A water wheel is a

machine A machine is a physical system using Power (physics), power to apply Force, forces and control Motion, movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to na ...

for converting the energy of flowing or falling water into useful forms of power, often in a

watermill A watermill or water mill is a mill that uses hydropower. It is a structure that uses a water wheel or water turbine to drive a mechanical process such as milling (grinding), rolling, or hammering. Such processes are needed in the production of ...

. A water wheel consists of a wheel (usually constructed from wood or metal), with a number of

blade A blade is the portion of a tool, weapon, or machine with an edge that is designed to puncture, chop, slice or scrape surfaces or materials. Blades are typically made from materials that are harder than those they are to be used on. Historic ...

s or

bucket A bucket is typically a watertight, vertical Cylinder (geometry), cylinder or Truncation (geometry), truncated Cone (geometry), cone or square, with an open top and a flat bottom, attached to a semicircular carrying handle (grip), handle called ...

s arranged on the outside rim forming the driving car. Water wheels were still in commercial use well into the 20th century but they are no longer in common use. Uses included milling flour in

gristmill A gristmill (also: grist mill, corn mill, flour mill, feed mill or feedmill) grinds cereal grain into flour and Wheat middlings, middlings. The term can refer to either the Mill (grinding), grinding mechanism or the building that holds it. Grist i ...

s, grinding wood into pulp for

papermaking Papermaking is the manufacture of paper and cardboard, which are used widely for printing, writing, and packaging, among many other purposes. Today almost all paper is made using industrial machinery, while handmade paper survives as a speciali ...

, hammering

wrought iron Wrought iron is an iron alloy with a very low carbon content (less than 0.08%) in contrast to that of cast iron (2.1% to 4%). It is a semi-fused mass of iron with fibrous slag Inclusion (mineral), inclusions (up to 2% by weight), which give it a ...

, machining, ore crushing and pounding fibre for use in the manufacture of

cloth Textile is an umbrella term that includes various fiber-based materials, including fibers, yarns, filaments, threads, different fabric types, etc. At first, the word "textiles" only referred to woven fabrics. However, weaving is not the ...

. Some water wheels are fed by water from a mill pond, which is formed when a flowing stream is

dammed ''Dammed: The Politics of Loss and Survival in Anishinaabe Territory'' is a 2020 book by Brittany Luby, Associate Professor of History at the University of Guelph. The book charts the impacts of the damming of the Winnipeg River in the Lake of ...

. A channel for the water flowing to or from a water wheel is called a

mill race A mill race, millrace or millrun, mill lade (Scotland) or mill leat (Southwest England) is the current of water that turns a water wheel, or the channel ( sluice) conducting water to or from a water wheel. Compared with the broad waters of a mi ...

. The race bringing water from the mill pond to the water wheel is a headrace; the one carrying water after it has left the wheel is commonly referred to as a tailrace.Dictionary definition of "tailrace"
/ref> Waterwheels were used for various purposes from

agriculture Agriculture or farming is the practice of cultivating plants and livestock. Agriculture was the key development in the rise of sedentary human civilization, whereby farming of domesticated species created food surpluses that enabled people to ...

metallurgy Metallurgy is a domain of materials science and engineering that studies the physical and chemical behavior of metallic elements, their inter-metallic compounds, and their mixtures, which are known as alloys. Metallurgy encompasses both the sc ...

in ancient civilizations spanning the Hellenistic Greek world,

Rome , established_title = Founded , established_date = 753 BC , founder = King Romulus (legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...

China China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...

and

India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...

. Waterwheels saw continued use in the

Post-classical age In world history, post-classical history refers to the period from about 500 AD to 1500, roughly corresponding to the European Middle Ages. The period is characterized by the expansion of civilizations geographically and development of trade n ...

, like the Middle Ages of Europe and the

Islamic Golden Age The Islamic Golden Age was a period of cultural, economic, and scientific flourishing in the history of Islam, traditionally dated from the 8th century to the 14th century. This period is traditionally understood to have begun during the reign ...

, but also elsewhere. In the mid to late 18th century

John Smeaton John Smeaton (8 June 1724 – 28 October 1792) was a British civil engineer responsible for the design of bridges, canals, harbours and lighthouses. He was also a capable mechanical engineer and an eminent physicist. Smeaton was the fir ...

's scientific investigation of the water wheel led to significant increases in efficiency supplying much needed power for the

Industrial Revolution The Industrial Revolution was the transition to new manufacturing processes in Great Britain, continental Europe, and the United States, that occurred during the period from around 1760 to about 1820–1840. This transition included going f ...

. Water wheels began being displaced by the smaller, less expensive and more efficient

turbine A turbine ( or ) (from the Greek , ''tyrbē'', or Latin ''turbo'', meaning vortex) is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. The work produced by a turbine can be used for generating e ...

, developed by

Benoît Fourneyron Benoît Fourneyron (31 October 1802 – 31 July 1867) was a French engineer, born in Saint-Étienne, Loire. Fourneyron made significant contributions to the development of water turbines. Benoît Fourneyron was educated at the École Nationa ...

, beginning with his first model in 1827. Turbines are capable of handling high ''

heads A head is the part of an organism which usually includes the ears, brain, forehead, cheeks, chin, eyes, nose, and mouth, each of which aid in various sensory functions such as sight, hearing, smell, and taste. Some very simple animals may no ...

'', or

elevation The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum § Vert ...

s, that exceed the capability of practical-sized waterwheels. The main difficulty of water wheels is their dependence on flowing water, which limits where they can be located. Modern

hydroelectric dam Hydroelectricity, or hydroelectric power, is electricity generated from hydropower (water power). Hydropower supplies one sixth of the world's electricity, almost 4500 TWh in 2020, which is more than all other renewable sources combined and ...

s can be viewed as the descendants of the water wheel, as they too take advantage of the movement of water downhill.

Types

Water wheels come in two basic designs: * a horizontal wheel with a vertical axle; or * a vertical wheel with a horizontal axle. The latter can be subdivided according to where the water hits the wheel into backshot (pitch-back) overshot, breastshot, undershot, and stream-wheels.Stream wheel term and specifics
/ref> The term undershot can refer to any wheel where the water passes under the wheel but it usually implies that the water entry is low on the wheel. Overshot and backshot water wheels are typically used where the available height difference is more than a couple of meters. Breastshot wheels are more suited to large flows with a moderate

head A head is the part of an organism which usually includes the ears, brain, forehead, cheeks, chin, eyes, nose, and mouth, each of which aid in various sensory functions such as sight, hearing, smell, and taste. Some very simple animals may ...

. Undershot and stream wheel use large flows at little or no head. There is often an associated

millpond A mill pond (or millpond) is a body of water used as a reservoir for a water-powered mill. Description Mill ponds were often created through the construction of a mill dam or weir (and mill stream) across a waterway. In many places, the com ...

, a reservoir for storing water and hence energy until it is needed. Larger heads store more

gravitational potential energy Gravitational energy or gravitational potential energy is the potential energy a massive object has in relation to another massive object due to gravity. It is the potential energy associated with the gravitational field, which is released (conv ...

for the same amount of water so the reservoirs for overshot and backshot wheels tend to be smaller than for breast shot wheels. Overshot and pitchback water wheels are suitable where there is a small stream with a height difference of more than , often in association with a small reservoir. Breastshot and undershot wheels can be used on rivers or high volume flows with large reservoirs.

Summary of types

Vertical axis

A horizontal wheel with a vertical axle. Commonly called a tub wheel, Norse mill or Greek mill, the horizontal wheel is a primitive and inefficient form of the modern turbine. However, if it delivers the required power then the efficiency is of secondary importance. It is usually mounted inside a mill building below the working floor. A jet of water is directed on to the paddles of the water wheel, causing them to turn. This is a simple system usually without gearing so that the vertical axle of the water wheel becomes the drive spindle of the mill.

Stream

A stream wheel is a vertically mounted water wheel that is rotated by the water in a water course striking paddles or blades at the bottom of the wheel. This type of water wheel is the oldest type of horizontal axis wheel. They are also known as

free surface In physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids. An example of two such homogeneous fluids would be a body of water (liquid) and the air in ...

wheels because the water is not constrained by millraces or wheel pits. Stream wheels are cheaper and simpler to build and have less of an environmental impact, than other types of wheels. They do not constitute a major change of the river. Their disadvantages are their low efficiency, which means that they generate less power and can only be used where the flow rate is sufficient. A typical flat board undershot wheel uses about 20 percent of the energy in the flow of water striking the wheel as measured by English civil engineer

in the 18th century. More modern wheels have higher efficiencies. Stream wheels gain little or no advantage from the head, a difference in water level. Stream wheels mounted on floating platforms are often referred to as hip wheels and the mill as a

ship mill A ship mill, more commonly known as a boat mill is a type of watermill. The milling and grinding technology and the drive (waterwheel) are built on a floating platform on this type of mill. "Deutsches Museum: Ship Mill", The Deutsches Museum' ...

. They were sometimes mounted immediately downstream from

bridges A bridge is a structure built to Span (engineering), span a physical obstacle (such as a body of water, valley, road, or rail) without blocking the way underneath. It is constructed for the purpose of providing passage over the obstacle, whic ...

where the flow restriction of the bridge piers increased the speed of the current. Historically they were very inefficient but major advances were made in the eighteenth century.

Undershot wheel

An undershot wheel is a vertically mounted water wheel with a horizontal axle that is rotated by the water from a low weir striking the wheel in the bottom quarter. Most of the energy gain is from the movement of the water and comparatively little from the head. They are similar in operation and design to stream wheels. The term undershot is sometimes used with related but different meanings: * all wheels where the water passes under the wheel * wheels where the water enters in the bottom quarter. * wheels where paddles are placed into the flow of a stream. See stream above. This is the oldest type of vertical water wheel.

