions to entered head. It then uses ideal jet speed √(2gh) at the middle height and multiplies by nozzle area. These calculations do not solve vessel pressure, changing water levels or flow losses. The illustration keeps water levels fixed and shows flow directions only.
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