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Saturday, September 10, 2022

Iconoclasm

From Wikipedia, the free encyclopedia

A painting
In this Elizabethan work of propaganda, the top right of the picture depicts men busy pulling down and smashing icons, while power is shifting from the dying King Henry VIII at left, pointing to his far more staunchly Protestant son, the boy-king Edward VI at centre.
National Portrait Gallery, London

Iconoclasm (from Greek: εἰκών, eikṓn, 'figure, icon' + κλάω, kláō, 'to break') is the social belief in the importance of the destruction of icons and other images or monuments, most frequently for religious or political reasons. People who engage in or support iconoclasm are called iconoclasts, a term that has come to be figuratively applied to any individual who challenges "cherished beliefs or venerated institutions on the grounds that they are erroneous or pernicious."

Conversely, one who reveres or venerates religious images is called (by iconoclasts) an iconolater; in a Byzantine context, such a person is called an iconodule or iconophile. Iconoclasm does not generally encompass the destruction of the images of a specific ruler after his or her death or overthrow, a practice better known as damnatio memoriae.

While iconoclasm may be carried out by adherents of a different religion, it is more commonly the result of sectarian disputes between factions of the same religion. The term originates from the Byzantine Iconoclasm, the struggles between proponents and opponents of religious icons in the Byzantine Empire from 726 to 842 AD. Degrees of iconoclasm vary greatly among religions and their branches, but are strongest in religions which oppose idolatry, including the Abrahamic religions. Outside of the religious context, iconoclasm can refer to movements for widespread destruction in symbols of an ideology or cause, such as the destruction of monarchist symbols during the French Revolution.

Early religious iconoclasm

Ancient era

In the Bronze Age, the most significant episode of iconoclasm occurred in Egypt during the Amarna Period, when Akhenaten, based in his new capital of Akhetaten, instituted a significant shift in Egyptian artistic styles alongside a campaign of intolerance towards the traditional gods and a new emphasis on a state monolatristic tradition focused on the god Aten, the Sun disk—many temples and monuments were destroyed as a result:

In rebellion against the old religion and the powerful priests of Amun, Akhenaten ordered the eradication of all of Egypt's traditional gods. He sent royal officials to chisel out and destroy every reference to Amun and the names of other deities on tombs, temple walls, and cartouches to instill in the people that the Aten was the one true god.

Public references to Akhenaten were destroyed soon after his death. Comparing the ancient Egyptians with the Israelites, Jan Assmann writes:

For Egypt, the greatest horror was the destruction or abduction of the cult images. In the eyes of the Israelites, the erection of images meant the destruction of divine presence; in the eyes of the Egyptians, this same effect was attained by the destruction of images. In Egypt, iconoclasm was the most terrible religious crime; in Israel, the most terrible religious crime was idolatry. In this respect Osarseph alias Akhenaten, the iconoclast, and the Golden Calf, the paragon of idolatry, correspond to each other inversely, and it is strange that Aaron could so easily avoid the role of the religious criminal. It is more than probable that these traditions evolved under mutual influence. In this respect, Moses and Akhenaten became, after all, closely related.

Judaism

According to the Hebrew Bible, God instructed the Israelites to "destroy all [the] engraved stones, destroy all [the] molded images, and demolish all [the] high places" of the indigenous Canaanite population as soon as they entered the Promised Land.

In Judaism, King Hezekiah purged Solomon's Temple in Jerusalem and all figures were also destroyed in the Land of Israel, including the Nehushtan, as recorded in the Second Book of Kings. His reforms were reversed in the reign of his son Manasseh.

Iconoclasm in Christian history

Saint Benedict's monks destroy an image of Apollo, worshiped in the Roman Empire

Scattered expressions of opposition to the use of images have been reported: in 305–306 AD, the Synod of Elvira appeared to endorse iconoclasm; Canon 36 states, "Pictures are not to be placed in churches, so that they do not become objects of worship and adoration." Proscription ceased after the destruction of pagan temples. However, widespread use of Christian iconography only began as Christianity increasingly spread among gentiles after the legalization of Christianity by Roman Emperor Constantine (c. 312 AD). During the process of Christianisation under Constantine, Christian groups destroyed the images and sculptures expressive of the Roman Empire's polytheist state religion.