Breastshot wheel

The word breastshot is used in a variety of ways. Some authors restrict the term to wheels where the water enters at about the 10 o’clock position, others 9 o’clock, and others for a range of heights. In this article it is used for wheels where the water entry is significantly above the bottom and significantly below the top, typically the middle half. They are characterized by: * buckets carefully shaped to minimize turbulence as water enters * buckets ventilated with holes in the side to allow air to escape as the water enters * a masonry "apron" closely conforming to the wheel face, which helps contain the water in the buckets as they progress downwards Both

kinetic Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to: * Kinetic theory of gases, Kinetic theory, describing a gas as particles in random motion * Kinetic energy, the energy of an object that it possesses due to i ...

(movement) and

potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple re ...

(height and weight) energy are utilised. The small clearance between the wheel and the masonry requires that a breastshot wheel has a good

trash rack A trash rack (US) or debris screen is a wooden or metal structure, frequently supported by masonry, that prevents water-borne debris (such as logs, boats, animals, masses of cut waterweed, etc.) from entering the intake of a water mill, pumping sta ...

('screen' in British English) to prevent debris from jamming between the wheel and the apron and potentially causing serious damage. Breastshot wheels are less efficient than overshot and backshot wheels but they can handle high flow rates and consequently high power. They are preferred for steady, high-volume flows such as are found on the

Fall Line A fall line (or fall zone) is the area where an upland region and a coastal plain meet and is typically prominent where rivers cross it, with resulting rapids or waterfalls. The uplands are relatively hard crystalline basement rock, and the coa ...

of the North American East Coast. Breastshot wheels are the most common type in the United States of America and are said to have powered the industrial revolution.

Overshot wheel

A vertically mounted water wheel that is rotated by water entering buckets just past the top of the wheel is said to be overshot. The term is sometimes, erroneously, applied to backshot wheels, where the water goes down behind the wheel. A typical overshot wheel has the water channeled to the wheel at the top and slightly beyond the axle. The water collects in the buckets on that side of the wheel, making it heavier than the other "empty" side. The weight turns the wheel, and the water flows out into the tail-water when the wheel rotates enough to invert the buckets. The overshot design is very efficient, it can achieve 90%, and does not require rapid flow. Nearly all of the energy is gained from the weight of water lowered to the tailrace although a small contribution may be made by the kinetic energy of the water entering the wheel. They are suited to larger heads than the other type of wheel so they are ideally suited to hilly countries. However even the largest water wheel, the

Laxey Wheel The Laxey Wheel (also known as Lady Isabella) is built into the hillside above the village of Laxey in the Isle of Man. It is the largest surviving original working waterwheel in the world. Designed by Robert Casement, the wheel has a diameter ...

in the

Isle of Man ) , anthem = "O Land of Our Birth" , image = Isle of Man by Sentinel-2.jpg , image_map = Europe-Isle_of_Man.svg , mapsize = , map_alt = Location of the Isle of Man in Europe , map_caption = Location of the Isle of Man (green) in Europe ...

, only utilises a head of around . The world's largest head turbines,

Bieudron Hydroelectric Power Station The Bieudron Hydroelectric Power Station is a hydroelectric power plant located in the Swiss Alps in the Canton of Valais in Switzerland. The power plant is fed with water from the Grande Dixence Dam's reservoir, Lac des Dix and is part of the C ...

Switzerland ). Swiss law does not designate a ''capital'' as such, but the federal parliament and government are installed in Bern, while other federal institutions, such as the federal courts, are in other cities (Bellinzona, Lausanne, Luzern, Neuchâtel ...

, utilise about . Overshot wheels require a large head compared to other types of wheel which usually means significant investment in constructing the headrace. Sometimes the final approach of the water to the wheel is along a

flume A flume is a human-made channel for water, in the form of an open declined gravity chute whose walls are raised above the surrounding terrain, in contrast to a trench or ditch. Flumes are not to be confused with aqueducts, which are built to tr ...

penstock A penstock is a sluice or gate or intake structure that controls water flow, or an enclosed pipe that delivers water to hydro turbines and sewerage systems. The term is inherited from the earlier technology of mill ponds and watermills. H ...

, which can be lengthy.

Backshot wheel

A backshot wheel (also called pitchback) is a variety of overshot wheel where the water is introduced just before the summit of the wheel. In many situations, it has the advantage that the bottom of the wheel is moving in the same direction as the water in the tailrace which makes it more efficient. It also performs better than an overshot wheel in flood conditions when the water level may submerge the bottom of the wheel. It will continue to rotate until the water in the wheel pit rises quite high on the wheel. This makes the technique particularly suitable for streams that experience significant variations in flow and reduces the size, complexity, and hence cost of the tailrace. The direction of rotation of a backshot wheel is the same as that of a breastshot wheel but in other respects, it is very similar to the overshot wheel. See below.

Hybrid

Overshot and backshot

Finch Foundary Water Wheel, Devon, UK - Diliff

Some wheels are overshot at the top and backshot at the bottom thereby potentially combining the best features of both types. The photograph shows an example at

Finch Foundry Finch Foundry is a 19th-century water-powered forge situated in the village of Sticklepath near Okehampton, Devon, England. It was originally used to produce agricultural and mining hand tools and at its peak produced around 400 edge-tools a d ...

in Devon, UK. The head race is the overhead timber structure and a branch to the left supplies water to the wheel. The water exits from under the wheel back into the stream.

Reversible

A special type of overshot/backshot wheel is the reversible water wheel. This has two sets of blades or buckets running in opposite directions so that it can turn in either direction depending on which side the water is directed. Reversible wheels were used in the

mining Mining is the extraction of valuable minerals or other geological materials from the Earth, usually from an ore body, lode, vein, seam, reef, or placer deposit. The exploitation of these deposits for raw material is based on the economic via ...

industry in order to power various means of ore conveyance. By changing the direction of the wheel, barrels or baskets of ore could be lifted up or lowered down a shaft or inclined plane. There was usually a cable drum or a chain basket on the axle of the wheel. It is essential that the wheel have braking equipment to be able to stop the wheel (known as a braking wheel). The oldest known drawing of a reversible water wheel was by

Georgius Agricola Georgius Agricola (; born Georg Pawer or Georg Bauer; 24 March 1494 – 21 November 1555) was a German Humanist scholar, mineralogist and metallurgist. Born in the small town of Glauchau, in the Electorate of Saxony of the Holy Roman Empir ...

and dates to 1556.

History

As in all machinery, rotary motion is more efficient in water-raising devices than oscillating one. In terms of power source, waterwheels can be turned by either human respectively animal force or by the water current itself. Waterwheels come in two basic designs, either equipped with a vertical or a horizontal axle. The latter type can be subdivided, depending on where the water hits the wheel paddles, into overshot, breastshot and undershot wheels. The two main functions of waterwheels were historically water-lifting for irrigation purposes and milling, particularly of grain. In case of horizontal-axle mills, a system of gears is required for power transmission, which vertical-axle mills do not need.

China

The earliest waterwheel working like a lever was described by

Zhuangzi Zhuangzi may refer to: * ''Zhuangzi'' (book) (莊子), an ancient Chinese collection of anecdotes and fables, one of the foundational texts of Daoism **Zhuang Zhou Zhuang Zhou (), commonly known as Zhuangzi (; ; literally "Master Zhuang"; als ...

in the late

Warring States period The Warring States period () was an era in History of China#Ancient China, ancient Chinese history characterized by warfare, as well as bureaucratic and military reforms and consolidation. It followed the Spring and Autumn period and concluded ...

(476-221 BC). It says that the waterwheel was invented by Zigong, a disciple of

Confucius Confucius ( ; zh, s=, p=Kǒng Fūzǐ, "Master Kǒng"; or commonly zh, s=, p=Kǒngzǐ, labels=no; – ) was a Chinese philosopher and politician of the Spring and Autumn period who is traditionally considered the paragon of Chinese sages. C ...

in the 5th century BC. By at least the 1st century AD, the

Chinese Chinese can refer to: * Something related to China * Chinese people, people of Chinese nationality, citizenship, and/or ethnicity **''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation ** List of ethnic groups in China, people of va ...

of the

Eastern Han Dynasty The Han dynasty (, ; ) was an imperial dynasty of China (202 BC – 9 AD, 25–220 AD), established by Liu Bang (Emperor Gao) and ruled by the House of Liu. The dynasty was preceded by the short-lived Qin dynasty (221–207 BC) and a warr ...

were using water wheels to crush grain in mills and to power the piston-

bellows A bellows or pair of bellows is a device constructed to furnish a strong blast of air. The simplest type consists of a flexible bag comprising a pair of rigid boards with handles joined by flexible leather sides enclosing an approximately airtigh ...

in forging

iron ore Iron ores are rocks and minerals from which metallic iron can be economically extracted. The ores are usually rich in iron oxides and vary in color from dark grey, bright yellow, or deep purple to rusty red. The iron is usually found in the fo ...

into

cast iron Cast iron is a class of iron–carbon alloys with a carbon content more than 2%. Its usefulness derives from its relatively low melting temperature. The alloy constituents affect its color when fractured: white cast iron has carbide impuriti ...

. In the text known as the ''Xin Lun'' written by

Huan Tan Huan Tan (BC– AD28) was a Chinese philosopher, poet, and politician of the Western Han and its short-lived interregnum between AD9 and 23, known as the Xin Dynasty. Life Huan worked as an official under the administrations of Emperor Ai of ...

about 20 AD (during the usurpation of

Wang Mang Wang Mang () (c. 45 – 6 October 23 CE), courtesy name Jujun (), was the founder and the only Emperor of China, emperor of the short-lived Chinese Xin dynasty. He was originally an official and consort kin of the Han dynasty and later ...

