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paradox$57723$ - translation to greek
![wake]],<br>
•5: post-critical separated flow, with a turbulent boundary layer.](https://commons.wikimedia.org/wiki/Special:FilePath/Drag coefficient on a sphere vs. Reynolds number - main trends.svg?width=200 "wake]],<br>
•5: post-critical separated flow, with a turbulent boundary layer.")
![Pressure distribution for the flow around a circular cylinder. The dashed blue line is the pressure distribution according to [[potential flow]] theory, resulting in d'Alembert's paradox. The solid blue line is the mean pressure distribution as found in experiments at high [[Reynolds number]]s. The pressure is the radial distance from the cylinder surface; a positive pressure (overpressure) is inside the cylinder, towards the centre, while a negative pressure (underpressure) is drawn outside the cylinder.](https://commons.wikimedia.org/wiki/Special:FilePath/Flow pressure with friction.svg?width=200 "Pressure distribution for the flow around a circular cylinder. The dashed blue line is the pressure distribution according to [[potential flow]] theory, resulting in d'Alembert's paradox. The solid blue line is the mean pressure distribution as found in experiments at high [[Reynolds number]]s. The pressure is the radial distance from the cylinder surface; a positive pressure (overpressure) is inside the cylinder, towards the centre, while a negative pressure (underpressure) is drawn outside the cylinder.")
![circular]] cylinder in a uniform onflow.](https://commons.wikimedia.org/wiki/Special:FilePath/Potential cylinder.svg?width=200 "circular]] cylinder in a uniform onflow.")
![isotherms]]. Most corals live within this boundary. Note the cooler waters caused by upwelling on the southwest coast of Africa and off the coast of Peru.](https://commons.wikimedia.org/wiki/Special:FilePath/20 Grad Isotherme.png?width=200 "isotherms]]. Most corals live within this boundary. Note the cooler waters caused by upwelling on the southwest coast of Africa and off the coast of Peru.")
![Deep-water [[cloud sponge]]](https://commons.wikimedia.org/wiki/Special:FilePath/Aphrocallistes vastus.jpg?width=200 "Deep-water [[cloud sponge]]")
![bay Islands]] are part of the mesoamerican coral reef system. Due to this, the authorities have made huge investments for its preservation.](https://commons.wikimedia.org/wiki/Special:FilePath/Arrecife coralino de Roatán.jpg?width=200 "bay Islands]] are part of the mesoamerican coral reef system. Due to this, the authorities have made huge investments for its preservation.")
![A major coral bleaching event took place on this part of the [[Great Barrier Reef]] in Australia](https://commons.wikimedia.org/wiki/Special:FilePath/Bleached coral (24577819729).jpg?width=200 "A major coral bleaching event took place on this part of the [[Great Barrier Reef]] in Australia")
![NOAA]] Ocean Education Service. Retrieved January 9, 2010.</ref>](https://commons.wikimedia.org/wiki/Special:FilePath/Coral atoll formation animation.gif?width=200 "NOAA]] Ocean Education Service. Retrieved January 9, 2010.</ref>")
![polyp]] anatomy](https://commons.wikimedia.org/wiki/Special:FilePath/Coral polyp.jpg?width=200 "polyp]] anatomy")
![[[Coralline algae]] ''[[Lithothamnion]] sp.''](https://commons.wikimedia.org/wiki/Special:FilePath/Coralline algae 2.jpg?width=200 "[[Coralline algae]] ''[[Lithothamnion]] sp.''")
![Fringing reef at [[Eilat]] at the southern tip of [[Israel]]](https://commons.wikimedia.org/wiki/Special:FilePath/EilatFringingReef.jpg?width=200 "Fringing reef at [[Eilat]] at the southern tip of [[Israel]]")
![Table coral, ''[[Acropora]] sp.''](https://commons.wikimedia.org/wiki/Special:FilePath/FFS Table bottom.jpg?width=200 "Table coral, ''[[Acropora]] sp.''")
![Inhabited [[cay]] in the [[Maldives]]](https://commons.wikimedia.org/wiki/Special:FilePath/Maldives - Kurumba Island.jpg?width=200 "Inhabited [[cay]] in the [[Maldives]]")
![A small [[atoll]] in the [[Maldives]]](https://commons.wikimedia.org/wiki/Special:FilePath/Maldives small island.jpg?width=200 "A small [[atoll]] in the [[Maldives]]")
![The colour of corals depends on the combination of brown shades provided by their [[zooxanthellae]] and pigmented proteins (reds, blues, greens, etc.) produced by the corals themselves.](https://commons.wikimedia.org/wiki/Special:FilePath/Multy color corals.JPG?width=200 "The colour of corals depends on the combination of brown shades provided by their [[zooxanthellae]] and pigmented proteins (reds, blues, greens, etc.) produced by the corals themselves.")