Among early church theologians, iconoclastic tendencies were supported by theologians such as: Tertullian, Clement of Alexandria, Origen, Lactantius, Justin Martyr, Eusebius and Epiphanus.

Byzantine era

The period after the reign of Byzantine Emperor Justinian (527–565) evidently saw a huge increase in the use of images, both in volume and quality, and a gathering aniconic reaction.

One notable change within the Byzantine Empire came in 695, when Justinian II's government added a full-face image of Christ on the obverse of imperial gold coins. The change caused the Caliph Abd al-Malik to stop his earlier adoption of Byzantine coin types. He started a purely Islamic coinage with lettering only. A letter by the Patriarch Germanus, written before 726 to two iconoclast bishops, says that "now whole towns and multitudes of people are in considerable agitation over this matter," but there is little written evidence of the debate.

Government-led iconoclasm began with Byzantine Emperor Leo III, who issued a series of edicts between 726 and 730 against the veneration of images. The religious conflict created political and economic divisions in Byzantine society; iconoclasm was generally supported by the Eastern, poorer, non-Greek peoples of the Empire who had to frequently deal with raids from the new Muslim Empire. On the other hand, the wealthier Greeks of Constantinople and the peoples of the Balkan and Italian provinces strongly opposed iconoclasm.

Pre-Reformation

Peter of Bruys opposed the usage of religious images, the Strigolniki were also possibly iconoclastic. Claudius of Turin was the bishop of Turin from 817 until his death. He is most noted for teaching iconoclasm.

Reformation era

The first iconoclastic wave happened in Wittenberg in the early 1520s under reformers Thomas Müntzer and Andreas Karlstadt, in the absence of Martin Luther, who then, concealed under the pen-name of 'Junker Jörg', intervened to calm things down. Luther argued that the mental picturing of Christ when reading the Scriptures was similar in character to artistic renderings of Christ.

In contrast to the Lutherans who favoured certain types of sacred art in their churches and homes, the Reformed (Calvinist) leaders, in particular Andreas Karlstadt, Huldrych Zwingli and John Calvin, encouraged the removal of religious images by invoking the Decalogue's prohibition of idolatry and the manufacture of graven (sculpted) images of God. As a result, individuals attacked statues and images, most famously in the beeldenstorm across the Netherlands in 1566. However, in most cases, civil authorities removed images in an orderly manner in the newly Reformed Protestant cities and territories of Europe.

Extent (in blue) of the Beeldenstorm through the Spanish Netherlands
 
16th-century iconoclasm in the Protestant Reformation. Relief statues in St. Stevenskerk in Nijmegen, the Netherlands, were attacked and defaced by Calvinists in the Beeldenstorm.

The belief of iconoclasm caused havoc throughout Europe. In 1523, specifically due to the Swiss reformer Huldrych Zwingli, a vast number of his followers viewed themselves as being involved in a spiritual community that in matters of faith should obey neither the visible Church nor lay authorities. According to Peter George Wallace "Zwingli's attack on images, at the first debate, triggered iconoclastic incidents in Zurich and the villages under civic jurisdiction that the reformer was unwilling to condone." Due to this action of protest against authority, "Zwingli responded with a carefully reasoned treatise that men could not live in society without laws and constraint."

Significant iconoclastic riots took place in Basel (in 1529), Zurich (1523), Copenhagen (1530), Münster (1534), Geneva (1535), Augsburg (1537), Scotland (1559), Rouen (1560), and Saintes and La Rochelle (1562). Calvinist iconoclasm in Europe "provoked reactive riots by Lutheran mobs" in Germany and "antagonized the neighbouring Eastern Orthodox" in the Baltic region.

