A luminous fountain introduces light into a water jet near its nozzle. Explore that arrangement and compare exit speed and bore diameter with ideal jet height, flow, flight time and kinetic power.
Ideal Vertical-Jet Kinematics Calculator
Enter nozzle exit velocity and circular bore diameter. Results describe a steady, uniform, lossless vertical jet; they do not predict breakup, wind effects, optical quality, pump input power or a real fountain installation.
Equation Used
- The jet leaves vertically at uniform speed from a circular bore.
- Standard gravity g=9.80665 m/s^2 and water density rho=1000 kg/m^3 are used.
- Air drag, breakup, wind, nozzle contraction/losses, pipe losses, pump efficiency, static lift and optical behavior are excluded.
Exit speed determines the ideal height and flight time. The nozzle area also affects volume flow and the kinetic power carried by the water; the light path is illustrated separately from these calculations.
Pump, nozzle, jet and light source
A pump supplies water to a nozzle that forms the rising stream. Luminous-fountain patents place a projector or light source near the nozzle so light enters the jet; later designs likewise describe light propagating in the water stream by repeated internal reflection. The actual optical result depends on the nozzle, jet surface and light geometry.
The animation separates the ideal ballistic water path from an optical illustration. It does not calculate light transport or reproduce a particular patented device.
Ideal arithmetic, not installation design
Use the calculator to relate a deliberately entered exit speed and bore diameter to ideal apex height, volume flow, flight time and water-jet kinetic power. Select a real pump, nozzle, filtration system, luminaire and electrical installation only from their engineering data and applicable safety requirements.
Ideal vertical-jet and continuity relationships
The height and round-trip time follow constant-gravity vertical motion. Volume flow is exit area times uniform velocity. Jet kinetic power is the kinetic-energy rate carried by the water; it is not pump input power.
Arithmetic example
At v=10 m/s and d=20 mm, ideal apex height is 5.10 m, ideal flow is 188.5 L/min, ideal round-trip time is 2.04 s and jet kinetic power is 157.1 W. Real height is lower and real pump input is higher because omitted losses matter.
Model boundary
A real fountain requires total dynamic head, static elevation, pipe and fitting losses, pump curve, nozzle discharge behavior, wind, droplet breakup, water quality, lighting geometry, electrical protection and site-specific safety. The calculator does not determine whether a real jet remains smooth enough to guide light or specify the lighting controls and maintenance requirements.
Luminous-fountain questions
Will a 10 m/s jet actually rise 5.10 m?
No. That is the no-drag ideal upper bound measured above the nozzle; real losses and breakup reduce it.
Does the bore diameter change ideal apex height?
Not in the ideal particle equation at fixed exit speed, but it changes flow and kinetic power.
Does the calculator predict whether the jet will carry light?
No. The light rays in the diagram are an explanatory illustration only.
Primary and technical references
- EP 0 327 779 A1, Luminous fountain: describes a pump, nozzle and projector near the nozzle that emits light into the liquid stream.
- EP 0 862 016 B1, Light device for water jet: describes a light source and propagation in the jet by multiple reflections.
- USGS, Velocity-Area Method: states discharge as area multiplied by velocity.
- NIST Guide to the SI, standard acceleration of gravity: gives 9.80665 m/s^2.
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