), it states that the legendary mythological king known as

Fu Xi Fuxi or Fu Hsi (伏羲 ~ 伏犧 ~ 伏戲) is a culture hero in Chinese legend and mythology, credited along with his sister and wife Nüwa with creating humanity and the invention of music, hunting, fishing, domestication, and cooking as well ...

was the one responsible for the pestle and mortar, which evolved into the tilt-hammer and then trip hammer device (see

trip hammer A trip hammer, also known as a tilt hammer or helve hammer, is a massive powered hammer. Traditional uses of trip hammers include pounding, decorticating and polishing of grain in agriculture. In mining, trip hammers were used for crushing meta ...

). Although the author speaks of the mythological Fu Xi, a passage of his writing gives hint that the water wheel was in widespread use by the 1st century AD in

( Wade-Giles spelling):

Fu Hsi invented the pestle and mortar, which is so useful, and later on it was cleverly improved in such a way that the whole weight of the body could be used for treading on the tilt-hammer (''tui''), thus increasing the efficiency ten times. Afterwards the power of animals—donkeys, mules, oxen, and horses—was applied by means of machinery, and water-power too used for pounding, so that the benefit was increased a hundredfold.Needham, p. 392

In the year 31 AD, the engineer and

Prefect Prefect (from the Latin ''praefectus'', substantive adjectival form of ''praeficere'': "put in front", meaning in charge) is a magisterial title of varying definition, but essentially refers to the leader of an administrative area. A prefect's ...

Nanyang Nanyang is the romanization of two common Chinese place names. It may refer to: Written as 南洋 (Southern Ocean) * Nanyang (region), a Chinese term denoting the Southeast Asian lands surrounding the South China Sea ;China * Nanyang Fleet, Qing ...

Du Shi Du Shi (, d. 38'' Book of Later Han'', vol. 31Crespigny, 183.) was a Chinese hydrologist, inventor, mechanical engineer, metallurgist, and politician of the Eastern Han Dynasty. Du Shi is credited with being the first to apply hydraulic power (i ...

(d. 38), applied a complex use of the water wheel and machinery to power the

of the

blast furnace A blast furnace is a type of metallurgical furnace used for smelting to produce industrial metals, generally pig iron, but also others such as lead or copper. ''Blast'' refers to the combustion air being "forced" or supplied above atmospheric ...

to create

. Du Shi is mentioned briefly in the ''

Book of Later Han The ''Book of the Later Han'', also known as the ''History of the Later Han'' and by its Chinese name ''Hou Hanshu'' (), is one of the Twenty-Four Histories and covers the history of the Han dynasty from 6 to 189 CE, a period known as the Later ...

'' (''Hou Han Shu'') as follows (in Wade-Giles spelling):

In the seventh year of the Chien-Wu reign period (31 AD) Tu Shih was posted to be Prefect of Nanyang. He was a generous man and his policies were peaceful; he destroyed evil-doers and established the dignity (of his office). Good at planning, he loved the common people and wished to save their labor. He invented a water-power reciprocator (''shui phai'') for the casting of (iron) agricultural implements. Those who smelted and cast already had the push-bellows to blow up their charcoal fires, and now they were instructed to use the rushing of the water (''chi shui'') to operate it ... Thus the people got great benefit for little labor. They found the 'water(-powered) bellows' convenient and adopted it widely.Needham, p. 370

Water wheels in

found practical uses such as this, as well as extraordinary use. The Chinese inventor

Zhang Heng Zhang Heng (; AD 78–139), formerly romanized as Chang Heng, was a Chinese polymathic scientist and statesman who lived during the Han dynasty. Educated in the capital cities of Luoyang and Chang'an, he achieved success as an astronomer, ma ...

(78–139) was the first in history to apply motive power in rotating the astronomical instrument of an

armillary sphere An armillary sphere (variations are known as spherical astrolabe, armilla, or armil) is a model of objects in the sky (on the celestial sphere), consisting of a spherical framework of rings, centered on Earth or the Sun, that represent lines of ...

, by use of a water wheel.Morton, p. 70 The

mechanical engineer Mechanical may refer to: Machine * Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement * Mechanical calculator, a device used to perform the basic operations of ...

Ma Jun (c. 200–265) from

Cao Wei Wei ( Hanzi: 魏; pinyin: ''Wèi'' <

Middle Chinese

: *''ŋjwei^C'' <

once used a water wheel to power and operate a large mechanical puppet theater for the

Emperor Ming of Wei Cao Rui () (204 or 206 – 22 January 239), courtesy name Yuanzhong, was the second emperor of the state of Cao Wei during the Three Kingdoms period. His parentage is in dispute: his mother, Lady Zhen, was Yuan Xi's wife, but she later remarri ...

( 226–239).Needham, p. 158

Western world

Greco-Roman world

The

ancient Greeks Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cultu ...

invented the waterwheel independently and used it in nearly all of the forms and functions described above, including its application for watermilling.; ; ; The technological breakthrough occurred in the technologically developed

Hellenistic period In Classical antiquity, the Hellenistic period covers the time in Mediterranean history after Classical Greece, between the death of Alexander the Great in 323 BC and the emergence of the Roman Empire, as signified by the Battle of Actium in 3 ...

between the 3rd and 1st century BC. ;Water-lifting WaterwheelsSp

The compartmented water wheel comes in two basic forms, the wheel with compartmented body (

Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...

''tympanum'') and the wheel with compartmented rim or a rim with separate, attached containers. The wheels could be either turned by men treading on its outside or by animals by means of a

sakia A sāqiyah or saqiya ( ar, ساقية), also spelled sakia or saqia) is a mechanical water lifting device. It is also called a Persian wheel, tablia, rehat, and in Latin tympanum. It is similar in function to a scoop wheel, which uses buckets, j ...

gear. While the tympanum had a large discharge capacity, it could lift the water only to less than the height of its own radius and required a large torque for rotating. These constructional deficiencies were overcome by the wheel with a compartmented rim which was a less heavy design with a higher lift. The earliest literary reference to a water-driven, compartmented wheel appears in the technical treatise ''Pneumatica'' (chap. 61) of the Greek engineer

Philo of Byzantium Philo of Byzantium ( el, , ''Phílōn ho Byzántios'', ca. 280 BC – ca. 220 BC), also known as Philo Mechanicus, was a Greek engineer, physicist and writer on mechanics, who lived during the latter half of the 3rd century BC. Although he was f ...

(ca. 280−220 BC). In his ''Parasceuastica'' (91.43−44), Philo advises the use of such wheels for submerging siege mines as a defensive measure against enemy sapping. Compartmented wheels appear to have been the means of choice for draining

dry dock A dry dock (sometimes drydock or dry-dock) is a narrow basin or vessel that can be flooded to allow a load to be floated in, then drained to allow that load to come to rest on a dry platform. Dry docks are used for the construction, maintenance, ...

s in

Alexandria Alexandria ( or ; ar, ٱلْإِسْكَنْدَرِيَّةُ ; grc-gre, Αλεξάνδρεια, Alexándria) is the second largest city in Egypt, and the largest city on the Mediterranean coast. Founded in by Alexander the Great, Alexandria ...

under the reign of

Ptolemy IV egy, Iwaennetjerwymenkhwy Setepptah Userkare Sekhemankhamun Clayton (2006) p. 208. , predecessor = Ptolemy III , successor = Ptolemy V , horus = ''ḥnw-ḳni sḫꜤi.n-sw-it.f'Khunuqeni sekhaensuitef'' The strong youth whose f ...

(221−205 BC). Several Greek

papyri Papyrus ( ) is a material similar to thick paper that was used in ancient times as a writing surface. It was made from the pith of the papyrus plant, ''Cyperus papyrus'', a wetland sedge. ''Papyrus'' (plural: ''papyri'') can also refer to a d ...

of the 3rd to 2nd century BC mention the use of these wheels, but don't give further details. The non-existence of the device in the

Ancient Near East The ancient Near East was the home of early civilizations within a region roughly corresponding to the modern Middle East: Mesopotamia (modern Iraq, southeast Turkey, southwest Iran and northeastern Syria), ancient Egypt, ancient Iran ( Elam, ...

before Alexander's conquest can be deduced from its pronounced absence from the otherwise rich oriental iconography on irrigation practices. Unlike other water-lifting devices and pumps of the period though, the invention of the compartmented wheel cannot be traced to any particular Hellenistic engineer and may have been made in the late 4th century BC in a rural context away from the metropolis of Alexandria. Archscrew2

The earliest depiction of a compartmented wheel is from a tomb painting in Ptolemaic Egypt which dates to the 2nd century BC. It shows a pair of yoked oxen driving the wheel via a

gear, which is here for the first time attested, too. The Greek sakia gear system is already shown fully developed to the point that "modern Egyptian devices are virtually identical". It is assumed that the scientists of the Museum of Alexandria, at the time the most active Greek research center, may have been involved in its invention. An episode from the

Alexandrian War Caesar's civil war (49–45 BC) was one of the last politico-military conflicts of the Roman Republic before its reorganization into the Roman Empire. It began as a series of political and military confrontations between Gaius Julius Caesar and ...

in 48 BC tells of how Caesar's enemies employed geared waterwheels to pour sea water from elevated places on the position of the trapped Romans. Around 300 AD, the

noria A noria ( ar, ناعورة, ''nā‘ūra'', plural ''nawāʿīr'', from syr, ܢܥܘܪܐ, ''nā‘orā'', lit. "growler") is a hydropowered ''scoop wheel'' used to lift water into a small aqueduct (water supply), aqueduct, either for the purpos ...

was finally introduced when the wooden compartments were replaced with inexpensive ceramic pots that were tied to the outside of an open-framed wheel. The Romans used waterwheels extensively in

projects, with enormous Roman-era waterwheels found in places like modern-day

Spain , image_flag = Bandera de España.svg , image_coat = Escudo de España (mazonado).svg , national_motto = ''Plus ultra'' (Latin)(English: "Further Beyond") , national_anthem = (English: "Royal March") , i ...