The Seventeen Provinces (now the Netherlands, Belgium, and parts of Northern France) were disrupted by widespread Calvinist iconoclasm in the summer of 1566. This period, known as the Beeldenstorm, began with the destruction of the statuary of the Monastery of Saint Lawrence in Steenvoorde after a "Hagenpreek," or field sermon, by Sebastiaan Matte on 10 August 1566; by October the wave of furor had gone all through the Spanish Netherlands up to Groningen. Hundreds of other attacks included the sacking of the Monastery of Saint Anthony after a sermon by Jacob de Buysere. The Beeldenstorm marked the start of the revolution against the Spanish forces and the Catholic Church.

Looting of the Churches of Lyon by the Calvinists in 1562 by Antoine Caron.

During the Reformation in England, which started during the reign of Anglican monarch Henry VIII, and was urged on by reformers such as Hugh Latimer and Thomas Cranmer, limited official action was taken against religious images in churches in the late 1530s. Henry's young son, Edward VI, came to the throne in 1547 and, under Cranmer's guidance, issued injunctions for Religious Reforms in the same year and in 1550, an Act of Parliament "for the abolition and putting away of divers books and images." During the English Civil War, Bishop Joseph Hall of Norwich described the events of 1643 when troops and citizens, encouraged by a Parliamentary ordinance against superstition and idolatry, behaved thus:

Lord what work was here! What clattering of glasses! What beating down of walls! What tearing up of monuments! What pulling down of seats! What wresting out of irons and brass from the windows! What defacing of arms! What demolishing of curious stonework! What tooting and piping upon organ pipes! And what a hideous triumph in the market-place before all the country, when all the mangled organ pipes, vestments, both copes and surplices, together with the leaden cross which had newly been sawn down from the Green-yard pulpit and the service-books and singing books that could be carried to the fire in the public market-place were heaped together.

Protestant Christianity was not uniformly hostile to the use of religious images. Martin Luther taught the "importance of images as tools for instruction and aids to devotion," stating: "If it is not a sin but good to have the image of Christ in my heart, why should it be a sin to have it in my eyes?" Lutheran churches retained ornate church interiors with a prominent crucifix, reflecting their high view of the real presence of Christ in Eucharist. As such, "Lutheran worship became a complex ritual choreography set in a richly furnished church interior." For Lutherans, "the Reformation renewed rather than removed the religious image."

Lutheran scholar Jeremiah Ohl writes:

Zwingli and others for the sake of saving the Word rejected all plastic art; Luther, with an equal concern for the Word, but far more conservative, would have all the arts to be the servants of the Gospel. "I am not of the opinion" said [Luther], "that through the Gospel all the arts should be banished and driven away, as some zealots want to make us believe; but I wish to see them all, especially music, in the service of Him Who gave and created them." Again he says: "I have myself heard those who oppose pictures, read from my German Bible.… But this contains many pictures of God, of the angels, of men, and of animals, especially in the Revelation of St. John, in the books of Moses, and in the book of Joshua. We therefore kindly beg these fanatics to permit us also to paint these pictures on the wall that they may be remembered and better understood, inasmuch as they can harm as little on the walls as in books. Would to God that I could persuade those who can afford it to paint the whole Bible on their houses, inside and outside, so that all might see; this would indeed be a Christian work. For I am convinced that it is God's will that we should hear and learn what He has done, especially what Christ suffered. But when I hear these things and meditate upon them, I find it impossible not to picture them in my heart. Whether I want to or not, when I hear, of Christ, a human form hanging upon a cross rises up in my heart: just as I see my natural face reflected when I look into water. Now if it is not sinful for me to have Christ's picture in my heart, why should it be sinful to have it before my eyes?

The Ottoman Sultan Suleiman the Magnificent, who had pragmatic reasons to support the Dutch Revolt (the rebels, like himself, were fighting against Spain) also completely approved of their act of "destroying idols," which accorded well with Muslim teachings.

