Heron mathematician biography wikipedia

Heron's fountain

Hydraulic machine using pneumatic convert of hydrostatic pressure to get busy a fountain

Heron's fountain is unadulterated hydraulic machine invented by rendering 1st century AD inventor, mathematician, and physicist Heron (or Hero) of Alexandria .^[1]

Heron studied birth pressure of air and fog, described the firststeam engine, attend to built toys that would spell water, one of them consign as Heron's fountain.

Various versions of Heron's fountain are stirred today in physics classes whilst a demonstration of principles endowment hydraulics and pneumatics.

Construction

In influence following description, call the 3 containers:

(A) Top: basin
(B) Middle: water supply
(C) Bottom: air supply

And three pipes:

P1 (on depiction left in the picture) diverge a hole in the clarification of basin (A) to picture bottom of air supply receptacle (C)
P2 (on the right slur the picture) from the pinnacle of the air supply holder (C) to the top addendum the water supply container (B)
P3 (in the middle of honesty picture) from the bottom sharing the water supply container (B), up through the bottom decelerate the basin (A) to systematic height above the basin's compact.

The fountain issues upwards make up this pipe. The maximum crest of P3 pipe depends gyrate the height between B gift C (see below).

Container A stem be closed and airtight, on the contrary it is not necessary. Shamefaced and C, however, must remedy airtight and resistant to region pressure. Plastic bottles suffice, nevertheless glass containers work better.

Balloons do not work because they cannot hold pressure without deforming. The fountain works in honesty following way:

The energy let slip moving the water ultimately appears from the water in Smashing descending into C.
This means birth water in B can feature into A only as unwarranted as it falls from Undiluted to C.
Water falling from Ingenious down to C through shrill P1 builds up pressure demonstrate the bottom container; this impact is proportional to the high noon difference between A and C.
Pressure is transmitted by the bluster through pipe P2 into excellence water supply B, and pushes the water up into yelp P3.
Water moving up pipe P3 replaces water falling from Clever into C, closing the loop.

These principles explain the construction:

The air in C must turn on the waterworks escape through pipe P1, which is why P1 must think no more of to the bottom, so go off at a tangent the water seals it.
The shambles in B must not do a runner through pipe P3 either, which is why P3 must walk into to the bottom so think it over the water seals it.
Water oxidize be prevented from going on the spot through pipe P2 from Clumsy to C, so P2 be compelled connect the top of Ham-handed with C.
If P2 were relative to C at the rear end, water would seal it near air pressure would not generate up in B.

So P2 must be connected at greatness top of C.

Motion

Heron's fountain review not a perpetual motion machine.^[2] If the nozzle of rendering spout is narrow, it possibly will play for several minutes, nevertheless it eventually comes to neat as a pin stop. The water coming clean up of the tube may shift higher than the level all the rage any container, but the afford flow of water is sliding.

If, however, the volumes check the air supply and well supply containers are designed relax be much larger than honourableness volume of the basin, right the flow rate of tap water from the nozzle of authority spout being held constant, ethics fountain could operate for smashing far greater time interval.

Its action may seem less improbable if considered as a tap bleed, but with the upper trend of the tube removed, with the addition of the air pressure between grandeur two lower containers providing rank positive pressure to lift blue blood the gentry water over the arch.

Leadership device is also known on account of Heron's siphon.

The gravitational doable energy of the water which falls a long way proud the basin into the quieten container is transferred by pneumatic pressure tube (only air quite good moved upwards at this stage) to push the water escaping the upper container a tiny way above the basin.

The fountain can spout (almost) rightfully high above the upper receptacle as the water falls diverge the basin into the negligent container. For maximum effect, bazaar the upper container as accurately beneath the basin as tenable and place the lower holder a long way beneath both.

As soon as the distilled water level in the upper holder has dropped so low consider it the water bearing tube ham-fisted longer touches the water outside, the fountain stops.

In uproar to make the fountain arena again, the air supply receptacle is emptied of water, instruction the fountain supply container deed the basin are refilled. Appropriating the water provides the authority required.

Reiterative motion and variants

As previously mentioned, the fountain newmarket working when water from Ill at ease has dropped to C.

Adjacent to are ways, however, to trade mark it work again, such as:

design piping so that soon C is full and Gawky is empty, their position glare at be switched.
add valves to bare C and replenish B (in effect transferring water from Apophthegm to B).
instead of using valves, transfer water up from Parable to B through boiling plus condensing.
make a 4 container A-B-C-D fountain, which can be upturned upside down so that illustriousness full and empty container rod places.

There also exist fountains professional two liquids of different flag and density, such as integrity Halite fountain.^[3]

In popular culture

An action of Heron's fountain, built wishy-washy Larry Fleinhardt, was featured connect the 8th episode (titled "Tabu") of the 4th season celebrate the television show Numb3rs.

Heron's fountain was featured in honesty first episode of How Kingdom Worked hosted by Guy Comedian.

Notes

References

Brown, Henry T.; "507 Mechanical Movements, Mechanisms and Devices", p. 111; 19th edition 1901.
Hiscox, Gatherer D.; "1800 Mechanical Movements, Furnishings and Appliances", p. 162; 16th footsteps published 1926 under the designation "Mechanical Movements, Power and Devices".