. They were

reverse overshot water-wheel Frequently used in mines and probably elsewhere (such as agricultural drainage), the reverse overshot water wheel was a Roman innovation to help remove water from the lowest levels of underground workings. It is described by Vitruvius in his work ' ...

s designed for dewatering deep underground mines. Several such devices are described by

Vitruvius Vitruvius (; c. 80–70 BC – after c. 15 BC) was a Roman architect and engineer during the 1st century BC, known for his multi-volume work entitled ''De architectura''. He originated the idea that all buildings should have three attribute ...

, including the

and the

Archimedean screw The Archimedes screw, also known as the Archimedean screw, hydrodynamic screw, water screw or Egyptian screw, is one of the earliest hydraulic machines. Using Archimedes screws as water pumps (Archimedes screw pump (ASP) or screw pump) dates back ...

. Many were found during modern mining at the

copper Copper is a chemical element with the symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. A freshly exposed surface of pure copper has a pinkis ...

mines at

Rio Tinto Rio Tinto, meaning "red river", may refer to: Businesses * Rio Tinto (corporation), an Anglo-Australian multinational mining and resources corporation ** Rio Tinto Alcan, based in Canada ** Rio Tinto Borax in America *** Rio Tinto Borax Mine, a ...

, one system involving 16 such wheels stacked above one another so as to lift water about 80 feet from the mine sump. Part of such a wheel was found at

Dolaucothi The Dolaucothi Gold Mines (; cy, Mwynfeydd Aur Dolaucothi) (), also known as the Ogofau Gold Mine, are ancient Roman surface and underground mines located in the valley of the River Cothi, near Pumsaint, Carmarthenshire, Wales. The gold min ...

, a Roman

gold mine Gold Mine may refer to: *Gold Mine (board game) *Gold Mine (Long Beach), an arena *"Gold Mine", a song by Joyner Lucas from the 2020 album '' ADHD'' See also * ''Gold'' (1974 film), based on the novel ''Gold Mine'' by Wilbur Smith *Gold mining ...

in south

Wales Wales ( cy, Cymru ) is a Countries of the United Kingdom, country that is part of the United Kingdom. It is bordered by England to the Wales–England border, east, the Irish Sea to the north and west, the Celtic Sea to the south west and the ...

in the 1930s when the mine was briefly re-opened. It was found about 160 feet below the surface, so must have been part of a similar sequence as that discovered at Rio Tinto. It has recently been

carbon dated Radiocarbon dating (also referred to as carbon dating or carbon-14 dating) is a method for determining the age of an object containing organic material by using the properties of radiocarbon, a radioactive isotope of carbon. The method was dev ...

to about 90 AD, and since the wood from which it was made is much older than the deep mine, it is likely that the deep workings were in operation perhaps 30–50 years after. It is clear from these examples of drainage wheels found in sealed underground galleries in widely separated locations that building water wheels was well within their capabilities, and such verticals water wheels commonly used for industrial purposes. ;Watermilling Roda de Vitruvi

Taking indirect evidence into account from the work of the Greek technician

Apollonius of Perge Apollonius of Perga ( grc-gre, Ἀπολλώνιος ὁ Περγαῖος, Apollṓnios ho Pergaîos; la, Apollonius Pergaeus; ) was an Ancient Greek geometer and astronomer known for his work on conic sections. Beginning from the contribution ...

, the British historian of technology M.J.T. Lewis dates the appearance of the vertical-axle watermill to the early 3rd century BC, and the horizontal-axle watermill to around 240 BC, with

Byzantium Byzantium () or Byzantion ( grc, Βυζάντιον) was an ancient Greek city in classical antiquity that became known as Constantinople in late antiquity and Istanbul today. The Greek name ''Byzantion'' and its Latinization ''Byzantium'' cont ...

and

as the assigned places of invention. A watermill is reported by the Greek geographer

Strabon Strabo''Strabo'' (meaning "squinty", as in strabismus) was a term employed by the Romans for anyone whose eyes were distorted or deformed. The father of Pompey was called "Pompeius Strabo". A native of Sicily so clear-sighted that he could see ...

(ca. 64 BC–AD 24) to have existed sometime before 71 BC in the palace of the Pontian king

Mithradates VI Eupator Mithridates or Mithradates VI Eupator ( grc-gre, Μιθραδάτης; 135–63 BC) was ruler of the Kingdom of Pontus in northern Anatolia from 120 to 63 BC, and one of the Roman Republic's most formidable and determined opponents. He was an e ...

, but its exact construction cannot be gleaned from the text (XII, 3, 30 C 556). The first clear description of a geared watermill offers the late 1st century BC Roman architect Vitruvius who tells of the sakia gearing system as being applied to a watermill. Vitruvius's account is particularly valuable in that it shows how the watermill came about, namely by the combination of the separate Greek inventions of the toothed gear and the waterwheel into one effective mechanical system for harnessing water power. Vitruvius' waterwheel is described as being immersed with its lower end in the watercourse so that its paddles could be driven by the velocity of the running water (X, 5.2). Römische Sägemühle

About the same time, the overshot wheel appears for the first time in a poem by

Antipater of Thessalonica Antipater of Thessalonica ( grc-gre, Ἀντίπατρος ὁ Θεσσαλονικεύς; c. 10 BC - c. AD 38) was a Greek epigrammatist of the Roman period. Biography Antipater lived during the latter part of the reign of Augustus, and perha ...

, which praises it as a labour-saving device (IX, 418.4–6). The motif is also taken up by

Lucretius Titus Lucretius Carus ( , ; – ) was a Roman poet and philosopher. His only known work is the philosophical poem ''De rerum natura'', a didactic work about the tenets and philosophy of Epicureanism, and which usually is translated into E ...

(ca. 99–55 BC) who likens the rotation of the waterwheel to the motion of the stars on the firmament (V 516). The third horizontal-axled type, the breastshot waterwheel, comes into archaeological evidence by the late 2nd century AD context in central Gaul. Most excavated Roman watermills were equipped with one of these wheels which, although more complex to construct, were much more efficient than the vertical-axle waterwheel. In the 2nd century AD Barbegal watermill complex a series of sixteen overshot wheels was fed by an artificial aqueduct, a proto-industrial grain factory which has been referred to as "the greatest known concentration of mechanical power in the ancient world". In

Roman North Africa Africa Proconsularis was a Roman province on the northern African coast that was established in 146 BC following the defeat of Carthage in the Third Punic War. It roughly comprised the territory of present-day Tunisia, the northeast of Algeria, ...

, several installations from around 300 AD were found where vertical-axle waterwheels fitted with angled blades were installed at the bottom of a water-filled, circular shaft. The water from the mill-race which entered tangentially the pit created a swirling water column that made the fully submerged wheel act like true

water turbine A water turbine is a rotary machine that converts kinetic energy and potential energy of water into mechanical work. Water turbines were developed in the 19th century and were widely used for industrial power prior to electrical grids. Now, t ...

s, the earliest known to date.; ; ;Navigation De Rebus Bellicis, XVth Century Miniature

Apart from its use in milling and water-raising, ancient engineers applied the paddled waterwheel for

automaton An automaton (; plural: automata or automatons) is a relatively self-operating machine, or control mechanism designed to automatically follow a sequence of operations, or respond to predetermined instructions.Automaton – Definition and More ...

s and in navigation. Vitruvius (X 9.5–7) describes multi-geared paddle wheels working as a ship

odometer An odometer or odograph is an instrument used for measuring the distance traveled by a vehicle, such as a bicycle or car. The device may be electronic, mechanical, or a combination of the two (electromechanical). The noun derives from ancient Gr ...

, the earliest of its kind. The first mention of paddle wheels as a means of propulsion comes from the 4th–5th century military treatise ''

De Rebus Bellicis ''De rebus bellicis'' ("On the Things of Wars") is an anonymous work of the 4th or 5th century which suggests remedies for the military and financial problems in the Roman Empire, including a number of fanciful war machines. It was written af ...

'' (chapter XVII), where the anonymous Roman author describes an ox-driven paddle-wheel warship.

Early Medieval Europe

Ancient water-wheel technology continued unabated in the early medieval period where the appearance of new documentary genres such as

legal code A code of law, also called a law code or legal code, is a systematic collection of statutes. It is a type of legislation that purports to exhaustively cover a complete system of laws or a particular area of law as it existed at the time the cod ...

monastic Monasticism (from Ancient Greek , , from , , 'alone'), also referred to as monachism, or monkhood, is a religion, religious way of life in which one renounces world (theology), worldly pursuits to devote oneself fully to spiritual work. Monastic ...

charter A charter is the grant of authority or rights, stating that the granter formally recognizes the prerogative of the recipient to exercise the rights specified. It is implicit that the granter retains superiority (or sovereignty), and that the rec ...

s, but also

hagiography A hagiography (; ) is a biography of a saint or an ecclesiastical leader, as well as, by extension, an adulatory and idealized biography of a founder, saint, monk, nun or icon in any of the world's religions. Early Christian hagiographies migh ...

was accompanied with a sharp increase in references to watermills and wheels. The earliest vertical-wheel in a

tide mill A tide mill is a water mill driven by tidal rise and fall. A dam with a sluice is created across a suitable tidal inlet, or a section of river estuary is made into a reservoir. As the tide comes in, it enters the mill pond through a one-way gate ...

is from 6th-century Killoteran near

Waterford "Waterford remains the untaken city" , mapsize = 220px , pushpin_map = Ireland#Europe , pushpin_map_caption = Location within Ireland##Location within Europe , pushpin_relief = 1 , coordinates ...

Ireland Ireland ( ; ga, Éire ; Ulster Scots dialect, Ulster-Scots: ) is an island in the Atlantic Ocean, North Atlantic Ocean, in Northwestern Europe, north-western Europe. It is separated from Great Britain to its east by the North Channel (Grea ...

