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61-480: A paddle wheel is a form of waterwheel or impeller in which a number of paddles are set around the periphery of the wheel. It has several uses, of which some are: The paddle wheel is an ancient invention but is still used today in a wide range of industrial and agriculture applications. Paddle wheels would enable ships to travel without needing wind or oars. They were made obsolete by propellers , which had greater propulsion with lower weight and fuel usage. This

122-402: A deviation which is dominated by the effects of surface tension . This calculation uses Earth's mean radius at sea level, however a liquid will be slightly flatter at the poles . Over large distances or planetary scale, the surface of an undisturbed liquid tends to conform to equigeopotential surfaces; for example, mean sea level follows approximately the geoid . If the free surface of

183-465: A free surface if unconfined from above. Under mechanical equilibrium this free surface must be perpendicular to the forces acting on the liquid; if not there would be a force along the surface, and the liquid would flow in that direction. Thus, on the surface of the Earth, all free surfaces of liquids are horizontal unless disturbed (except near solids dipping into them, where surface tension distorts

244-428: A large globule of oil placed below the surface of a mixture of water and alcohol having the same density so the oil has neutral buoyancy . Flatness refers to the shape of a liquid 's free surface. On Earth, the flatness of a liquid is a function of the curvature of the planet, and from trigonometry , can be found to deviate from true flatness by approximately 19.6 nanometers over an area of 1 square meter ,

305-399: 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 or penstock , which can be lengthy. 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

366-413: A liquid is disturbed, waves are produced on the surface. These waves are not elastic waves due to any elastic force ; they are gravity waves caused by the force of gravity tending to bring the surface of the disturbed liquid back to its horizontal level. Momentum causes the wave to overshoot , thus oscillating and spreading the disturbance to the neighboring portions of the surface. The velocity of

427-446: A mill pond, which is formed when a flowing stream is dammed . 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 . Waterwheels were used for various purposes from things such as agriculture to metallurgy in ancient civilizations spanning

488-544: 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 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

549-449: A reversible water wheel was by Georgius Agricola and dates to 1556. As in all machinery, rotary motion is more efficient in water-raising devices than oscillating motion. 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

610-410: 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. Free surface In physics , a free surface is the surface of a fluid that is subject to zero parallel shear stress , such as

671-414: 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

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732-484: A water wheel. The mechanical engineer Ma Jun (c. 200–265) from Cao Wei once used a water wheel to power and operate a large mechanical puppet theater for the Emperor Ming of Wei ( r. 226–239). The technological breakthrough occurred in the technologically developed Hellenistic period between the 3rd and 1st century BC. A poem by Antipater of Thessalonica praised the water wheel for freeing women from

793-407: Is a simple system usually without gearing so that the vertical axle of the water wheel becomes the drive spindle of the mill. 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 wheels because

854-597: 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 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 was finally introduced when the wooden compartments were replaced with inexpensive ceramic pots that were tied to

915-507: Is needed. Larger heads store more gravitational potential energy 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 2 metres (6.5 ft), often in association with a small reservoir. Breastshot and undershot wheels can be used on rivers or high volume flows with large reservoirs. A horizontal wheel with

976-408: 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. 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

1037-461: Is the pressure, ρ {\displaystyle \rho } is the density of the fluid, r {\displaystyle r} is the radius of the cylinder, ω {\displaystyle \omega } is the angular frequency , and g {\displaystyle g} is the gravitational acceleration . Taking a surface of constant pressure ( d P = 0 ) {\displaystyle (dP=0)}

1098-414: Is the resultant of the force of gravity and the centrifugal force from the motion of each point in a circle. Since the main mirror in a telescope must be parabolic, this principle is used to create liquid-mirror telescopes . Consider a cylindrical container filled with liquid rotating in the z direction in cylindrical coordinates, the equations of motion are: where P {\displaystyle P}

1159-495: 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: Both kinetic (movement) and potential (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 ('screen' in British English) to prevent debris from jamming between

1220-481: The Ancient Near East 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

1281-640: The Hellenistic Greek world , Rome , China and India . Waterwheels saw continued use in the post-classical age , like in 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 . Water wheels began being displaced by

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1342-544: The copper mines at Rio Tinto in Spain , 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 , a Roman gold mine in south Wales 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 to about 90 AD, and since

1403-465: The interface between two homogeneous fluids . An example of two such homogeneous fluids would be a body of water (liquid) and the air in the Earth's atmosphere (gas mixture). Unlike liquids , gases cannot form a free surface on their own. Fluidized / liquified solids, including slurries , granular materials, and powders may form a free surface. A liquid in a gravitational field will form

1464-414: The mining 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

1525-469: 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

1586-442: 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. Apart from its use in milling and water-raising, ancient engineers applied the paddled waterwheel for automatons and in navigation. Vitruvius (X 9.5–7) describes multi-geared paddle wheels working as

1647-400: 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). About the same time, the overshot wheel appears for the first time in

1708-411: The descendants of the water wheel, as they too take advantage of the movement of water downhill. Water wheels come in two basic designs: The latter can be subdivided according to where the water hits the wheel into backshot (pitch-back ), overshot, breastshot, undershot, and stream-wheels. The term undershot can refer to any wheel where the water passes under the wheel but it usually implies that

