Water wheel: Difference between revisions

[[File:KincirBrucker airWasserrad 01.webm|thumb|A traditional water wheel in [[PayakumbuhErlangen]], [[Indonesia]]Germany]]

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 [[blade]]s or [[bucket]]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 today. Uses included milling flour in [[gristmill]]s, grinding wood into pulp for [[papermaking]], hammering [[wrought iron]], machining, ore crushing and pounding fibre for use in the manufacture of [[cloth]].

Some water wheels are fed by water from a mill pond, which is formed when a flowing stream is [[Dam|dammeddam]]med. A channel for the water flowing to or from a water wheel is called a [[mill race]]. 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'''.<ref name="Ref-1">[http://dictionary.reference.com/browse/tailrace Dictionary definition of "tailrace"]</ref>

Waterwheels were used for various purposes from things such as [[History of agriculture|agriculture]] to [[History of ferrous metallurgy|metallurgy]] in ancient civilizations spanning the [[Hellenistic period|Hellenistic Greek world]], [[Ancient Rome|Rome]], [[History of China|China]] and [[History of India|India]]. Waterwheels saw continued use in the [[Post-classical history|post-classical age]], like thein [[Medieval Europe|Middle Ages of|medieval Europe]] and the [[Islamic Golden Age]], but also elsewhere. In the mid- to late 18th century [[John Smeaton]]'s scientific investigation of the water wheel led to significant increases in efficiency, supplying much -needed power for the [[Industrial Revolution]].<ref name="Robinson&Musson">

Water wheels come in two basic designs:<ref>{{Cite web|url=http://ffden-2.phys.uaf.edu/211_fall2010.web.dir/Brooks/types-of-water-wheels.html |title=Types of Water Wheels – The Physics of a Water Wheel|website=ffden-2.phys.uaf.edu |language=en|access-date=2017-07-10}}</ref>

The latter can be subdivided according to where the water hits the wheel into backshot (pitch-back<ref>[https://web.archive.org/web/20170815063910/https://en.oxforddictionaries.com/definition/pitch-back Article titlepitch-back] {{Bare URL inline|date=June 2022}}</ref>), overshot, breastshot, undershot, and stream-wheels.<ref name="Stream wheel term and specifics">[{{Cite web |url=http://www.energy.soton.ac.uk/hydro/waterwheels.html |title=Stream wheel term and specifics] |access-date=2009-04-07 |archive-date=2011-10-07 |archive-url=https://web.archive.org/web/20111007081641/http://www.energy.soton.ac.uk/hydro/waterwheels.html |url-status=dead }}</ref><ref>[https://www.merriam-webster.com/dictionary/undershot%20wheel Merriam Webster]</ref><ref>[http://www.powerinthelandscape.co.uk/water/water_wheels.html Power in the Landscape]</ref>

The term ''undershot'' can refer to any wheel where the water passes under the wheel<ref>[https://www.collinsdictionary.com/dictionary/english/undershot Collins English Dictionary]</ref> but it usually implies that the water entry is low on the wheel.

Commonly called a '''tub wheel''', '''Norse mill''' or '''Greek mill''',<ref>{{cite book|last1=Denny|first1=Mark |title=Ingenium: Five Machines That Changed the World|date=2007|publisher=Johns Hopkins University|isbn=9780801885860 |url=https://archive.org/details/ingeniumfivemach0000denn |url-access=registration|access-date=19 January 2018}}</ref><ref>{{cite web|last1=The Editors of Encyclopædia Britannica|title=Waterwheel|url=https://www.britannica.com/technology/waterwheel-engineering|website=Britannica.com |publisher=Encyclopædia Britannica, Inc.|access-date=19 January 2018}}</ref> 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.{{Citation needed|date=April 2017}}

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 [[John Smeaton]] in the 18th century.<ref>The History of Science and Technology by Bryan Bunch with Alexander Hellmans p.&nbsp;114</ref> More modern wheels have higher efficiencies.