, while the first known horizontal-wheel in such a type of mill is from the Irish Little Island (c. 630). As for the use in a common Norse or Greek mill, the oldest known horizontal-wheels were excavated in the Irish Ballykilleen, dating to c. 636. The earliest excavated water wheel driven by

tidal power Tidal power or tidal energy is harnessed by converting energy from tides into useful forms of power, mainly electricity using various methods. Although not yet widely used, tidal energy has the potential for future electricity generation. Ti ...

was the Nendrum Monastery mill in

Northern Ireland Northern Ireland ( ga, Tuaisceart Éireann ; sco, label= Ulster-Scots, Norlin Airlann) is a part of the United Kingdom, situated in the north-east of the island of Ireland, that is variously described as a country, province or region. Nort ...

which has been dated to 787, although a possible earlier mill dates to 619.

Tide mill A tide mill is a water mill driven by tidal rise and fall. A dam with a sluice is created across a suitable tidal inlet, or a section of river estuary is made into a reservoir. As the tide comes in, it enters the mill pond through a one-way gate ...

s became common in estuaries with a good tidal range in both Europe and America generally using undershot wheels. Waterwheel-Uzhhorod

Cistercian The Cistercians, () officially the Order of Cistercians ( la, (Sacer) Ordo Cisterciensis, abbreviated as OCist or SOCist), are a Catholic religious order of monks and nuns that branched off from the Benedictines and follow the Rule of Saint ...

monasteries A monastery is a building or complex of buildings comprising the domestic quarters and workplaces of monastics, monks or nuns, whether living in communities or alone (hermits). A monastery generally includes a place reserved for prayer which ...

, in particular, made extensive use of water wheels to power watermills of many kinds. An early example of a very large water wheel is the still extant wheel at the early 13th century

Real Monasterio de Nuestra Senora de Rueda Rueda Abbey or Rueda de Ebro Abbey ( es, Real Monasterio de Nuestra Señora de Rueda, or the "Royal Monastery of Our Lady of the Wheel") is a former Cistercian monastery in Sástago in the Ribera Baja del Ebro comarca, province of Zaragoza, Arag ...

, a Cistercian monastery in the

Aragon Aragon ( , ; Spanish and an, Aragón ; ca, Aragó ) is an autonomous community in Spain, coextensive with the medieval Kingdom of Aragon. In northeastern Spain, the Aragonese autonomous community comprises three provinces (from north to sou ...

region of

. Grist mills (for corn) were undoubtedly the most common, but there were also sawmills, fulling mills and mills to fulfil many other labour-intensive tasks. The water wheel remained competitive with the

steam engine A steam engine is a heat engine that performs mechanical work using steam as its working fluid. The steam engine uses the force produced by steam pressure to push a piston back and forth inside a cylinder. This pushing force can be trans ...

well into the

. At around the 8th to 10th century, a number of irrigation technologies were brought into Spain and thus introduced to Europe. One of those technologies is the Noria, which is basically a wheel fitted with buckets on the peripherals for lifting water. It is similar to the undershot water wheel mentioned later in this article. It allowed peasants to power watermills more efficiently. According to Thomas Glick's book, ''Irrigation and Society in Medieval Valencia'', the Noria probably originated from somewhere in

Persia Iran, officially the Islamic Republic of Iran, and also called Persia, is a country located in Western Asia. It is bordered by Iraq and Turkey to the west, by Azerbaijan and Armenia to the northwest, by the Caspian Sea and Turkmeni ...

. It has been used for centuries before the technology was brought into Spain by Arabs who had adopted it from the Romans. Thus the distribution of the Noria in the Iberian peninsula "conforms to the area of stabilized Islamic settlement". This technology has a profound effect on the life of peasants. The Noria is relatively cheap to build. Thus it allowed peasants to cultivate land more efficiently in Europe. Together with the

Spaniards Spaniards, or Spanish people, are a Romance peoples, Romance ethnic group native to Spain. Within Spain, there are a number of National and regional identity in Spain, national and regional ethnic identities that reflect the country's complex Hist ...

, the technology spread to the

New World The term ''New World'' is often used to mean the majority of Earth's Western Hemisphere, specifically the Americas."America." ''The Oxford Companion to the English Language'' (). McArthur, Tom, ed., 1992. New York: Oxford University Press, p. 3 ...

Mexico Mexico (Spanish: México), officially the United Mexican States, is a country in the southern portion of North America. It is bordered to the north by the United States; to the south and west by the Pacific Ocean; to the southeast by Guatema ...

and

South America South America is a continent entirely in the Western Hemisphere and mostly in the Southern Hemisphere, with a relatively small portion in the Northern Hemisphere at the northern tip of the continent. It can also be described as the southe ...

following Spanish expansion

Domesday inventory of English mills c. 1086

The assembly convened by

William of Normandy William I; ang, WillelmI (Bates ''William the Conqueror'' p. 33– 9 September 1087), usually known as William the Conqueror and sometimes William the Bastard, was the first Norman king of England, reigning from 1066 until his death in 108 ...

, commonly referred to as the "

Domesday Domesday Book () – the Middle English spelling of "Doomsday Book" – is a manuscript record of the "Great Survey" of much of England and parts of Wales completed in 1086 by order of King William I, known as William the Conqueror. The manusc ...

" or Doomsday survey, took an inventory of all potentially taxable property in England, which included over six thousand mills spread across three thousand different locations.Robert, Friedel, ''A Culture of Improvement''. MIT Press. Cambridge, Massachusetts. London, England. (2007). pp. 31–2b.

Locations

The type of water wheel selected was dependent upon the location. Generally if only small volumes of water and high waterfalls were available a millwright would choose to use an

overshot wheel A water wheel is a machine for converting the energy of flowing or falling water into useful forms of power, often in a watermill. A water wheel consists of a wheel (usually constructed from wood or metal), with a number of blades or bucket ...

. The decision was influenced by the fact that the buckets could catch and use even a small volume of water. For large volumes of water with small waterfalls the undershot wheel would have been used, since it was more adapted to such conditions and cheaper to construct. So long as these water supplies were abundant the question of efficiency remained irrelevant. By the 18th century, with increased demand for power coupled with limited water locales, an emphasis was made on efficiency scheme.

Economic influence

By the 11th century there were parts of Europe where the exploitation of water was commonplace. The water wheel is understood to have actively shaped and forever changed the outlook of Westerners. Europe began to transit from human and animal muscle labor towards mechanical labor with the advent of the water wheel. Medievalist Lynn White Jr. contended that the spread of inanimate power sources was eloquent testimony to the emergence of the West of a new attitude toward, power, work, nature, and above all else technology. Harnessing water-power enabled gains in agricultural productivity, food surpluses and the large scale urbanization starting in the 11th century. The usefulness of water power motivated European experiments with other power sources, such as wind and tidal mills. Waterwheels influenced the construction of cities, more specifically canals. The techniques that developed during this early period such as stream jamming and the building of

canals Canals or artificial waterways are waterways or river engineering, engineered channel (geography), channels built for drainage management (e.g. flood control and irrigation) or for conveyancing water transport watercraft, vehicles (e.g. ...

, put Europe on a

hydraulically Hydraulics (from Greek language, Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is th ...

focused path, for instance water supply and irrigation technology was combined to modify supply power of the wheel. Illustrating the extent to which there was a great degree of technological innovation that met the growing needs of the

feudal state Feudalism, also known as the feudal system, was the combination of the legal, economic, military, cultural and political customs that flourished in Middle Ages, medieval Europe between the 9th and 15th centuries. Broadly defined, it was a wa ...

Applications of the water wheel

The water mill was used for grinding grain, producing flour for bread, malt for beer, or coarse meal for porridge. Hammermills used the wheel to operate hammers. One type was

fulling mill Fulling, also known as felting, tucking or walking ( Scots: ''waukin'', hence often spelled waulking in Scottish English), is a step in woollen clothmaking which involves the cleansing of woven or knitted cloth (particularly wool) to elimin ...

, which was used for cloth making. The

was also used for making

and for working iron into useful shapes, an activity that was otherwise labour-intensive. The water wheel was also used in

, beating material to a pulp. In the 13th century water mills used for hammering throughout Europe improved the productivity of early steel manufacturing. Along with the mastery of gunpowder, waterpower provided European countries worldwide military leadership from the 15th century.

17th- and 18th-century Europe

Millwrights distinguished between the two forces, impulse and weight, at work in water wheels long before 18th-century Europe. Fitzherbert, a 16th-century agricultural writer, wrote "druieth the wheel as well as with the weight of the water as with strengthe mpulse.

Leonardo da Vinci Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, Drawing, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially res ...

also discussed water power, noting "the blow

f the water F, or f, is the sixth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''ef'' (pronounced ), and the plural is ''efs''. Hist ...

is not weight, but excites a power of weight, almost equal to its own power". However, even realisation of the two forces, weight and impulse, confusion remained over the advantages and disadvantages of the two, and there was no clear understanding of the superior efficiency of weight. Prior to 1750 it was unsure as to which force was dominant and was widely understood that both forces were operating with equal inspiration amongst one another.Torricelli, Evangelista, ''Opere'', ed. Gino Loria and Giuseppe Vassura (Rome, 1919.) The waterwheel sparked questions of the laws of nature, specifically the

laws of force Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in motio ...

Evangelista Torricelli Evangelista Torricelli ( , also , ; 15 October 160825 October 1647) was an Italian physicist and mathematician, and a student of Galileo. He is best known for his invention of the barometer, but is also known for his advances in optics and work o ...

's work on water wheels used an analysis of Galileo's work on falling bodies, that the velocity of a water sprouting from an orifice under its

was exactly equivalent to the velocity a drop of water acquired in falling freely from the same height.Torricella, Evangelica, ''Opere'', ed. Gino Loria and Giuseppe Vassura (Rome, 1919.)

Industrial Europe

The water wheel was a driving force behind the earliest stages of industrialization in Britain. Water-powered reciprocating devices were used in trip hammers and blast furnace bellows.

Richard Arkwright Sir Richard Arkwright (23 December 1732 – 3 August 1792) was an English inventor and a leading entrepreneur during the early Industrial Revolution. He is credited as the driving force behind the development of the spinning frame, known as t ...

