Water wheel

History

As in all machinery, rotary motion is more efficient in water-raising devices than oscillating motion. In terms of power source, water wheels can be turned by either human respectively animal force or by the water current itself. water wheels 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 water wheels 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.

Ancient Near East

The water wheel first appeared in the ancient Near East, specifically ancient Egypt, in the 4th century BC. Elsewhere in the Near East, there is archaeological evidence indicating possible water wheel usage in West Asia during the 4th century BC, but there is a lack of literary evidence for water wheel usage in Mesopotamia prior to the 3rd century BC. The water wheel was used in the Near East by the 3rd century BC for use in moving millstones and small-scale grain grinding. Terry S. Reynolds suggests that the first water wheels were norias and, by the 2nd century BC, evolved into the vertical watermill in Syria and Asia Minor, from where it spread to Greece and the Roman Empire. Water wheels were used in the Near East during the Hellenistic period between the 3rd and 1st centuries BC, and the sāqiya spread rapidly across the Near East during this period.

Water-lifting in Egypt

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

Paddle-driven water-lifting wheels had appeared in ancient Egypt by the 4th century BC. The Egyptians are credited with inventing the water wheel with attached pots, a water wheel with water compartments and a bucket chain, which ran over a pulley with buckets attached to it. The invention of the compartmentalized water wheel occurred in ancient Egypt around the 4th century BC, in a rural context, away from the metropolis of Hellenistic Alexandria, and then spread to other parts of North Africa.

According to John Peter Oleson, both the compartmented wheel and the hydraulic noria appeared in Egypt by the 4th century BC, with the Sakia being invented there a century later. This is supported by archeological finds at Faiyum, where the oldest archeological evidence of a water-wheel has been found, in the form of a Sakia dating back to the 3rd century BC. A papyrus dating to the 2nd century BC also found in Faiyum mentions a water wheel used for irrigation, a 2nd-century BC fresco found at Alexandria depicts a compartmented Sakia, and the writings of Callixenus of Rhodes mention the use of a Sakia in Ptolemaic Egypt during the reign of Ptolemy IV in the late 3rd century BC.

In Ptolemaic Egypt, water wheels were used between the 3rd and 1st centuries BC. The earliest literary reference to a water-driven, compartmented wheel appears in a medieval Arabic translation of Pneumatica (chap. 61) by Philo of Byzantium (c. 280 – c. 220 BC), describing its use in Egyptian irrigation. In his Parasceuastica (91.43−44), Philo advises the use of such wheels for submerging siege mines as a defensive measure against enemy sapping. Unlike other water-lifting devices and pumps of the period, 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 Egyptian context away from the Hellenistic metropolis of Alexandria. The origins of water power is attributed to the reality of rural Egyptian life along the Nile, rather than the intellectual capital of Alexandria which had no stream suitable for driving a paddle wheel. Compartmented wheels later appear to have been the means of choice for draining dry docks in Alexandria under the reign of Ptolemy IV (221−205 BC). Several Greek papyri from Ptolemaic Egypt dated to the 3rd and 2nd centuries BC mention the use of these wheels, but do not give further details.

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 sakia gear, which is here for the first time attested, too. The sakia gear system is already shown fully developed to the point that "modern Egyptian devices are virtually identical". It is believed that scientists or technicians from the Museum of Alexandria may have been involved in its development. An episode from the Alexandrian War in 48 BC tells of how Caesar's enemies employed geared water wheels to pour sea water from elevated places on the position of the trapped Romans.

Watermills

The invention of the watermill is a question open to scholarly discussion. According to historian Helaine Selin, there is evidence indicating that the watermill originated from the Persian Empire before 350 BC, likely in what are today Iran or Iraq, originally for the purpose of grinding grain. There were quarries known for their millstones in Iran and on the upper Tigris in what is today Turkey. The mills invented at this date had horizontal, propeller-like water wheels that drove the millstones directly. However, there is a lack of literary evidence of water wheels being used in Mesopotamia at the time.