* wheels where paddles are placed into the flow of a stream. See the stream above.<ref>{{cite web

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.<ref>{{Cite journal |lastlast1=Müller |firstfirst1=G. |last2=Wolter |first2=C. |date=2004 |title=The breastshot waterwheel: design and model tests |url=https://hmf.enseeiht.fr/travaux/CD0708/beiere/3/html/bi/3/fichiers/Muller_exp.pdf |journal=Proceedings of the Institution of Civil Engineers - Engineering Sustainability |language=en |volume=157 |issue=4 |pages=203–211 |doi=10.1680/ensu.2004.157.4.203 |issn=1478-4629 |via=Semantic Scholar}}</ref> 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.

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%,<ref>{{Cite web|date=2021-04-12|title=What type of water wheel is most efficient?|url=https://faq-ans.com/en/Q%26A/page=6b333be1485a8633ba94ae74c9b8bf70 |access-date=2021-11-23|website=faq-ans.com|language=en}}</ref> and does not require rapid flow.

As in all machinery, rotary motion is more efficient in water-raising devices than oscillating onemotion.<ref name="Oleson 2000, 229">{{harvnb|Oleson|2000|p=229}}</ref> 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.

The earliest waterwheel working like a lever was described by [[Zhuang Zhou|Zhuangzi]] in the late [[Warring States period]] (476-221 BC). It says that the waterwheel was invented by Zigong, a disciple of [[Confucius]] in the 5th century BC.<ref>{{Cite book|url=https://wwwbooks.google.cacom/books/edition/How_Water_Influences_Our_Lives/7teSDQAAQBAJ?hlid=en&gbpv=17teSDQAAQBAJ&dq=water+wheel+china+history&pg=PA139&printsec=frontcover|isbn=9789811019388|title=How Water Influences Our Lives|date=22 November 2016|publisher=Springer}}</ref> By at least the 1st century&nbsp;AD, the [[China|Chinese]] of the [[Eastern Han Dynasty]] were using water wheels to crush grain in mills and to power the piston-[[bellows]] in forging [[iron ore]] into [[cast iron]].<ref name=Hansen/>

The [[Ancient Greece|ancient Greeks]] invented the waterwheel independently and used it in nearly all of the forms and functions described above, including its application for watermilling.<ref name="Oleson 1984, 325ff.">{{harvnb|Oleson|1984|pp=325ff.}}; {{harvnb|Oleson|2000|pp=217–302}}{{page range too broad|date=January 2022}}; {{harvnb|Donners|Waelkens|Deckers|2002|pp=10−15}}{{page range too broad|date=January 2022}}; {{harvnb|Wikander|2000|pp=371−400}}{{page range too broad|date=January 2022}}</ref> The technological breakthrough occurred in the technologically developed [[Hellenistic period]] between the 3rd and 1st century BC.<ref>{{harvnb|Wikander|2000|p=395}}; {{harvnb|Oleson|2000|p=229}}{{blockquote|It is no surprise that all the water-lifting devices that depend on subdivided wheels or cylinders originate in the sophisticated, scientifically advanced Hellenistic period, ...}}</ref>