![[[Eastern oyster]]s (''Crassostrea virginica'')](https://commons.wikimedia.org/wiki/Special:FilePath/Oyster bed, Brunswick, GA, US.jpg?width=200 "[[Eastern oyster]]s (''Crassostrea virginica'')")
.png?width=200 "Coral polyps}}")
![shoals]], that is, it slows down and the wave height increases.](https://commons.wikimedia.org/wiki/Special:FilePath/Propagation du tsunami en profondeur variable.gif?width=200 "shoals]], that is, it slows down and the wave height increases.")
![sessile]] and take root on the ocean floor. But unlike plants, corals do not make their own food.<ref>[https://oceanservice.noaa.gov/facts/coral.html Are corals animals or plants?] ''NOAA: National Ocean Service''. Accessed 11 February 2020. Updated: 7 January 2020.</ref>](https://commons.wikimedia.org/wiki/Special:FilePath/Uderwater Paradise.jpg?width=200 "sessile]] and take root on the ocean floor. But unlike plants, corals do not make their own food.<ref>[https://oceanservice.noaa.gov/facts/coral.html Are corals animals or plants?] ''NOAA: National Ocean Service''. Accessed 11 February 2020. Updated: 7 January 2020.</ref>")
![This map shows areas of [[upwelling]] in red. Coral reefs are not found in coastal areas where colder and nutrient-rich upwellings occur.](https://commons.wikimedia.org/wiki/Special:FilePath/Upwelling image1.jpg?width=200 "This map shows areas of [[upwelling]] in red. Coral reefs are not found in coastal areas where colder and nutrient-rich upwellings occur.")
![[[Zooxanthellae]], the microscopic algae that lives inside coral, gives it colour and provides it with food through photosynthesis](https://commons.wikimedia.org/wiki/Special:FilePath/Zooxanthellae.jpg?width=200 "[[Zooxanthellae]], the microscopic algae that lives inside coral, gives it colour and provides it with food through photosynthesis")
![volcanic island]] which becomes extinct](https://commons.wikimedia.org/wiki/Special:FilePath/Atoll forming-volcano.png?width=200 "volcanic island]] which becomes extinct")
![As the island and ocean floor subside, coral growth builds a [[fringing reef]], often including a shallow lagoon between the land and the main reef.](https://commons.wikimedia.org/wiki/Special:FilePath/Atoll forming-Fringing reef.png?width=200 "As the island and ocean floor subside, coral growth builds a [[fringing reef]], often including a shallow lagoon between the land and the main reef.")
![As the subsidence continues, the fringing reef becomes a larger barrier reef further from the shore with a bigger and deeper [[lagoon]] inside.](https://commons.wikimedia.org/wiki/Special:FilePath/Atoll forming-Barrier reef.png?width=200 "As the subsidence continues, the fringing reef becomes a larger barrier reef further from the shore with a bigger and deeper [[lagoon]] inside.")
![Ultimately, the island sinks below the sea, and the barrier reef becomes an [[atoll]] enclosing an open lagoon.](https://commons.wikimedia.org/wiki/Special:FilePath/Atoll forming-Atoll.png?width=200 "Ultimately, the island sinks below the sea, and the barrier reef becomes an [[atoll]] enclosing an open lagoon.")
.jpg?width=200 "Spiral wire coral")
![[[Mushroom coral]]](https://commons.wikimedia.org/wiki/Special:FilePath/Muchroom coral.JPG?width=200 "[[Mushroom coral]]")
![[[Staghorn coral]]](https://commons.wikimedia.org/wiki/Special:FilePath/Staghorn-coral-1.jpg?width=200 "[[Staghorn coral]]")
![[[Pillar coral]]](https://commons.wikimedia.org/wiki/Special:FilePath/PillarCoral.jpg?width=200 "[[Pillar coral]]")
![[[Brain coral]]](https://commons.wikimedia.org/wiki/Special:FilePath/Brain coral.jpg?width=200 "[[Brain coral]]")
![[[Maze coral]]](https://commons.wikimedia.org/wiki/Special:FilePath/Meandrina meandrites (Maze Coral).jpg?width=200 "[[Maze coral]]")
![[[Black coral]]](https://commons.wikimedia.org/wiki/Special:FilePath/Black coral.jpg?width=200 "[[Black coral]]")
![[[Elkhorn coral]]](https://commons.wikimedia.org/wiki/Special:FilePath/Elkhorn Coral with a Yellowtail Damselfish in the Caribbean Sea in Curaçao.jpg?width=200 "[[Elkhorn coral]]")
![Schooling]] [[reef fish]]](https://commons.wikimedia.org/wiki/Special:FilePath/Prionurus laticlavius.jpg?width=200 "Schooling]] [[reef fish]]")
![[[Caribbean reef squid]]](https://commons.wikimedia.org/wiki/Special:FilePath/Caribbean reef squid.jpg?width=200 "[[Caribbean reef squid]]")
