For water wheels used to drive boats, see paddle wheel. For wheels used solely to lift water see noria. For factories or industries driven by water wheels see watermill.
A water wheel is a hydropower system; a machine for extracting power from the flow of water. Water wheels and hydropower was widely used in the Middle Ages, powering most industry in Europe, along with the windmill. The most common use of the water wheel was to mill flour in gristmills, but other uses included foundry work and machining, and pounding linen for use in paper.
A water wheel consists of a large wooden or metal wheel, with a number of blades or buckets arranged on the outside rim forming the driving surface. Most commonly, the wheel is mounted vertically on a horizontal axle, but the tub or Norse wheel is mounted horizontally on a vertical shaft. Vertical wheels can transmit power either through the axle or via a ring gear and typically drive belts or gears; horizontal wheels usually directly drive their load. A channel created for the water to follow after leaving the wheel is commonly referred to as a "tailrace."

History of Water Wheel Technology
The first use of the water wheel may possibly have occurred in 4th century BC India. According to Terry S. Reynolds, "Joseph Needham noted in 1965 that certain ancient Indian texts from around 350 BC mentioned a cakkavattaka (turning wheel) which commentaries explained as arahatta-ghatĩ-yanta (machine with wheel-pots attached)", on which basis Needham "suggested that the machine in question was a noria and that it was the first water powered prime mover." However Reynolds also writes that "the term used in Indian texts is ambiguous and does not clearly indicate a water-powered device. In fact, as Thorkild Schiøler has noted, it is far 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."

India
The technology of the water wheel had long been known, but it was not put into widespread use until the Middle Ages when an acute shortage of labor made machines such as the water wheel cost effective. However, the water wheels in ancient Rome and ancient China found many practical uses in powering mills for pounding grain and other substances. The Romans used both fixed and floating water wheels and introduced water power to other countries of the Roman Empire. The Romans were known to use waterwheels extensively in mining projects, with enormous Roman-era waterwheels found in places like modern-day Spain. In the 1st century BC, the Greek epigrammatist Antipater of Thessalonica was the first to make a reference to the waterwheel. He praised it for its use in grinding grain and the reduction of human labor:
Cease from grinding, oh you toilers; women slumber still, Even if the crowing rooster calls the morning star. For Demeter has appointed nymphs to turn your mill, And upon the waterwheel alighting here they are. See how quick they twirl the axle whose revolving rays spin heavy rollers quarried overseas. So again we savor the delights of ancient days, Taught to eat the fruits of Mother Earth in ease.

Ancient China
Muslim engineers during the medieval Islamic period employed water wheels as early as the 7th century, excavation of a canal in the Basra region discovered remains of a water wheel dating from this period. Hama in Syria still preserves one of its large wheels, on the river Orontes, although they are no longer in use. The largest had a diameter of about 20 metres 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.
By the 13th century, what we might call water raising machine technology lifted off with the works of al-Jazari and Taqi al-Din. They both carried out a number of experiments, building fantastic machines, which led to the invention of automated machinery and this has made an enormous impact on civilisation today.

Islamic period
Cistercian monasteries, in particular, made extensive use of water wheels to power watermills of many kinds. An early example of a very large waterwheel 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 fulfill many other labor-intensive tasks. The water wheel remained competitive with the steam engine well into the Industrial Revolution.
The main difficulty of water wheels was their inseparability from water. This meant that mills often needed to be located far from population centers and away from natural resources. Water mills were still in commercial use well into the twentieth century, however.
Overshot & pitchback waterwheels are suitable where there is a small stream with a height difference of more than 2 meters, often in association with a small reservoir. Breastshot and undershot wheels can be used on rivers or high volume flows with large reservoirs.
The most powerful waterwheel built in the United Kingdom was the 100 hp Quarry Bank Mill Waterwheel 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.
Modern Hydro-electric dams can be viewed as the descendants of the water wheel as they too take advantage of the movement of water downhill.

Medieval Europe and Modern

Types
A vertically-mounted water wheel that is rotated by water striking paddles or blades at the bottom of the wheel is said to be undershot. This is generally the least efficient, oldest type of wheel (with the exception of the poncelet wheel). It has the advantage of being cheaper and simpler to build, but is less powerful and can only be used where the flow rate is sufficient to provide torque.
Undershot wheels gain no advantage from head. They are most suited to shallow streams in flat country.
Undershot wheels are also well suited to installation on floating platforms. The earliest were probably constructed by the Roman general Belisarius during the siege of Rome in 537. Later they were sometimes mounted immediately downstream from bridges where the flow restriction of arched bridge piers increased the speed of the current.

Undershot wheel
A vertically-mounted water wheel that is rotated by falling water striking buckets near the center of the wheel's edge, or just above it, is said to be breastshot. Breastshot wheels are the most common type in the United States of America and are said to have powered the American industrial revolution.
Breastshot wheels are less efficient than overshot wheels (see below), more efficient than undershot wheels, and are not backshot (see below). The individual blades of a breastshot wheel are actually buckets, as are those of most overshot wheels, and not simple paddles like those of most undershot wheels (the Poncelet design being a notable exception). A breastshot wheel requires a good trash rake and typically has a masonry "apron" closely conforming to the wheel face, which helps contain the water in the buckets as they progress downwards. Breastshot wheels are preferred for steady, high-volume flows such as are found on the fall line of the North American East Coast.

Breastshot wheel
A vertically-mounted water wheel that is rotated by falling water striking paddles, blades or buckets near the top of the wheel is said to be overshot. In true overshot wheels the water passes over the top of the wheel, but the term is sometimes applied to backshot or pitchback wheels where the water goes down behind the waterwheel.
A typical overshot wheel has the water channeled to the wheel at the top and slightly to one side in the direction of rotation. 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 can use all of the water flow for power (unless there is a leak) and does not require rapid flow.
Unlike undershot wheels, overshot wheels gain a double advantage from gravity. Not only is the force of the flowing water partially transferred to the wheel, the weight of the water descending in the wheel's buckets also imparts additional energy. The mechanical power derived from an overshot wheel is determined by the wheel's physical size and the available head, so they are ideally suited to hilly or mountainous country.
Overshot wheels demand exact engineering and significant head, which usually means significant investment in constructing a dam, millpond and waterways. Sometimes the final approach of the water to the wheel is along a lengthy flume or penstock.

Overshot wheel
A backshot wheel (also called pitchback) is a variety of overshot wheel where the water is introduced just behind the summit of the wheel. It combines the advantages from breastshot and overshot systems, since the full amount of the potential energy released by the falling water is harnessed as the water descends the back of the wheel.
A backshot wheel continues to function until the water in the wheel pit rises well above the height of the axle, when any other overshot wheel will be stopped or even destroyed. This makes the technique particularly suitable for streams that experience extreme seasonal variations in flow, and reduces the need for complex sluice and tail race configurations. A backshot wheel may also gain power from the water's current past the bottom of the wheel, and not just the weight of the water falling in the wheel's buckets.

Backshot wheel
Although traditionally water wheels have been made mostly from wood, the use of iron or steel in overshot (and pitchback) wheels allows faster rotation (possibly reducing the need for gearing) without extreme reductions in available torque. A wooden wheel with a wooden axle that can easily turn low-speed, high-torque loads such as a run of millstones cannot necessarily sustain high speeds such as are needed for hydroelectric power generation.
Overshot (and particularly backshot) wheels are the most efficient type; a backshot steel wheel can be more efficient than all but the most advanced and well-constructed turbines. Nevertheless, in some situations an overshot wheel is vastly preferable to any turbine.

See also