;===== Water-lifting =====

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]] (ca. 280−220{{Circa|280|220 BC}}).<ref>{{harvnb|Oleson|2000|p=233}}</ref> In his ''Parasceuastica'' (91.43−44), Philo advises the use of such wheels for submerging siege mines as a defensive measure against enemy sapping.<ref name="Oleson 2000, 234">{{harvnb|Oleson|2000|pp=234}}</ref> Compartmented wheels appear to have been the means of choice for draining [[dry dock]]s in [[Alexandria]] under the reign of [[Ptolemy IV]] (221−205 BC).<ref name="Oleson 2000, 234"/> Several Greek [[papyri]] of the 3rd to 2nd century BC mention the use of these wheels, but don'tdo not give further details.<ref name="Oleson 2000, 234"/> The non-existence of the device in the [[Ancient Near East]] before [[Wars of Alexander the Great|Alexander's conquest]] can be deduced from its pronounced absence from the otherwise rich oriental iconography on irrigation practices.<ref>{{harvnb|Oleson|2000|pp=235}}: {{blockquote|The sudden appearance of literary and archaological evidence for the compartmented wheel in the third century B.C. stand in marked contrast to the complete absence of earlier testimony, suggesting that the device was invented not long before.}}</ref>{{failed verification|reason=could not find mention of Alexander or conquests|date=January 2022}}<ref>An isolated passage in the Hebrew [[Deuteronomy]] (11.10−11) about Egypt as a country ''where you sowed your seed and watered it with your feet'' is interpreted as an metaphor referring to the digging of irrigation channels rather than treading a waterwheel ({{harvnb|Oleson|2000|pp=234}}).</ref><ref>As for a Mesopotamian connection: {{harvnb|Schioler|1973|p=165−167}}: {{blockquote|References to water-wheels in ancient [[Mesopotamia]], found in handbooks and popular accounts, are for the most part based on the false assumption that the [[Akkadian language|Akkadian]] equivalent of the logogram GIS.APIN was ''nartabu'' and denotes an instrument for watering ("instrument for making moist").}}{{blockquote|As a result of his investigations, Laessoe writes as follows on the question of the saqiya: "I consider it unlikely that any reference to the saqiya will appear in ancient Mesopotamian sources." In his opinion, we should turn our attention to Alexandria, "where it seems plausible to assume that the saqiya was invented."}}</ref><ref>{{citation|title=Water architecture in the lands of Syria: the water-wheels|author=Adriana de Miranda|publisher=L'Erma di Bretschneider|year=2007|isbn=978-8882654337|pages=48f}} concludes that the Akkadian passages "are counched in terms too general too allow any conclusion as to the excat structure" of the irrigation apparatus, and states that "the latest official [[Chicago Assyrian Dictionary]] reports meanings not related to types of irrigation system".</ref> 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.<ref name="Oleson 2000, 235">{{harvnb|Oleson|2000|pp=235}}</ref>

;===== Watermilling =====

Taking indirect evidence into account from the work of the Greek technician [[Apollonius of Perge]], 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]] and [[Alexandria]] as the assigned places of invention.<ref>{{harvnb|Wikander|2000|p=396f.}}; {{harvnb|Donners|Waelkens|Deckers|2002|p=11}}; {{harvnb|Wilson|2002|pp=7f.}}</ref> A watermill is reported by the Greek geographer [[Strabon]] (ca. {{Circa|64 BC–ADBC|AD 24}}) to have existed sometime before 71 BC in the palace of the [[Kingdom of Pontus|Pontian]] king [[Mithradates VI Eupator]], but its exact construction cannot be gleaned from the text (XII, 3, 30 C 556).<ref>{{harvnb|Wikander|1985|p=160}}; {{harvnb|Wikander|2000|p=396}}</ref>

;===== Navigation =====

[[Cistercian]] [[Monastery|monasteries]], in particular, made extensive use of water wheels to power watermills of many kinds.<ref name=Hansen>{{cite web |last1=Hansen |first1=Roger D. |title=Water Wheels |url=http://www.waterhistory.org/histories/waterwheels/waterwheels.pdf |website=waterhistory.org |archive-url=https://web.archive.org/web/20220414221333/http://www.waterhistory.org/histories/waterwheels/waterwheels.pdf |archive-date=14 April 2022 |date=2005 |url-status=live}}</ref> 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]], a Cistercian monastery in the [[Aragon]] region of [[Spain]]. 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]] well into the [[Industrial Revolution]]. 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]]. 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".<ref>Glick, p. 178</ref> 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]], the technology spread to the [[New World]] in [[Mexico]] and [[South America]] following [[Spanish Empire|Spanish expansion]]

The assembly convened by [[William of Normandy]], commonly referred to as the "[[Domesday]]" 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.,<ref name="Friedel31">Robert, Friedel, ''A Culture of Improvement''. MIT Press. Cambridge, Massachusetts. London, England. (2007). pp. 31–2b.</ref> up from less than a hundred in the previous century.<ref name=Hansen/>