's water frame was powered by a water wheel. The most powerful water wheel built in the United Kingdom was the 100 hp

Quarry Bank Mill Quarry Bank Mill (also known as Styal Mill) in Styal, Cheshire, England, is one of the best preserved textile factories of the Industrial Revolution. Built in 1784, the cotton mill is recorded in the National Heritage List for England as a ...

water wheel near Manchester. A high breastshot design, it was retired in 1904 and replaced with several turbines. It has now been restored and is a museum open to the public. The biggest working water wheel in mainland Britain has a diameter of and was built by the De Winton company of Caernarfon. It is located within the Dinorwic workshops of the National Slate Museum in Llanberis, North

. The largest working water wheel in the world is the

(also known as ''Lady Isabella'') in the village of

Laxey Laxey ( gv, Laksaa) is a village on the east coast of the Isle of Man. Its name derives from the Old Norse ''Laxa'' meaning 'Salmon River'. Its key distinguishing features are its three working vintage railways and the largest working waterwhee ...

. It is in diameter and wide and is maintained by

Manx National Heritage Manx National Heritage ( gv, Eiraght Ashoonagh Vannin) is the national heritage organisation for the Isle of Man. The organisation manages a significant proportion of the island’s physical heritage assets including over 3,000 acres of coastlin ...

. During the

, in the first half of the 19th century engineers started to design better wheels. In 1823

Jean-Victor Poncelet Jean-Victor Poncelet (; 1 July 1788 – 22 December 1867) was a French engineer and mathematician who served most notably as the Commanding General of the École Polytechnique. He is considered a reviver of projective geometry, and his work ''Tr ...

invented a very efficient undershot wheel design that could work on very low heads, which was commercialized and became popular by late 1830s. Other designs, as the

Sagebien wheel The Sagebien wheel is a type of water wheel invented by Alphonse Sagebien of France, a hydrological engineer and a graduate of the École Centrale des Arts et Manufactures. It was one of the most efficient breastshot water wheel designs of its era; ...

, followed later. At the same time

Claude Burdin Claude Burdin (; 19 March 1788 – 12 November 1873) was a French engineer. Born in Lépin-le-Lac, Savoie, when it was known as the Duchy of Savoy, he was professor at the school of mines, École nationale supérieure des mines de Saint-� ...

was working on a radically different machine which he called ''turbine'', and his pupil

designed the first commercial one in the 1830s. Development of

s led to decreased popularity of water wheels. The main advantage of turbines is that its ability to harness

is much greater than the diameter of the turbine, whereas a water wheel cannot effectively harness head greater than its diameter. The migration from water wheels to modern turbines took about one hundred years.

North America

Water wheels were used to power sawmills, grist mills and for other purposes during development of the United States. The diameter water wheel at McCoy, Colorado, built in 1922, is a surviving one out of many which lifted water for irrigation out of the

Colorado River The Colorado River ( es, Río Colorado) is one of the principal rivers (along with the Rio Grande) in the Southwestern United States and northern Mexico. The river drains an expansive, arid drainage basin, watershed that encompasses parts of ...

. Two early improvements were suspension wheels and rim gearing. Suspension wheels are constructed in the same manner as a bicycle wheel, the rim being supported under tension from the hub- this led to larger lighter wheels than the former design where the heavy spokes were under compression. Rim-gearing entailed adding a notched wheel to the rim or shroud of the wheel. A stub gear engaged the rim-gear and took the power into the mill using an independent line shaft. This removed the rotative stress from the axle which could thus be lighter, and also allowed more flexibility in the location of the power train. The shaft rotation was geared up from that of the wheel which led to less power loss. An example of this design pioneered by Thomas Hewes and refined by

William Armstrong Fairburn William Armstrong Fairburn (12 October 1876 – 1 October 1947) was a noted American author, naval architect, marine engineer, industrial executive, and chemist. Biography He was the son of Thomas W. Fairburn and Elizabeth Jemima Frosdick,Cen ...

can be seen at the 1849 restored wheel at the Portland Basin Canal Warehouse. Somewhat related were

fish wheel A fish wheel, also known as a salmon wheel, is a device situated in rivers to catch fish which looks and operates like a watermill. However, in addition to paddles, a fish wheel is outfitted with wire baskets designed to catch and carry fish fro ...

s used in the American Northwest and Alaska, which lifted

salmon Salmon () is the common name for several list of commercially important fish species, commercially important species of euryhaline ray-finned fish from the family (biology), family Salmonidae, which are native to tributary, tributaries of the ...

out of the flow of rivers.

Australia

Garfield water wheel (State Library of Victoria IE1864826)

Australia has a relatively dry climate, nonetheless, where suitable water resources were available, water wheels were constructed in 19th-century Australia. These were used to power sawmills, flour mills, and stamper batteries used to crush gold-bearing ore. Notable examples of water wheels used in gold recovery operations were the large

Garfield water wheel The Garfield water wheel, sometimes referred to as the Forrest Creek Mine water wheel, was a large water wheel used to power a stamper battery at a gold mine near Chewton, Victoria, Australia. Constructed in 1887, the water wheel was used until ...

near Chewton—one of at least seven water wheels in the surrounding area—and the two water wheels at Adelong Falls; some remnants exist at both sites. The mining area at Walhalla once had at least two water wheels, one of which was rolled to its site from

Port Albert Port Albert is a coastal town in Victoria, Australia, on the coast of Corner Inlet on the Yarram - Port Albert Road, south-east of Morwell, south-east of Melbourne, in the Shire of Wellington. At the , Port Albert had a population of 293. L ...

, on its rim using a novel trolley arrangement, taking nearly 90 days. A water wheel at Jindabyne, constructed in 1847, was the first machine used to extract energy—for flour milling—from the

Snowy River The Snowy River is a major river in south-eastern Australia. It originates on the slopes of Mount Kosciuszko, Australia's highest mainland peak, draining the eastern slopes of the Snowy Mountains in New South Wales, before flowing through the ...

. Compact water wheels, known as

Dethridge wheel The Dethridge Wheel is an irrigation tool that was invented in 1910 by John Stewart Dethridge (1865–1926). It works in a similar way to a traditional water wheel and rotates as water passes through its vanes. The rotations are then measured T ...

s, were used not as sources of power but to measure water flows to irrigated land.

New Zealand

Water wheels were used extensively in New Zealand. The well-preserved remains of the Young Australian mine's overshot water wheel exist near the ghost town of Carricktown, and those of the Phoenix flour mill's water wheel are near

Oamaru Oamaru (; mi, Te Oha-a-Maru) is the largest town in North Otago, in the South Island of New Zealand, it is the main town in the Waitaki District. It is south of Timaru and north of Dunedin on the Pacific coast; State Highway 1 and the railway ...

India

The early history of the watermill in

is obscure. Ancient Indian texts dating back to the 4th century BC refer to the term ''cakkavattaka'' (turning wheel), which commentaries explain as ''arahatta-ghati-yanta'' (machine with wheel-pots attached). On this basis,

Joseph Needham Noel Joseph Terence Montgomery Needham (; 9 December 1900 – 24 March 1995) was a British biochemist, historian of science and sinologist known for his scientific research and writing on the history of Chinese science and technology, in ...

suggested that the machine was a

. Terry S. Reynolds, however, argues that the "term used in Indian texts is ambiguous and does not clearly indicate a water-powered device." Thorkild Schiøler argued that it is "more likely that these passages refer to some type of tread- or hand-operated water-lifting device, instead of a water-powered water-lifting wheel." According to Greek historical tradition, India received water-mills from the Roman Empire in the early 4th century AD when a certain Metrodoros introduced "water-mills and baths, unknown among them

he Brahmans He or HE may refer to: Language * He (pronoun), an English pronoun * He (kana), the romanization of the Japanese kana へ * He (letter), the fifth letter of many Semitic alphabets * He (Cyrillic), a letter of the Cyrillic script called ''He'' in ...

till then". Irrigation water for crops was provided by using water raising wheels, some driven by the force of the current in the river from which the water was being raised. This kind of water raising device was used in

ancient India According to consensus in modern genetics, anatomically modern humans first arrived on the Indian subcontinent from Africa between 73,000 and 55,000 years ago. Quote: "Y-Chromosome and Mt-DNA data support the colonization of South Asia by m ...

, predating, according to Pacey, its use in the later Roman Empire or China, even though the first literary, archaeological and pictorial evidence of the water wheel appeared in the Hellenistic world. Around 1150, the astronomer Bhaskara Achārya observed water-raising wheels and imagined such a wheel lifting enough water to replenish the stream driving it, effectively, a

perpetual motion Perpetual motion is the motion of bodies that continues forever in an unperturbed system. A perpetual motion machine is a hypothetical machine that can do work infinitely without an external energy source. This kind of machine is impossible, a ...

machine. The construction of water works and aspects of water technology in India is described in

Arabic Arabic (, ' ; , ' or ) is a Semitic languages, Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C ...

and

Persian Persian may refer to: * People and things from Iran, historically called ''Persia'' in the English language ** Persians, the majority ethnic group in Iran, not to be conflated with the Iranic peoples ** Persian language, an Iranian language of the ...

works. During medieval times, the diffusion of Indian and Persian irrigation technologies gave rise to an advanced irrigation system which bought about economic growth and also helped in the growth of material culture.

Islamic world

After the spread of Islam engineers of the Islamic world continued the water technologies of the ancient Near East; as evident in the excavation of a canal in the Basra region with remains of a water wheel dating from the 7th century.

Hama , timezone = EET , utc_offset = +2 , timezone_DST = EEST , utc_offset_DST = +3 , postal_code_type = , postal_code = , ar ...