A bit later in Dutch history, in 1627 the artist Johannes van der Beeck was arrested and tortured, charged with being a religious non-conformist and a blasphemer, heretic, atheist, and Satanist. The 25 January 1628 judgment from five noted advocates of The Hague pronounced him guilty of "blasphemy against God and avowed atheism, at the same time as leading a frightful and pernicious lifestyle. At the court's order his paintings were burned, and only a few of them survive."

Other instances

From the 16th through the 19th centuries, many of the polytheistic religious deities and texts of pre-colonial Americas, Oceania, and Africa were destroyed by Christian missionaries and their converts, such as during the Spanish conquest of the Aztec Empire and the Spanish conquest of the Inca Empire.

Many of the moai of Easter Island were toppled during the 18th century in the iconoclasm of civil wars before any European encounter. Other instances of iconoclasm may have occurred throughout Eastern Polynesia during its conversion to Christianity in the 19th century.

After the Second Vatican Council in the late 20th century, some Roman Catholic parish churches discarded much of their traditional imagery, art, and architecture.

Muslim iconoclasm

Islam has a much stronger tradition of forbidding the depiction of figures, especially religious figures, with Sunni Islam forbidding it more than Shia Islam. In the history of Islam, the act of removing idols from the Ka'ba in Mecca has great symbolic and historic importance for all believers.

In general, Muslim societies have avoided the depiction of living beings (both animals and humans) within such sacred spaces as mosques and madrasahs. This ban on figural representation is not based on the Qur'an, instead, it is based on traditions which are described within the Hadith. The prohibition of figuration has not always been extended to the secular sphere, and a robust tradition of figural representation exists within Muslim art. However, Western authors have tended to perceive "a long, culturally determined, and unchanging tradition of violent iconoclastic acts" within Islamic society.

Early Islam in Arabia

The first act of Muslim iconoclasm dates to the beginning of Islam, in 630, when the various statues of Arabian deities housed in the Kaaba in Mecca were destroyed. There is a tradition that Muhammad spared a fresco of Mary and Jesus. This act was intended to bring an end to the idolatry which, in the Muslim view, characterized Jahiliyyah.

The destruction of the idols of Mecca did not, however, determine the treatment of other religious communities living under Muslim rule after the expansion of the caliphate. Most Christians under Muslim rule, for example, continued to produce icons and to decorate their churches as they wished. A major exception to this pattern of tolerance in early Islamic history was the "Edict of Yazīd", issued by the Umayyad caliph Yazīd II in 722–723. This edict ordered the destruction of crosses and Christian images within the territory of the caliphate. Researchers have discovered evidence that the order was followed, particularly in present-day Jordan, where archaeological evidence shows the removal of images from the mosaic floors of some, although not all, of the churches that stood at this time. But Yazīd's iconoclastic policies were not continued by his successors, and Christian communities of the Levant continued to make icons without significant interruption from the sixth century to the ninth.

Egypt

The Sphinx profile in 2010, without the nose

Al-Maqrīzī, writing in the 15th century, attributes the missing nose on the Great Sphinx of Giza to iconoclasm by Muhammad Sa'im al-Dahr, a Sufi Muslim in the mid-1300s. He was reportedly outraged by local Muslims making offerings to the Great Sphinx in the hope of controlling the flood cycle, and he was later executed for vandalism. However, whether this was actually the cause of the missing nose has been debated by historians. Mark Lehner, having performed an archaeological study, concluded that it was broken with instruments at an earlier unknown time between the 3rd and 10th centuries.

Ottoman conquests

Certain conquering Muslim armies have used local temples or houses of worship as mosques. An example is Hagia Sophia in Istanbul (formerly Constantinople), which was converted into a mosque in 1453. Most icons were desecrated and the rest were covered with plaster. In the 1934 the government of Turkey decided to convert the Hagia Sophia into a museum and the restoration of the mosaics was undertaken by the American Byzantine Institute beginning in 1932.

Contemporary events

Certain Muslim denominations continue to pursue iconoclastic agendas. There has been much controversy within Islam over the recent and apparently on-going destruction of historic sites by Saudi Arabian authorities, prompted by the fear they could become the subject of "idolatry."