Taking indirect evidence into account from the work of the Greek technician Apollonius of Perge, the British historian of technology M.J.T. Lewis hypothesizes the appearance of the vertical-axle watermill to the early 3rd century BC, and the horizontal-axle watermill to around 240 BC, assigning Byzantium (in Asia Minor) and Alexandria (in Ptolemaic Egypt) as the places of invention. However, Örjan Wikander notes the hypothesis is open to scholarly discussion. A watermill is reported by the Greek geographer Strabon (c. 64 BC – c. AD 24) to have existed sometime before 71 BC in the palace of the Pontian king Mithradates VI Eupator, but its exact construction cannot be gleaned from the text (XII, 3, 30 C 556).

China

According to Joseph Needham and other historians, the text known as the Xin Lun written by Huan Tan about 20 AD (during the usurpation of Wang Mang) infers that water wheels had been used for pounding machinery in grain mills. The Xin Lun states that the legendary mythological king known as Fu Xi was the one responsible for the pestle and mortar, which evolved into the tilt-hammer and then trip hammer device (see trip hammer). 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 China (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.

In the year 31 AD, the engineer and Prefect of Nanyang, Du Shi (d. 38), applied a complex use of the water wheel and machinery to power the bellows of the blast furnace to create cast iron. Du Shi is mentioned briefly in the Book of Later Han (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.

According to the Book of Jin, Zhang Heng (78-139) invented a water-powered armillary sphere which could "turn around by water leakage" around 130. Later generations speculated that this meant a water wheel.

According to the Records of the Three Kingdoms, the mechanical engineer Ma Jun (c. 200–265) from Cao Wei used a water wheel to power and operate a large mechanical puppet theater for Emperor Ming of Wei (r. 226–239). The device was carved using large wood, wheel shaped, and operated parallel to the ground to lift water in order to drive an assortment of puppets as well as mills with pestle. The Prefect Han Ji was made Superintendent of Metallurgical Production sometime before 238. He "adapted the furnace bellows to the use of ever-flowing water, and an efficiency three times greater than before was attained." Twenty years later, a new design was introduced by a man named Du Yu. A record dated to 263 or later mentions a device known as shui dui that made use of water wheels:

Beside the river, a shui dui is made, and water wheels are set behind it. A crosspiece is installed to run through the wheels. The two ends of the crosspiece are linked alternately to a long wood of about two chi and directly impact the rear wood of the shui dui. When the water is lifted to impact the wheel, the wheel will rotate, which drives the alternate wood to impact the rear wood of the shui dui to hull grain, using no manpower. The device is thus called shui dui.

In the beginning of the Yuanjia era (424-429), an artificial lake was created for water powered blowing bellows used in smelting and casting works. However it was discovered that the earthworks of the lake leaked and were insufficient for their intended purpose. They were destroyed and replaced by man-powered "treadmill bellows".

Roman Empire

A poem by Antipater of Thessalonica praised the water wheel for freeing women from the exhausting labor of milling and grinding.

Around 300 AD, the noria was introduced when the wooden compartments were replaced with inexpensive ceramic pots that were tied to the outside of an open-framed wheel.

Watermilling

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 water wheel into one effective mechanical system for harnessing water power. Vitruvius' water wheel 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).

About the same time, the overshot wheel appears for the first time in a poem by Antipater of Thessalonica, which praises it as a labour-saving device (IX, 418.4–6). The motif is also taken up by Lucretius (ca. 99–55 BC) who likens the rotation of the water wheel to the motion of the stars on the firmament (V 516). The third horizontal-axled type, the breastshot water wheel, 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 water wheel. 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, 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 turbines, the earliest known to date.

Navigation

Apart from its use in milling and water-raising, ancient engineers applied the paddled water wheel for automatons and in navigation. Vitruvius (X 9.5–7) describes multi-geared paddle wheels working as a ship odometer, 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 (chapter XVII), where the anonymous Roman author describes an ox-driven paddle-wheel warship.

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 in Syria 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 20 metres (66 ft) 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 Moorish system during al-Andalus is otherwise virtually unchanged. Some medieval Islamic compartmented water wheels could lift water as high as 30 metres (100 ft). Muhammad ibn Zakariya al-Razi's Kitab al-Hawi in the 10th century described a noria in Iraq that could lift as much as 153,000 litres per hour (34,000 imp gal/h), or 2,550 litres per minute (560 imp gal/min). This is comparable to the output of modern norias in East Asia, which can lift up to 288,000 litres per hour (63,000 imp gal/h), or 4,800 litres per minute (1,100 imp gal/min).