Syria Syria ( ar, سُورِيَا or سُورِيَة, translit=Sūriyā), officially the Syrian Arab Republic ( ar, الجمهورية العربية السورية, al-Jumhūrīyah al-ʻArabīyah as-Sūrīyah), is a Western Asian country loc ...

still preserves some of its large wheels, on the river Orontes, although they are no longer in use. One of the largest had a diameter of about and its rim was divided into 120 compartments. Another wheel that is still in operation is found at

Murcia Murcia (, , ) is a city in south-eastern Spain, the capital and most populous city of the autonomous community of the Region of Murcia, and the seventh largest city in the country. It has a population of 460,349 inhabitants in 2021 (about one ...

, La Nora, and although the original wheel has been replaced by a steel one, the

Moorish The term Moor, derived from the ancient Mauri, is an exonym first used by Christian Europeans to designate the Muslim inhabitants of the Maghreb, the Iberian Peninsula, Sicily and Malta during the Middle Ages. Moors are not a distinct or se ...

system during

al-Andalus Al-Andalus DIN 31635, translit. ; an, al-Andalus; ast, al-Ándalus; eu, al-Andalus; ber, ⴰⵏⴷⴰⵍⵓⵙ, label=Berber languages, Berber, translit=Andalus; ca, al-Àndalus; gl, al-Andalus; oc, Al Andalús; pt, al-Ândalus; es, ...

is otherwise virtually unchanged. Some medieval Islamic compartmented water wheels could lift water as high as .

Muhammad ibn Zakariya al-Razi Abū Bakr al-Rāzī (full name: ar, أبو بکر محمد بن زکریاء الرازي, translit=Abū Bakr Muḥammad ibn Zakariyyāʾ al-Rāzī, label=none), () rather than ar, زکریاء, label=none (), as for example in , or in . In m ...

's ''Kitab al-Hawi'' in the 10th century described a

in Iraq that could lift as much as , or . This is comparable to the output of modern norias in

East Asia East Asia is the eastern region of Asia, which is defined in both geographical and ethno-cultural terms. The modern states of East Asia include China, Japan, Mongolia, North Korea, South Korea, and Taiwan. China, North Korea, South Korea and ...

, which can lift up to , or . COLLECTIE TROPENMUSEUM Kintjir of waterschepwiel in Djambi Sumatra TMnr 10007886

The industrial uses of watermills in the Islamic world date back to the 7th century, while horizontal-wheeled and vertical-wheeled water mills were both in widespread use by the 9th century. A variety of industrial watermills were used in the Islamic world, including

huller A rice huller or rice husker is an agricultural machine used to automate the process of removing the chaff (the outer husks) of grains of rice. Throughout history, there have been numerous techniques to hull rice. Traditionally, it would be po ...

sawmill A sawmill (saw mill, saw-mill) or lumber mill is a facility where logs are cut into lumber. Modern sawmills use a motorized saw to cut logs lengthwise to make long pieces, and crosswise to length depending on standard or custom sizes (dimensi ...

s, shipmills,

stamp mill A stamp mill (or stamp battery or stamping mill) is a type of mill machine that crushes material by pounding rather than grinding, either for further processing or for extraction of metallic ores. Breaking material down is a type of unit operatio ...

steel mill A steel mill or steelworks is an industrial plant for the manufacture of steel. It may be an integrated steel works carrying out all steps of steelmaking from smelting iron ore to rolled product, but may also be a plant where steel semi-finish ...

sugar mills A sugar cane mill is a factory that processes sugar cane to produce raw or white sugar. The term is also used to refer to the equipment that crushes the sticks of sugar cane to extract the juice. Processing There are a number of steps in prod ...

, and

s. By the 11th century, every province throughout the Islamic world had these industrial watermills in operation, from

and

North Africa North Africa, or Northern Africa is a region encompassing the northern portion of the African continent. There is no singularly accepted scope for the region, and it is sometimes defined as stretching from the Atlantic shores of Mauritania in ...

to the

Middle East The Middle East ( ar, الشرق الأوسط, ISO 233: ) is a geopolitical region commonly encompassing Arabian Peninsula, Arabia (including the Arabian Peninsula and Bahrain), Anatolia, Asia Minor (Asian part of Turkey except Hatay Pro ...

and

Central Asia Central Asia, also known as Middle Asia, is a subregion, region of Asia that stretches from the Caspian Sea in the west to western China and Mongolia in the east, and from Afghanistan and Iran in the south to Russia in the north. It includes t ...

. Muslim and Christian engineers also used

crankshaft A crankshaft is a mechanical component used in a piston engine to convert the reciprocating motion into rotational motion. The crankshaft is a rotating shaft containing one or more crankpins, that are driven by the pistons via the connecting ...

s and

gear A gear is a rotating circular machine part having cut teeth or, in the case of a cogwheel or gearwheel, inserted teeth (called ''cogs''), which mesh with another (compatible) toothed part to transmit (convert) torque and speed. The basic pr ...

s in watermills and water-raising

s, and

dam A dam is a barrier that stops or restricts the flow of surface water or underground streams. Reservoirs created by dams not only suppress floods but also provide water for activities such as irrigation, human consumption, industrial use, a ...

s as a source of water, used to provide additional power to watermills and water-raising machines. Fulling mills and steel mills may have spread from Islamic Spain to Christian Spain in the 12th century. Industrial water mills were also employed in large

factory A factory, manufacturing plant or a production plant is an industrial facility, often a complex consisting of several buildings filled with machinery, where workers manufacture items or operate machines which process each item into another. T ...

complexes built in

between the 11th and 13th centuries. The engineers of the Islamic world developed several solutions to achieve the maximum output from a water wheel. One solution was to mount them to

pier image:Brighton Pier, Brighton, East Sussex, England-2Oct2011 (1).jpg, Seaside pleasure pier in Brighton, England. The first seaside piers were built in England in the early 19th century. A pier is a raised structure that rises above a body of ...

s of

bridge A bridge is a structure built to span a physical obstacle (such as a body of water, valley, road, or rail) without blocking the way underneath. It is constructed for the purpose of providing passage over the obstacle, which is usually somethi ...

s to take advantage of the increased flow. Another solution was the shipmill, a type of

water mill A watermill or water mill is a mill that uses hydropower. It is a structure that uses a water wheel or water turbine to drive a mechanical process such as milling (grinding), rolling, or hammering. Such processes are needed in the production o ...

ship A ship is a large watercraft that travels the world's oceans and other sufficiently deep waterways, carrying cargo or passengers, or in support of specialized missions, such as defense, research, and fishing. Ships are generally distinguished ...

moored A mooring is any permanent structure to which a vessel may be secured. Examples include quays, wharfs, jetties, piers, anchor buoys, and mooring buoys. A ship is secured to a mooring to forestall free movement of the ship on the water. An ''anc ...

in midstream. This technique was employed along the

Tigris The Tigris () is the easternmost of the two great rivers that define Mesopotamia, the other being the Euphrates. The river flows south from the mountains of the Armenian Highlands through the Syrian and Arabian Deserts, and empties into the ...

and

Euphrates The Euphrates () is the longest and one of the most historically important rivers of Western Asia. Tigris–Euphrates river system, Together with the Tigris, it is one of the two defining rivers of Mesopotamia ( ''the land between the rivers'') ...

rivers in 10th-century

Iraq Iraq,; ku, عێراق, translit=Êraq officially the Republic of Iraq, '; ku, کۆماری عێراق, translit=Komarî Êraq is a country in Western Asia. It is bordered by Turkey to Iraq–Turkey border, the north, Iran to Iran–Iraq ...

, where large shipmills made of

teak Teak (''Tectona grandis'') is a tropical hardwood tree species in the family Lamiaceae. It is a large, deciduous tree that occurs in mixed hardwood forests. ''Tectona grandis'' has small, fragrant white flowers arranged in dense clusters (panicl ...

and

iron Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in f ...

could produce 10

ton Ton is the name of any one of several units of measure. It has a long history and has acquired several meanings and uses. Mainly it describes units of weight. Confusion can arise because ''ton'' can mean * the long ton, which is 2,240 pounds ...

s of flour from corn every day for the

granary A granary is a storehouse or room in a barn for threshed grain or animal feed. Ancient or primitive granaries are most often made of pottery. Granaries are often built above the ground to keep the stored food away from mice and other animal ...

Baghdad Baghdad (; ar, بَغْدَاد , ) is the capital of Iraq and the second-largest city in the Arab world after Cairo. It is located on the Tigris near the ruins of the ancient city of Babylon and the Sassanid Persian capital of Ctesiphon ...

.Hill; see als
Mechanical Engineering
The

flywheel A flywheel is a mechanical device which uses the conservation of angular momentum to store rotational energy; a form of kinetic energy proportional to the product of its moment of inertia and the square of its rotational speed. In particular, ass ...

mechanism, which is used to smooth out the delivery of power from a driving device to a driven machine, was invented by Ibn Bassal (

fl. ''Floruit'' (; abbreviated fl. or occasionally flor.; from Latin for "they flourished") denotes a date or period during which a person was known to have been alive or active. In English, the unabbreviated word may also be used as a noun indicatin ...

1038–1075) of

Al-Andalus Al-Andalus DIN 31635, translit. ; an, al-Andalus; ast, al-Ándalus; eu, al-Andalus; ber, ⴰⵏⴷⴰⵍⵓⵙ, label=Berber languages, Berber, translit=Andalus; ca, al-Àndalus; gl, al-Andalus; oc, Al Andalús; pt, al-Ândalus; es, ...

; he pioneered the use of the flywheel in the

saqiya Saqiya ( ar, ساقِية, the Arabic name of a mechanical water lifting device) was a village in Palestine (Jaffa district) away from Jaffa, depopulated in 1948. Location The village was located east of Jaffa, above sea level, on uneven lan ...

(

chain pump The chain pump is type of a water pump in which several circular discs are positioned on an endless chain. One part of the chain dips into the water, and the chain runs through a tube, slightly bigger than the diameter of the discs. As the chain is ...