A recent act of iconoclasm was the 2001 destruction of the giant Buddhas of Bamyan by the then-Taliban government of Afghanistan. The act generated worldwide protests and was not supported by other Muslim governments and organizations. It was widely perceived in the Western media as a result of the Muslim prohibition against figural decoration. Such an account overlooks "the coexistence between the Buddhas and the Muslim population that marveled at them for over a millennium" before their destruction. The Buddhas had twice in the past been attacked by Nadir Shah and Aurengzeb. According to art historian F. B. Flood, analysis of the Taliban's statements regarding the Buddhas suggest that their destruction was motivated more by political than by theological concerns. Taliban spokespeople have given many different explanations of the motives for the destruction.

During the Tuareg rebellion of 2012, the radical Islamist militia Ansar Dine destroyed various Sufi shrines from the 15th and 16th centuries in the city of Timbuktu, Mali. In 2016, the International Criminal Court (ICC) sentenced Ahmad al-Faqi al-Mahdi, a former member of Ansar Dine, to nine years in prison for this destruction of cultural world heritage. This was the first time that the ICC convicted a person for such a crime.

The short-lived Islamic State of Iraq and the Levant carried out iconoclastic attacks such as the destruction of Shia mosques and shrines. Notable incidents include blowing up the Mosque of the Prophet Yunus (Jonah) and destroying the Shrine to Seth in Mosul.

Iconoclasm in India

In early Medieval India, there were numerous recorded instances of temple desecration by Indian kings against rival Indian kingdoms, which involved conflicts between devotees of different Hindu deities, as well as conflicts between Hindus, Buddhists, and Jains.

In 642, the Pallava king Narasimhavarman I looted a Ganesha temple in the Chalukyan capital of Vatapi. In c. 692, Chalukya armies invaded northern India where they looted temples of Ganga and Yamuna.

In the 8th century, Bengali troops from the Buddhist Pala Empire desecrated temples of Vishnu Vaikuṇṭha, the state deity of Lalitaditya's kingdom in Kashmir. In the early 9th century, Indian Hindu kings from Kanchipuram and the Pandyan king Srimara Srivallabha looted Buddhist temples in Sri Lanka. In the early 10th century, the Pratihara king Herambapala looted an image from a temple in the Sahi kingdom of Kangra, which was later looted by the Pratihara king Yasovarman.

During the Muslim conquest of Sindh

Records from the campaign recorded in the Chach Nama record the destruction of temples during the early 8th century when the Umayyad governor of Damascus, al-Hajjaj ibn Yusuf, mobilized an expedition of 6000 cavalry under Muhammad bin Qasim in 712.

Historian Upendra Thakur records the persecution of Hindus and Buddhists:

Muhammad triumphantly marched into the country, conquering Debal, Sehwan, Nerun, Brahmanadabad, Alor and Multan one after the other in quick succession, and in less than a year and a half, the far-flung Hindu kingdom was crushed ... There was a fearful outbreak of religious bigotry in several places and temples were wantonly desecrated. At Debal, the Nairun and Aror temples were demolished and converted into mosques.

Chola to Paramara dynasty

In the early 11th century, the Chola king Rajendra I looted temples in a number of neighbouring kingdoms, including:

In the mid-11th century, the Chola king Rajadhiraja plundered a temple in Kalyani. In the late 11th century, the Hindu king Harsha of Kashmir plundered temples as an institutionalised activity. In the late 12th to early 13th centuries, the Paramara dynasty attacked and plundered Jain temples in Gujarat.