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 [impulse]".<ref>[[Anthony Fitzherbert]], ''Surveying'' (London, 1539, reprinted in [Robert Vansitarrt, ed] ''Certain Ancient Tracts Concerning the Management of Landed Property'' Reprinted [London, 1767.] pg. 92.</ref> [[Leonardo da Vinci]] also discussed water power, noting "the blow [of the water] is not weight, but excites a power of weight, almost equal to its own power".<ref>Leonardo da Vinci, MS F, 44r, in ''Les manuscrits de Leonardo da Vinci'', ed Charles Ravaisson-Moilien (Paris, 1889), vol.4; cf, Codex Madrid, vol. 1, 69r [The Madrid Codices], trans. And transcribed by Ladislao Reti (New York, 1974), vol. 4.</ref> 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.<ref>Smeaton, "An Experimental Inquiry Concerning the Natural Powers of Water and Wind to Turn Mills, and Other Machines, depending on Circular Motion," Royal Society, ''Philosophical Transactions of the Royal Society of London'' 51 (1759); 124–125</ref> 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.<ref name="Torricelli, Evangelista 1919">Torricelli, Evangelista, ''Opere'', ed. Gino Loria and Giuseppe Vassura (Rome, 1919.)</ref> The waterwheel sparked questions of the laws of nature, specifically the [[laws of force]]. [[Evangelista Torricelli]]'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 [[Hydrostatic head|head]] was exactly equivalent to the velocity a drop of water acquired in falling freely from the same height.<ref name="Torricella, Evangelica 1919">Torricella, Evangelica, ''Opere'', ed. Gino Loria and Giuseppe Vassura (Rome, 1919.)</ref>

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]]'s water frame was powered by a water wheel.<ref>{{Cite web|url= http://www.history.alberta.ca/energyheritage/energy/hydro-power/hydro-power-from-early-modern-to-the-industrial-age.aspx#page-1 |archive-url = https://web.archive.org/web/20191115022315/http://www.history.alberta.ca/energyheritage/energy/hydro-power/hydro-power-from-early-modern-to-the-industrial-age.aspx#page-1 |archive-date = 2019-11-15|title = Hydro Power from the Early Modern to the Industrial Age: Ca. 1500–1850 - Electricity & Alternative Energy - Alberta's Energy Heritage}}</ref>

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 [the Brahmans] till then".<ref>{{harvnb|Wikander|2000|p=400}}: {{blockquote|This is also the period when water-mills started to spread outside the former Empire. According to [[Cedrenus]] (Historiarum compendium), a certain Metrodoros who went to India in c. A.D. 325 "constructed water-mills and baths, unknown among them [the Brahmans] till then".}}</ref> 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 [[History of India|ancient India]], predating, according to Pacey, its use in the later Roman Empire or China,<ref>Pacey, p. 10</ref> even though the first literary, archaeological and pictorial evidence of the water wheel appeared in the Hellenistic world.<ref name="Oleson 1984, 325ff.">{{harvnb|Oleson|1984|pp=325ff.}}; {{harvnb|Oleson|2000|pp=217–302}}{{page range too broad|date=January 2022}}; {{harvnb|Donners|Waelkens|Deckers|2002|pp=10−15}}{{page range too broad|date=January 2022}}; {{harvnb|Wikander|2000|pp=371−400}}{{page range too broad|date=January 2022}}</ref>

[[File:Hama-3 norias.jpg|thumb|left|upright|The [[noriasNorias of Hama]] on the [[Orontes River]]]]