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 gristmills, hullers, sawmills, shipmills, stamp mills, steel mills, sugar mills, and tide mills. By the 11th century, every province throughout the Islamic world had these industrial watermills in operation, from al-Andalus and North Africa to West Asia and Central Asia. Muslim engineers also used crankshafts and water turbines, gears in watermills and water-raising machines, and dams 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 complexes built in al-Andalus 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 piers of bridges 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 ships 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 tons of flour from grain every day for the granary in Baghdad. 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 (fl. 1038–1075) of Al-Andalus; he pioneered the use of the flywheel in the saqiya (chain pump) and noria. The engineers Al-Jazari 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 clocks and automata.

Indian subcontinent

The early history of the watermill in the Indian subcontinent 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 suggested that the machine was a noria. 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 [the Brahmans] 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, predating, according to Pacey, its use in the later Roman Empire or China, though earlier 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 machine. The construction of water works and aspects of water technology in India is described in Arabic and Persian 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.

Ismail al-Jazari's Book of Knowledge of Ingenious Mechanical Devices (1206) uses the term "Sindhi wheel" to describe a sāqiya. This indicates it may have originated in the northwestern Indian subcontinent (modern Pakistan). During the Delhi Sultanate (1206–1526), geared water-raising wheels were introduced from the Islamic world to India.

Medieval Europe

Early medieval Europe

Ancient water-wheel technology continued unabated in the early medieval period where the appearance of new documentary genres such as legal codes, monastic charters, but also hagiography was accompanied with a sharp increase in references to watermills and wheels.

The earliest vertical-wheel in a tide mill is from 6th-century Killoteran near Waterford, Ireland, 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.

Cistercian monasteries, 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, a Cistercian monastery in the Aragon region of Spain. Grist mills (for grain) 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".

Late medieval Europe

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, up from less than a hundred in the previous century.

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. 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.

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. water wheels 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, put Europe on a hydraulically focused path, for instance water supply and irrigation technology was combined to modify supply power of the wheel.

The water mill was used for grinding grain, producing flour for bread, malt for beer, or coarse meal for porridge.

Early modern Western world

Early modern 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 [impulse]". 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". 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. 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 head was exactly equivalent to the velocity a drop of water acquired in falling freely from the same height.

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's water frame was powered by a water wheel.

North America

Water wheels were used to power sawmills, grist mills and for other purposes during development of the United States. The 40 feet (12 m) 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.

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

Australia

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 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, 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.

Compact water wheels, known as Dethridge wheels, 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.

Modern developments

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 20 m³ (710 cu ft) waterflow with a head of 1 to 3.5 m (3 to 11 ft). 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 wheel can be more efficient (about 60%) than all but the most advanced and well-constructed turbines. In some situations an overshot wheel is preferable to a turbine.

The development of the hydraulic turbine 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 – depends on how fast the water is moving when it enters the wheel
• Potential energy – 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 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 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.

Quantities and units

• ${\displaystyle \eta =}$ efficiency
• ${\displaystyle \rho =}$ density of water (1000 kg/m³)
• ${\displaystyle A=}$ cross sectional area of the channel (m²)
• ${\displaystyle D=}$ diameter of wheel (m)
• ${\displaystyle P=}$ power (W)
• ${\displaystyle d=}$ distance (m)
• ${\displaystyle g=}$ strength of gravity (9.81 m/s² = 9.81 N/kg)
• ${\displaystyle h=}$ head (m)
• ${\displaystyle h_p=}$ pressure head, the difference in water levels (m)
• ${\displaystyle h_v=}$ velocity head (m)
• ${\displaystyle k=}$ velocity correction factor. 0.9 for smooth channels.
• ${\displaystyle v=}$ velocity (m/s)
• ${\displaystyle \dot{q}=}$ volume flow rate (m³/s)
• ${\displaystyle t=}$ time (s)

^{dotted notation}

Measurements

The pressure head ${\displaystyle h_p}$ is the difference in height between the head race and tail race water surfaces. The velocity head ${\displaystyle h_v}$ 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) ${\displaystyle v}$ 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 volume flow rate. 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 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%).

These type of water wheels have high efficiency at part loads / variable flows and can operate at very low heads, < 1 m (3 ft 3 in). Combined with direct drive Axial Flux Permanent Magnet Alternators and power electronics they offer a viable alternative for low head hydroelectric power generation.

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