The Somnath temple and Mahmud of Ghazni

Perhaps the most notorious episode of iconoclasm in India was Mahmud of Ghazni's attack on the Somnath temple from across the Thar Desert. The temple was first raided in 725, when Junayad, the governor of Sind, sent his armies to destroy it. In 1024, during the reign of Bhima I, the prominent Turkic-Muslim ruler Mahmud of Ghazni raided Gujarat, plundering the Somnath temple and breaking its jyotirlinga despite pleas by Brahmins not to break it. He took away a booty of 20 million dinars. The attack may have been inspired by the belief that an idol of the goddess Manat had been secretly transferred to the temple. According to the Ghaznavid court-poet Farrukhi Sistani, who claimed to have accompanied Mahmud on his raid, Somnat (as rendered in Persian) was a garbled version of su-manat referring to the goddess Manat. According to him, as well as a later Ghaznavid historian Abu Sa'id Gardezi, the images of the other goddesses were destroyed in Arabia but the one of Manat was secretly sent away to Kathiawar (in modern Gujarat) for safekeeping. Since the idol of Manat was an aniconic image of black stone, it could have been easily confused with a lingam at Somnath. Mahmud is said to have broken the idol and taken away parts of it as loot and placed so that people would walk on it. In his letters to the Caliphate, Mahmud exaggerated the size, wealth and religious significance of the Somnath temple, receiving grandiose titles from the Caliph in return.

The wooden structure was replaced by Kumarapala (r. 1143–72), who rebuilt the temple out of stone.

Mamluk dynasty onward

Historical records compiled by Muslim historian Maulana Hakim Saiyid Abdul Hai attest to the religious violence during the Mamluk dynasty under Qutb-ud-din Aybak. The first mosque built in Delhi, the "Quwwat al-Islam" was built with demolished parts of 20 Hindu and Jain temples. This pattern of iconoclasm was common during his reign.

During the Delhi Sultanate, a Muslim army led by Malik Kafur, a general of Alauddin Khalji, pursued four violent campaigns into south India, between 1309 and 1311, against the Hindu kingdoms of Devgiri (Maharashtra), Warangal (Telangana), Dwarasamudra (Karnataka) and Madurai (Tamil Nadu). Many Temples were plundered; Hoysaleswara Temple and others were ruthlessly destroyed.

In Kashmir, Sikandar Shah Miri (1389–1413) began expanding, and unleashed religious violence that earned him the name but-shikan, or 'idol-breaker'. He earned this sobriquet because of the sheer scale of desecration and destruction of Hindu and Buddhist temples, shrines, ashrams, hermitages, and other holy places in what is now known as Kashmir and its neighboring territories. Firishta states, "After the emigration of the Bramins, Sikundur ordered all the temples in Kashmeer to be thrown down." He destroyed vast majority of Hindu and Buddhist temples in his reach in Kashmir region (north and northwest India).

In the 1460s, Kapilendra, founder of the Suryavamsi Gajapati dynasty, sacked the Saiva and Vaishnava temples in the Cauvery delta in the course of wars of conquest in the Tamil country. Vijayanagara king Krishnadevaraya looted a Bala Krishna temple in Udayagiri in 1514, and looted a Vittala temple in Pandharpur in 1520.

A regional tradition, along with the Hindu text Madala Panji, states that Kalapahad attacked and damaged the Konark Sun Temple in 1568, as well as many others in Orissa.

Some of the most dramatic cases of iconoclasm by Muslims are found in parts of India where Hindu and Buddhist temples were razed and mosques erected in their place. Aurangzeb, the 6th Mughal Emperor, destroyed the famous Hindu temples at Varanasi and Mathura, turning back on his ancestor Akbar's policy of religious freedom and establishing Sharia across his empire.

In modern India, the most high-profile case of iconoclasm was from 1992. Hindus, led by the Vishva Hindu Parishad and Bajrang Dal, destroyed the 430-year-old Islamic Babri Masjid in Ayodhya.

Iconoclasm in East Asia

China

There have been a number of anti-Buddhist campaigns in Chinese history that led to the destruction of Buddhist temples and images. One of the most notable of these campaigns was the Great Anti-Buddhist Persecution of the Tang dynasty.

During and after the 1911 Xinhai Revolution, there was widespread destruction of religious and secular images in China.

