FOUNTAIN HYDRAULICS · SI UNITS

Give water a form.

Experiment with nozzle geometry, build a fountain, and see its water shape change in three dimensions.

Explore the whole garden ↗

NEW STUDY / 03 · WATER ARCHITECTUREBuild a space out of water.

Experiment with vaults, curtain walls, circular rooms, canopies and colonnades.

New reference library · artists, landscapes & bathing design ↗

CHOOSE A STARTING FORM

What shape will water take?

Start with a nozzle. Tune its opening, direction, and rhythm.

LIVE FORM EXPERIMENT

Ring crown

12 nozzles

Drag to orbit · Scroll / pinch to zoom · Grid in metres

ON-STATE FLOW—

PEAK ABOVE POOL—

FORM ENVELOPE—

NET NOZZLE HEAD—

THE OPENING MAKES THE DIFFERENCE

Ring crown

Opening shown schematically

A form-finding experiment. Water follows ideal ballistic paths at the entered exit speed. Fan and cone distributions, sheets, and nozzle hardware are schematic; jet thickness is enlarged for visibility. Droplet breakup, air drag, collisions, and real nozzle pressure curves are not simulated. The sheet is an ideal surface, not a prediction of stable film thickness.

Explore real nozzle spray patterns ↗

START WITH A STUDYLive calculation

JET REACH—Horizontal distance to pool

APEX ABOVE POOL——

INSTANTANEOUS FLOW——

TOTAL REQUIRED HEAD——

PUMP INPUT—At entered overall efficiency

TIME TO LANDING—Ballistic flight after nozzle exit

LIVE 3D EXPERIMENT

One jet. Every parameter.

1 grid unit = 1 m

CONTINUOUS JET—

Drag to orbit · Scroll to zoomJet & hardware widths enlarged · all positions in metres

01 / FLIGHT GEOMETRY

The measured arc.

METRES

Ideal jet centreline Receiving pool elevation—

02 / ENERGY BUDGET

Where the head goes.

m WATER

PIPE VELOCITY—

REYNOLDS NUMBER—

DARCY FACTOR—

FLOW REGIME—

03 / FIXED GEOMETRY

System head curve.

Uniform flow through identical nozzles. The marked point is the entered design duty; a manufacturer’s pump curve is needed to find an operating point.

04 / VALVE TIMING

A rhythm becomes a slug.

—

ON / OFF—

INITIAL SLUG LENGTH—

COMMAND TO LANDING—

MEAN EMITTED FLOW—

Delay shifts the emitted stream; response time is checked against both the open and closed intervals. Flow and pump power above describe the simultaneous on-state. Duty cycle changes emitted volume, and does not by itself predict electrical savings.

DESIGN INPUTS

Set the conditions.

Numbers update every calculation and both plots. All nozzles are assumed identical.

01 Jet & nozzle

Define nozzle exit by

Exit velocity

m/s

Velocity coefficient C_v

—

Launch angle

deg

Exit above receiving pool

Nozzle bore

Simultaneous nozzles

qty

C_v relates available nozzle head to exit speed: v = C_v√(2gH). Flow uses the actual exit velocity and bore area, with contraction coefficient C_c = 1 for a filled round exit.

02 Supply pipe & pump

Common supply length

Internal pipe diameter

Absolute roughness ε

Combined fitting loss K

—

Supply surface to nozzle

Combined pump + motor efficiency

A common supply carries the total flow. Enter all equivalent fitting losses in K. Distribution branches, filters and treatment equipment require additional loss allowance. Overall efficiency is the combined pump and motor fraction used to estimate electrical input.

03 Water & valve command

Emission mode

Pulse frequency

Valve open fraction

Command-to-exit delay

Valve response time

Water at 20°C. The initial slug length uses v × open time. The animation uses an ideal on/off command with the entered delay.

TAKE THE CALCULATION

OPEN THE CALCULATION

Equations, not a black box.

The model links an ideal ballistic jet with steady incompressible pipe flow. Values are calculated in SI units and rounded only for display.

Model boundaries & assumptions

Still air; no air drag, jet breakup, wind or splash. Constant gravity and water properties at 20°C. The free jet is at atmospheric pressure; nozzle pressure is an upstream equivalent head. Darcy–Weisbach losses use the common supply pipe, with 64/Re in laminar flow, the Swamee–Jain approximation in turbulent flow, and a blended transition from Re 2,000 to 4,000. The pipe Reynolds number describes supply-pipe flow and does not certify a smooth, glassy free jet. No pump curve, suction/NPSH, cavitation, transient surge or water-quality design is included. Use measured nozzle and pump data for a real installation.

Calculated equations and results
Quantity	Relationship	Result

READ THE BASIS

Technical references.

Source equations and supporting fluid mechanics.