![[[Banded coral shrimp]]](https://commons.wikimedia.org/wiki/Special:FilePath/Stenopus hispidus (high res).jpg?width=200 "[[Banded coral shrimp]]")
![[[Whitetip reef shark]]](https://commons.wikimedia.org/wiki/Special:FilePath/Triaenodon obesus moc.jpg?width=200 "[[Whitetip reef shark]]")
![[[Green turtle]]](https://commons.wikimedia.org/wiki/Special:FilePath/Green turtle John Pennekamp.jpg?width=200 "[[Green turtle]]")
![[[Giant clam]]](https://commons.wikimedia.org/wiki/Special:FilePath/Red sea-reef 3627.jpg?width=200 "[[Giant clam]]")
![[[Banded sea krait]]](https://commons.wikimedia.org/wiki/Special:FilePath/Laticauda colubrina (Wakatobi).jpg?width=200 "[[Banded sea krait]]")
![The shell of ''[[Latiaxis wormaldi]]'', a coral snail](https://commons.wikimedia.org/wiki/Special:FilePath/Latiaxis wormaldi 002.jpg?width=200 "The shell of ''[[Latiaxis wormaldi]]'', a coral snail")
![''[[Sencha]]'' green tea, the most popular form of tea in Japan.](https://commons.wikimedia.org/wiki/Special:FilePath/2017 Kagoshima sencha.jpg?width=200 "''[[Sencha]]'' green tea, the most popular form of tea in Japan.")
.jpg?width=200 "Four varieties of green tea prior to brewing")
![''Gakjeochong'', a [[Goguryeo]] tomb, shows a knight drinking tea with two ladies (5-6th century)](https://commons.wikimedia.org/wiki/Special:FilePath/Goguryeo-Gakjeochong-Inner life.jpg?width=200 "''Gakjeochong'', a [[Goguryeo]] tomb, shows a knight drinking tea with two ladies (5-6th century)")
![Georgia]] to support green tea production.](https://commons.wikimedia.org/wiki/Special:FilePath/Plantação de Chá Gorreana, Camellia sinensis, Ribeira Grande, ilha de São Miguel, Açores.JPG?width=200 "Georgia]] to support green tea production.")
![Tea leaves: ''[[sejak]]'' (green tea), ''[[ujeon]]'' (green tea), and ''[[hwangcha]]'' (yellow tea) from [[Hadong County]]](https://commons.wikimedia.org/wiki/Special:FilePath/Sejak, ujeon, hwangcha tea leaves.jpg?width=200 "Tea leaves: ''[[sejak]]'' (green tea), ''[[ujeon]]'' (green tea), and ''[[hwangcha]]'' (yellow tea) from [[Hadong County]]")
Definition
Wikipedia
In fluid dynamics, d'Alembert's paradox (or the hydrodynamic paradox) is a contradiction reached in 1752 by French mathematician Jean le Rond d'Alembert. D'Alembert proved that – for incompressible and inviscid potential flow – the drag force is zero on a body moving with constant velocity relative to the fluid. Zero drag is in direct contradiction to the observation of substantial drag on bodies moving relative to fluids, such as air and water; especially at high velocities corresponding with high Reynolds numbers. It is a particular example of the reversibility paradox.
D’Alembert, working on a 1749 Prize Problem of the Berlin Academy on flow drag, concluded: "It seems to me that the theory (potential flow), developed in all possible rigor, gives, at least in several cases, a strictly vanishing resistance, a singular paradox which I leave to future Geometers [i.e. mathematicians - the two terms were used interchangeably at that time] to elucidate". A physical paradox indicates flaws in the theory.
Fluid mechanics was thus discredited by engineers from the start, which resulted in an unfortunate split – between the field of hydraulics, observing phenomena which could not be explained, and theoretical fluid mechanics explaining phenomena which could not be observed – in the words of the Chemistry Nobel Laureate Sir Cyril Hinshelwood.
According to scientific consensus, the occurrence of the paradox is due to the neglected effects of viscosity. In conjunction with scientific experiments, there were huge advances in the theory of viscous fluid friction during the 19th century. With respect to the paradox, this culminated in the discovery and description of thin boundary layers by Ludwig Prandtl in 1904. Even at very high Reynolds numbers, the thin boundary layers remain as a result of viscous forces. These viscous forces cause friction drag on streamlined objects, and for bluff bodies the additional result is flow separation and a low-pressure wake behind the object, leading to form drag.
The general view in the fluid mechanics community is that, from a practical point of view, the paradox is solved along the lines suggested by Prandtl. A formal mathematical proof is lacking, and difficult to provide, as in so many other fluid-flow problems involving the Navier–Stokes equations (which are used to describe viscous flow).