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]] in [[Syria]] still preserves [[Norias of Hama|some of its large wheels]], on the river [[Orontes river|Orontes]], although they are no longer in use.<ref>al-Hassani ''et al.'', p. 115</ref> One of the largest had a diameter of about {{Convert|20|m||abbr=}} and its rim was divided into 120 compartments. Another wheel that is still in operation is found at [[Murcia]] in [[Spain]], La Nora, and although the original wheel has been replaced by a steel one, the [[Moors|Moorish]] system during [[al-Andalus]] is otherwise virtually unchanged. Some medieval Islamic compartmented water wheels could lift water as high as {{Convert|30|m||abbr=|sigfig=1}}.<ref>{{citation|first=Adam|last=Lucas |year=2006|title=Wind, Water, Work: Ancient and Medieval Milling Technology|publisher=[[Brill Publishers]]|isbn=978-90-04-14649-5|page=26}}</ref> [[Muhammad ibn Zakariya al-Razi]]'s ''Kitab al-Hawi'' in the 10th century described a [[noria]] in Iraq that could lift as much as {{Convert|153,000|l/h|impgal/h|abbr=}}, or {{Convert|2550|l/min|impgal/min|abbr=}}. This is comparable to the output of modern norias in [[East Asia]], which can lift up to {{Convert|288000|l/h|impgal/h|abbr=}}, or {{Convert|4800|l/min|impgal/min|abbr=}}.<ref>{{citation|title=A history of engineering in classical and medieval times|author=Donald Routledge Hill|publisher=Routledge |year=1996|isbn=978-0-415-15291-4|pages=145–6}}</ref>

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]]s of [[bridge]]s to take advantage of the increased flow. Another solution was the shipmill, a type of [[water mill]] powered by water wheels mounted on the sides of [[ship]]s [[Mooring (watercraft)|moored]] in midstream. This technique was employed along the [[Tigris]] and [[Euphrates]] rivers in 10th-century [[Iraq]], where large shipmills made of [[teak]] and [[iron]] could produce 10 [[ton]]s of [[Gristmill|flour from corn]] every day for the [[granary]] in [[Baghdad]].<ref name=Hill2>Hill; see also [http://home.swipnet.se/islam/articles/HistoryofSciences.htm Mechanical Engineering] {{Webarchive|url=https://web.archive.org/web/20001212015400/http://home.swipnet.se/islam/articles/HistoryofSciences.htm |date=2000-12-12 }})</ref> The [[flywheel]] mechanism, which is used to smooth out the delivery of power from a driving device to a driven machine, was invented by Ibn Bassal ([[floruit|fl.]] 1038–1075) of [[Al-Andalus]]; he pioneered the use of the flywheel in the [[Sakia|saqiya]] ([[chain pump]]) and noria.<ref>[[Ahmad Y Hassan]], [http://www.history-science-technology.com/Notes/Notes%204.htm Flywheel Effect for a ''Saqiya''].</ref> The engineers [[Al-Jazari]] in the 13th century and [[Taqi al-Din Muhammad ibn Ma'ruf|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]]s and [[Automaton|automata]].

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&nbsp;kW and 200&nbsp;kW of electricity from a {{Convert|20|m3||abbr=on}} waterflow with a head of {{Convert|1 to 3.5|m|ft|0|abbr=on}}.<ref name=aqualienne>{{cite web| url=http://www.h3eindustries.com/How-does-an-Aqualienne%C2%AE-work? | archive-url=https://web.archive.org/web/20170711163044/http://www.h3eindustries.com/How-does-an-Aqualienne%C2%AE-work breastshot|archive-date=2017-07-11 |title=Comment fonctionne une Aqualienne?| wheellanguage=fr}}</ref> It is designed to produce electricity at the sites of former watermills.

* [[PotentialKinetic energy]] – depends on thehow change in height offast the water between entryis tomoving andwhen exitit fromenters the wheel

The [[power (physics)|power]] 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-stone|quern]] of Rome made about one-half of a [[horsepower]], 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.<ref name=Gies>{{cite book|title=Cathedral, Forge, and Waterwheel: Technology and Invention in the Middle Ages|first1=Frances|last1=Gies |first2=Joseph|last2=Gies |date=1994|page=115|publisher=HarperCollins Publishers|isbn=0060165901 |url=https://publicism.info/history/invention/6.html}}</ref>

