Water wheel in the context of Dam

In physics, the Coriolis force is a pseudo force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise (or counterclockwise) rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology.

Newton's laws of motion describe the motion of an object in an inertial (non-accelerating) frame of reference. When Newton's laws are transformed to a rotating frame of reference, the Coriolis and centrifugal accelerations appear. When applied to objects with masses, the respective forces are proportional to their masses. The magnitude of the Coriolis force is proportional to the rotation rate, and the magnitude of the centrifugal force is proportional to the square of the rotation rate. The Coriolis force acts in a direction perpendicular to two quantities: the angular velocity of the rotating frame relative to the inertial frame and the velocity of the body relative to the rotating frame, and its magnitude is proportional to the object's speed in the rotating frame (more precisely, to the component of its velocity that is perpendicular to the axis of rotation). The centrifugal force acts outwards in the radial direction and is proportional to the distance of the body from the axis of the rotating frame. These additional forces are termed inertial forces, fictitious forces, or pseudo forces. By introducing these fictitious forces to a rotating frame of reference, Newton's laws of motion can be applied to the rotating system as though it were an inertial system; these forces are correction factors that are not required in a non-rotating system.

A watermill or water mill is a mill that uses hydropower. It is a structure that uses a water wheel or water turbine to drive a mechanical process such as milling (grinding), rolling, or hammering. Such processes are needed in the production of many material goods, including flour, lumber, paper, textiles, and many metal products. These watermills may comprise gristmills, sawmills, paper mills, textile mills, hammermills, trip hammering mills, rolling mills, and wire drawing mills.

One major way to classify watermills is by wheel orientation (vertical or horizontal), one powered by a vertical waterwheel through a gear mechanism, and the other equipped with a horizontal waterwheel without such a mechanism. The former type can be further subdivided, depending on where the water hits the wheel paddles, into undershot, overshot, breastshot and pitchback (backshot or reverse shot) waterwheel mills. Another way to classify water mills is by an essential trait about their location: tide mills use the movement of the tide; ship mills are water mills onboard (and constituting) a ship.

This list of ancient watermills presents an overview of water-powered grain-mills and industrial mills in classical antiquity, including the Hellenistic period through the Roman period up until circa 500 AD.

The water wheel and watermill are the earliest instances of machines harnessing natural forces to replace human muscular labour (apart from the sail). As such, it holds a special place in the history of technology and also in economic studies where it is associated with growth.

A line shaft is a power-driven rotating shaft for power transmission that was used extensively from the Industrial Revolution until the early 20th century. Prior to the widespread use of electric motors small enough to be connected directly to each piece of machinery, line shafting was used to distribute power from a large central power source to machinery throughout a workshop or an industrial complex. The central power source could be a water wheel, turbine, windmill, animal power or a steam engine. Power was distributed from the shaft to the machinery by a system of belts, pulleys and gears known as millwork.

A trip hammer, also known as a tilt hammer or helve hammer, is a massive powered hammer. Traditional uses of trip hammers include pounding, decorticating and polishing of grain in agriculture. In mining, trip hammers were used for crushing metal ores into small pieces, although a stamp mill was more usual for this. In finery forges they were used for drawing out blooms made from wrought iron into more workable bar iron. They were also used for fabricating various articles of wrought iron, latten (an early form of brass), steel and other metals.

One or more trip hammers were set up in a forge, also known variously as a hammer mill, hammer forge or hammer works. The hammers were usually raised by a cam and then released to fall under the force of gravity. Historically, trip hammers were often powered hydraulically by a water wheel.

The Barbegal aqueduct and mills was a Roman watermill complex in the commune of Fontvieille, Bouches-du-Rhône, near the town of Arles, in southern France. The complex has been referred to as "the greatest known concentration of mechanical power in the ancient world" and the 16 overshot wheels are considered to be the largest ancient mill complex.

Another similar mill complex existed on the Janiculum in Rome, and there are suggestions that further such complexes existed at other major Roman sites, such as Amida (Mesopotamia).

A mill race, millrace or millrun, mill lade (Scotland) or mill leat (Southwest England) is the current of water that turns a water wheel, or the channel (sluice) conducting water to or from a water wheel. Compared with the broad waters of a mill pond, the narrow current is swift and powerful. The race leading to the water wheel on a wide stream or mill pond is called the head race (or headrace), and the race leading away from the wheel is called the tail race (or tailrace).

A mill race has many geographically specific names, such as leat, lade, flume, goit, penstock. These words all have more precise definitions and meanings will differ elsewhere. The original undershot waterwheel, described by Vitruvius, was a 'run of the river wheel' placed so a fast flowing stream would press against and turn the bottom of a bucketed wheel. In the first meaning of the term, the millrace was the stream; in the sense of the word, there was no separate channel, so no race. The example of Mill Lade in Godmanchester refers to a wide channel leading to moorings where laden vessels unload, similar waterways known by the similar name of Lode exist in neighbouring districts.

A treadwheel, or treadmill, is a form of engine typically powered by humans. It may resemble a water wheel in appearance, and can be worked either by a human treading paddles set into its circumference (treadmill), or by a human or animal standing inside it (treadwheel). These devices are no longer used for power or punishment, and the term "treadmill" has come to mean an exercise machine for running, walking or other exercises in place.

A line shaft or millworks is a power-driven rotating shaft for power transmission within factories and industrial complexes. They were used extensively from the Industrial Revolution until the early 20th century. Prior to the widespread use of electric motors small enough to be connected directly to each piece of machinery, line shafting was used to distribute power from a large central power source to machinery transmitted through branching belts or gear drives. The central power source could be a water wheel, turbine, windmill, animal power, or a steam engine. Power was distributed from the shaft to the machinery by a system of belts, pulleys and gears known as millworks.

Micro hydro is a type of hydroelectric power that typically produces from 5 kW to 100 kW of electricity using the natural flow of water. Installations below 5 kW are called pico hydro. These installations can provide power to an isolated home or small community, or are sometimes connected to electric power networks, particularly where net metering is offered.There are many of these installations around the world, particularly in developing nations as they can provide an economical source of energy without the purchase of fuel. Micro hydro systems complement solar PV power systems because in many areas water flow, and thus available hydro power, is highest in the winter when solar energy is at a minimum. Micro hydro is frequently accomplished with a pelton wheel for high head, low flow water supply. The installation is often just a small dammed pool, at the top of a waterfall, with several hundred feet of pipe leading to a small generator housing. In low head sites, generally water wheels and Archimedes' screws are used.

A scoop wheel or scoopwheel is a pump, usually used for land drainage.

A scoop wheel pump is similar in construction to a water wheel, but works in the opposite manner: a waterwheel is water-powered and used to drive machinery, a scoop wheel is engine-driven and is used to lift water from one level to another. Principally used for land drainage, early scoop wheels were wind-driven but later steam-powered beam engines were used. It can be regarded as a form of pump.