1769-443: The energy in the flow of water striking the wheel as measured by English civil engineer John Smeaton 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 . They were sometimes mounted immediately downstream from bridges where

1830-416: The exhausting labor of milling and grinding. 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

1891-431: 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. 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

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1952-420: The gravitational forces. Capillary ripples are damped both by sub-surface viscosity and by surface rheology . If a liquid is contained in a cylindrical vessel and is rotating around a vertical axis coinciding with the axis of the cylinder, the free surface will assume a parabolic surface of revolution known as a paraboloid . The free surface at each point is at a right angle to the force acting at it, which

2013-420: The head. They are similar in operation and design to stream wheels. The term undershot is sometimes used with related but different meanings: This is the oldest type of vertical water 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

2074-422: The industrial revolution. 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

2135-623: 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 in the Isle of Man , only utilises a head of around 30 m (100 ft). The world's largest head turbines, Bieudron Hydroelectric Power Station in Switzerland , utilise about 1,869 m (6,132 ft). Overshot wheels require

2196-613: 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. By at least the 1st century AD, the 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 . In the text known as the Xin Lun written by Huan Tan about 20 AD (during

2257-422: The linear motion of the fluid into rotation of the wheel. Such a rotation can be used as a source of power, or as an indication of the speed of flow. In the rotary-to-linear direction, it is driven by a prime mover such as an electric motor or steam engine and used to pump a fluid or propel a vehicle such as a paddle-wheel steamer or a steamship . Waterwheel Some water wheels are fed by water from

2318-475: The metropolis of Alexandria. 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 Greek sakia gear system is already shown fully developed to the point that "modern Egyptian devices are virtually identical". It

2379-493: The outside of an open-framed wheel. The Romans used waterwheels extensively in mining projects, with enormous Roman-era waterwheels found in places like modern-day Spain . They were reverse overshot water-wheels designed for dewatering deep underground mines. Several such devices are described by Vitruvius , including the reverse overshot water-wheel and the Archimedean screw . Many were found during modern mining at

2440-475: The palace of the Pontian king Mithradates VI Eupator , 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

2501-418: 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

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2562-497: 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. Water wheels in China found practical uses such as this, as well as extraordinary use. The Chinese inventor Zhang Heng (78–139) was the first in history to apply motive power in rotating the astronomical instrument of an armillary sphere , by use of

2623-478: 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. 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 in Devon, UK. The head race

2684-419: The smaller, less expensive and more efficient turbine , developed by Benoît Fourneyron , beginning with his first model in 1827. Turbines are capable of handling high heads , or elevations , 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 dams can be viewed as

2745-447: The surface in a region called the meniscus ). In a free liquid that is not affected by outside forces such as a gravitational field, internal attractive forces only play a role (e.g. Van der Waals forces , hydrogen bonds ). Its free surface will assume the shape with the least surface area for its volume: a perfect sphere . Such behaviour can be expressed in terms of surface tension . It can be demonstrated experimentally by observing

2806-424: The surface waves varies as the square root of the wavelength if the liquid is deep; therefore long waves on the sea go faster than short ones. Very minute waves or ripples are not due to gravity but to capillary action , and have properties different from those of the longer ocean surface waves , because the surface is increased in area by the ripples and the capillary forces are in this case large compared with

2867-413: The total differential becomes Integrating, the equation for the free surface becomes where h c {\displaystyle h_{c}} is the distance of the free surface from the bottom of the container along the axis of rotation. If one integrates the volume of the paraboloid formed by the free surface and then solves for the original height, one can find the height of the fluid along

2928-457: 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 docks in Alexandria under the reign of Ptolemy IV (221−205 BC). Several Greek papyri of the 3rd to 2nd century BC mention the use of these wheels, but do not give further details. The non-existence of the device in

2989-444: The usurpation of Wang Mang ), it 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

3050-448: 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 , several installations from around 300 AD were found where vertical-axle waterwheels fitted with angled blades were installed at

3111-400: 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 . Undershot and stream wheel use large flows at little or no head. There is often an associated millpond , a reservoir for storing water and hence energy until it

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3172-416: 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 Zhuangzi in

3233-434: 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

3294-560: 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 ( c.  280  – c.  220 BC ). In his Parasceuastica (91.43−44), Philo advises

3355-624: 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 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

3416-406: 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

3477-449: 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. Taking indirect evidence into account from

3538-510: 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. A watermill is reported by the Greek geographer Strabon ( c.  64 BC  – c.  AD 24 ) to have existed sometime before 71 BC in

3599-589: 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

3660-425: 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

3721-402: Was demonstrated by an 1845 tug-of-war competition between HMS  Rattler and HMS  Alecto with the screw-driven Rattler pulling the paddle steamer Alecto backward at 2.5 knots (4.6 km/h). The paddle wheel is a device for converting between rotary motion of a shaft and linear motion of a fluid. In the linear-to-rotary direction, it is placed in a fluid stream to convert

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