The pressure head <math>h_p</math> is the difference in height between the head race and tail race water surfaces. The velocity head <math>h_v</math> 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) <math>v</math> 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.<ref name="USFS">{{cite web|title=Float Method for Estimating Discharge|url=https://www.fs.fed.us/ARMdata/PDFfiles/floatmethod.doc |publisher=United States Forest Service|access-date=24 February 2017}}</ref>

*It is sometimes practicable to measure the volume flow rate by the bucket and stop watch method.<ref name="SoW">{{cite web|last1=Michaud|first1=Joy P.|last2=Wierenga|first2=Marlies |title=Estimating Discharge and Stream Flows|url=https://fortress.wa.gov/ecy/publications/documents/0510070.pdf |publisher=State of Washington|access-date=24 February 2017}}</ref>

| Power || <math>P=\eta \cdot \rho \cdot g \cdot h \cdot \dot q</math><ref>{{cite web|title=Calculation of Hydro Power|url=http://www.reuk.co.uk/wordpress/hydro/calculation-of-hydro-power/ |website=The Renewable Energy Website|access-date=25 February 2017}}</ref>

| Effective head || <math>h = h_p + h_v</math><ref name="Nagpurwala">{{cite web|last1=Nagpurwala|first1=Q.H. |title=Hydraulic Turbines|url=http://164.100.133.129:81/eCONTENT/Uploads/16-Hydraulic%20Turbines%20%5BCompatibility%20Mode%5D.pdfHydraulic |publisher=M.S. Ramaiah School of Advanced Studies|access-date=25 February 2017|page=44}}</ref>

| Velocity head ||<math>h_v = \frac{v^2}{2 \cdot g}</math><ref>{{cite web|title=Velocity Head|url=https://neutrium.net/fluid_flow/velocity-head/ |website=Neutrium|access-date=25 February 2017|date=September 27, 2012}}</ref><ref name="Nagpurwala"/>

| Optimal rotational speed || <math>\frac{21}{\sqrt{D}}</math> rpm<ref name="BHA01">{{cite web|title=Waterwheels|url=http://www.british-hydro.org/waterwheels.html |publisher=British Hydropower Association}}</ref>

* [[Hydroelectricity]]

* [[WatermillPelton wheel]]

* [[Water turbine]]

* [[Pelton wheelWatermill]]

== ReferencesExplanatory notes ==

* 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, {{ISBN|0-9552426-0-6}}

* Allan. April 18, 2008. Undershot Water Wheel. Retrieved from [http://www.builditsolar.com/Projects/Hydro/UnderShot/WaterWheel.htm Undershot Water Wheel]

*Shannon, R. 1997. Water{{cite Wheelweb| Engineeringurl=http://permaculturewest.org.au/ipc6/ch08/shannon/index.html Retrieved| fromtitle=Water Wheel Engineering| archive-url=https://web.archive.org/web/20170920211239/http://permaculturewest.org.au/ipc6/ch08/shannon/index.html | archive-date=2017-09-20 }}.

* [httphttps://www.angelfire.com/journal/millbuilder/terms.html Glossary of water wheel terms]

* [http://mw.concord.org/modeler1.3/mirror/mechanics/undershotwaterwheel.html Computer simulation of an undershot water wheel] {{Webarchive|url=https://web.archive.org/web/20090810165749/http://mw.concord.org/modeler1.3/mirror/mechanics/undershotwaterwheel.html |date=2009-08-10 }}

* [http://mw.concord.org/modeler1.3/mirror/mechanics/overshotwaterwheel.html Computer simulation of an overshot water wheel] {{Webarchive|url=https://web.archive.org/web/20090810165712/http://mw.concord.org/modeler1.3/mirror/mechanics/overshotwaterwheel.html |date=2009-08-10 }}

* [https://welshmills.org/wp-content/uploads/2015/08/Click-on-this-link-for-a-list-and-drawings-of-the-available-patterns..pdf Foundry Patterns for 18 different Welsh waterwheel shrouds- 2015]