) and noria. The engineers

Al-Jazari Badīʿ az-Zaman Abu l-ʿIzz ibn Ismāʿīl ibn ar-Razāz al-Jazarī (1136–1206, ar, بديع الزمان أَبُ اَلْعِزِ إبْنُ إسْماعِيلِ إبْنُ الرِّزاز الجزري, ) was a polymath: a scholar, ...

in the 13th century and Taqi al-Din in the 16th century described many inventive water-raising machines in their technological treatises. They also employed water wheels to power a variety of devices, including various

water clock A water clock or clepsydra (; ; ) is a timepiece by which time is measured by the regulated flow of liquid into (inflow type) or out from (outflow type) a vessel, and where the amount is then measured. Water clocks are one of the oldest time-m ...

s and

automata An automaton (; plural: automata or automatons) is a relatively self-operating machine, or control mechanism designed to automatically follow a sequence of operations, or respond to predetermined instructions.Automaton – Definition and More ...

Modern developments

Hydraulic wheel

A recent development of the breastshot wheel is a hydraulic wheel which effectively incorporates automatic regulation systems. The Aqualienne is one example. It generates between 37 kW and 200 kW of electricity from a waterflow with a head of .http://www.h3eindustries.com/How-does-an-Aqualienne%C2%AE-work? Aqualienne breastshot wheel It is designed to produce electricity at the sites of former watermills.

Efficiency

Overshot (and particularly backshot) wheels are the most efficient type; a backshot

steel Steel is an alloy made up of iron with added carbon to improve its strength and fracture resistance compared to other forms of iron. Many other elements may be present or added. Stainless steels that are corrosion- and oxidation-resistant ty ...

wheel can be more efficient (about 60%) than all but the most advanced and well-constructed

turbines A turbine ( or ) (from the Greek , ''tyrbē'', or Latin ''turbo'', meaning vortex) is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful Work (physics), work. The work produced by a turbine can be used ...

. In some situations an overshot wheel is preferable to a turbine. The development of the

hydraulic turbine A water turbine is a rotary machine that converts kinetic energy and potential energy of water into mechanical work. Water turbines were developed in the 19th century and were widely used for industrial power prior to electrical grids. Now, th ...

wheels with their improved efficiency (>67%) opened up an alternative path for the installation of water wheels in existing mills, or redevelopment of abandoned mills.

The power of a wheel

The energy available to the wheel has two components: *

Kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its accele ...

– depends on how fast the water is moving when it enters the wheel *

Potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potentia ...

– depends on the change in height of the water between entry to and exit from the wheel The kinetic energy can be accounted for by converting it into an equivalent head, the velocity head, and adding it to the actual head. For still water the velocity head is zero, and to a good approximation it is negligible for slowly moving water, and can be ignored. The velocity in the tail race is not taken into account because for a perfect wheel the water would leave with zero energy which requires zero velocity. That is impossible, the water has to move away from the wheel, and represents an unavoidable cause of inefficiency. The

power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...

is how fast that energy is delivered which is determined by the flow rate. It has been estimated that the ancient donkey or slave-powered

quern Quern ( da, Kværn) is a former municipality in the district of Schleswig-Flensburg, in Schleswig-Holstein, Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populo ...

of Rome made about one-half of a

horsepower Horsepower (hp) is a unit of measurement of power, or the rate at which work is done, usually in reference to the output of engines or motors. There are many different standards and types of horsepower. Two common definitions used today are the ...

, the horizontal waterwheel creating slightly more than one-half of a horsepower, the undershot vertical waterwheel produced about three horsepower, and the medieval overshot waterwheel produced up to forty to sixty horsepower.

Quantities and units

\eta=

efficiency Efficiency is the often measurable ability to avoid wasting materials, energy, efforts, money, and time in doing something or in producing a desired result. In a more general sense, it is the ability to do things well, successfully, and without ...

\rho=

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a ...

(1000 kg/m³) *

A=

cross sectional area In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections. The ...

of the channel (m²) *

D=

diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for ...

of wheel (m) *

P=

(W) *

d=

distance Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...

(m) *

g=

strength of gravity (9.81 m/s² = 9.81 N/kg) *

h=

(m) *

h_p=

pressure head In fluid mechanics, pressure head is the height of a liquid column that corresponds to a particular pressure exerted by the liquid column on the base of its container. It may also be called static pressure head or simply static head (but not ''sta ...

, the difference in water levels (m) *

h_v=

velocity head Hydraulic head or piezometric head is a specific measurement of liquid pressure above a vertical datum., 410 pages. See pp. 43–44., 650 pages. See p. 22. It is usually measured as a liquid surface elevation, expressed in units of length, ...

(m) *

k=

velocity correction factor. 0.9 for smooth channels. *

v=

velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...

(m/s) *

\dot q =

volume flow rate In physics and engineering, in particular fluid dynamics, the volumetric flow rate (also known as volume flow rate, or volume velocity) is the volume of fluid which passes per unit time; usually it is represented by the symbol (sometimes ). I ...

(m³/s) *

t=

time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...

(s)

Measurements

The pressure head

h_p

is the difference in height between the head race and tail race water surfaces. The velocity head

h_v

is calculated from the velocity of the water in the head race at the same place as the pressure head is measured from. The velocity (speed)

v

can be measured by the pooh sticks method, timing a floating object over a measured distance. The water at the surface moves faster than water nearer to the bottom and sides so a correction factor should be applied as in the formula below. There are many ways to measure the

. Two of the simplest are: *From the cross sectional area and the velocity. They must be measured at the same place but that can be anywhere in the head or tail races. It must have the same amount of water going through it as the wheel. *It is sometimes practicable to measure the volume flow rate by the bucket and stop watch method.

Formulae

Rules of thumb

Breast and overshot

Traditional undershot wheels

Hydraulic wheel part reaction turbine

A parallel development is the hydraulic wheel/part reaction turbine that also incorporates a weir into the centre of the wheel but uses blades angled to the water flow. The WICON-Stem Pressure Machine (SPM) exploits this flow. Estimated efficiency 67%. The

University of Southampton , mottoeng = The Heights Yield to Endeavour , type = Public research university , established = 1862 – Hartley Institution1902 – Hartley University College1913 – Southampton University Coll ...

School of Civil Engineering and the Environment in the UK has investigated both types of Hydraulic wheel machines and has estimated their hydraulic efficiency and suggested improvements, i.e. The Rotary Hydraulic Pressure Machine. (Estimated maximum efficiency 85%).Low Head Hydro
/ref> These type of water wheels have high efficiency at part loads / variable flows and can operate at very low heads, < . Combined with direct drive Axial Flux Permanent Magnet Alternators and power electronics they offer a viable alternative for low head hydroelectric power generation.

Notes

Dotted notation. A dot above the quantity indicates that it is a rate. In other how much each second or how much per second. In this article q is a volume of water and

\dot q

is a volume of water per second. q, as in quantity of water, is used to avoid confusion with v for velocity.

References

Bibliography

* Soto Gary, ''Water Wheel''. vol. 163. No. 4. (Jan., 1994), p. 197 * al-Hassani, S.T.S., Woodcock, E. and Saoud, R. (2006) ''1001 inventions : Muslim heritage in our world'', Manchester : Foundation for Science Technology and Civilisation, * Allan. April 18, 2008. Undershot Water Wheel. Retrieved from http://www.builditsolar.com/Projects/Hydro/UnderShot/WaterWheel.htm * *Glick, T.F. (1970) ''Irrigation and society in medieval Valencia'', Cambridge, MA: Belknap Press of Harvard University Press, * *Hill, D.R. (1991) "Mechanical Engineering in the Medieval Near East", ''Scientific American'', 264 (5:May), pp. 100–105 * *Lewis, M.J.T. (1997) ''Millstone and Hammer: the origins of water power'', University of Hull Press, *Morton, W.S. and Lewis, C.M. (2005) ''China: Its History and Culture'', 4th Ed., New York : McGraw-Hill, * *Needham, J. (1965) ''Science and Civilization in China – Vol. 4: Physics and physical technology – Part 2: Mechanical engineering'', Cambridge University Press, *Nuernbergk, D.M. (2005) ''Wasserräder mit Kropfgerinne: Berechnungsgrundlagen und neue Erkenntnisse'', Detmold : Schäfer, *Nuernbergk, D.M. (2007) ''Wasserräder mit Freihang: Entwurfs- und Berechnungsgrundlagen'', Detmold : Schäfer, *Pacey, A. (1991) ''Technology in World Civilization: A Thousand-year History'', 1st MIT Press ed., Cambridge, Massachusetts : MIT, * * * *Reynolds, T.S. (1983) ''Stronger Than a Hundred Men: A History of the Vertical Water Wheel'', Johns Hopkins studies in the history of technology: New Series 7, Baltimore: Johns Hopkins University Press, * *Shannon, R. 1997. Water Wheel Engineering. Retrieved from http://permaculturewest.org.au/ipc6/ch08/shannon/index.html. * *Syson, l. (1965) ''British Water-mills'', London : Batsford, 176 p. * * * *

External links

Glossary of water wheel terms

WaterHistory.org Several articles concerning water wheels

painting with explanatory text, at

British Library The British Library is the national library of the United Kingdom and is one of the largest libraries in the world. It is estimated to contain between 170 and 200 million items from many countries. As a legal deposit library, the British ...

website.
Computer simulation of an overshot water wheel

Guide to the Water Wheel Construction: A Thesis Presented to N.C. College of Agri. and Mech. Arts by L. T. Yarbrough 1893 June

Foundry Patterns for 18 different Welsh waterwheel shrouds- 2015
{{Authority control

Wheel A wheel is a circular component that is intended to rotate on an axle Bearing (mechanical), bearing. The wheel is one of the key components of the wheel and axle which is one of the Simple machine, six simple machines. Wheels, in conjunction wi ...

Articles containing video clips Ancient inventions Egyptian inventions Iranian inventions es:Hidráulica#La rueda hidráulica