During the Northern Expedition in Guangxi in 1926, Kuomintang General Bai Chongxi led his troops in destroying Buddhist temples and smashing Buddhist images, turning the temples into schools and Kuomintang party headquarters. It was reported that almost all of the viharas in Guangxi were destroyed and the monks were removed. Bai also led a wave of anti-foreignism in Guangxi, attacking Americans, Europeans, and other foreigners, and generally making the province unsafe for foreigners and missionaries. Westerners fled from the province and some Chinese Christians were also attacked as imperialist agents. The three goals of the movement were anti-foreignism, anti-imperialism and anti-religion. Bai led the anti-religious movement against superstition. Huang Shaohong, also a Kuomintang member of the New Guangxi clique, supported Bai's campaign. The anti-religious campaign was agreed upon by all Guangxi Kuomintang members.

There was extensive destruction of religious and secular imagery in Tibet after it was invaded and occupied by China.

Many religious and secular images were destroyed during the Cultural Revolution of 1966–1976, ostensibly because they were a holdover from China's traditional past (which the Communist regime led by Mao Zedong reviled). The Cultural Revolution included widespread destruction of historic artworks in public places and private collections, whether religious or secular. Objects in state museums were mostly left intact.

South Korea

According to an article in Buddhist-Christian Studies:

Over the course of the last decade [1990s] a fairly large number of Buddhist temples in South Korea have been destroyed or damaged by fire by Christian fundamentalists. More recently, Buddhist statues have been identified as idols, and attacked and decapitated in the name of Jesus. Arrests are hard to effect, as the arsonists and vandals work by stealth of night.

Angkor

Beginning around 1243 AD with the death of Indravarman II, the Khmer Empire went through a period of iconoclasm. At the beginning of the reign of the next king, Jayavarman VIII, the Kingdom went back to Hinduism and the worship of Shiva. Many of the Buddhist images were destroyed by Jayavarman VIII, who reestablished previously Hindu shrines that had been converted to Buddhism by his predecessor. Carvings of the Buddha at temples such as Preah Khan were destroyed, and during this period the Bayon Temple was made a temple to Shiva, with the central 3.6 meter tall statue of the Buddha cast to the bottom of a nearby well.

Political iconoclasm

Damnatio memoriae

Revolutions and changes of regime, whether through uprising of the local population, foreign invasion, or a combination of both, are often accompanied by the public destruction of statues and monuments identified with the previous regime. This may also be known as damnatio memoriae, the ancient Roman practice of official obliteration of the memory of a specific individual. Stricter definitions of "iconoclasm" exclude both types of action, reserving the term for religious or more widely cultural destruction. In many cases, such as Revolutionary Russia or Ancient Egypt, this distinction can be hard to make.

Among Roman emperors and other political figures subject to decrees of damnatio memoriae were Sejanus, Publius Septimius Geta, and Domitian. Several Emperors, such as Domitian and Commodus had during their reigns erected numerous statues of themselves, which were pulled down and destroyed when they were overthrown.

The perception of damnatio memoriae in the Classical world was an act of erasing memory has been challenged by scholars who have argued that it "did not negate historical traces, but created gestures which served to dishonor the record of the person and so, in an oblique way, to confirm memory," and was in effect a spectacular display of "pantomime forgetfulness." Examining cases of political monument destruction in modern Irish history, Guy Beiner has demonstrated that iconoclastic vandalism often entails subtle expressions of ambiguous remembrance and that, rather than effacing memory, such acts of de-commemorating effectively preserve memory in obscure forms.

During the French Revolution

Throughout the radical phase of the French Revolution, iconoclasm was supported by members of the government as well as the citizenry. Numerous monuments, religious works, and other historically significant pieces were destroyed in an attempt to eradicate any memory of the Old Regime. A statue of King Louis XV in the Paris square which until then bore his name, was pulled down and destroyed. This was a prelude to the guillotining of his successor Louis XVI in the same site, renamed "Place de la Révolution" (at present Place de la Concorde). Later that year, the bodies of many French kings were exhumed from the Basilica of Saint-Denis and dumped in a mass grave.

Some episodes of iconoclasm were carried out spontaneously by crowds of citizens, including the destruction of statues of kings during the insurrection of 10 August 1792 in Paris. Some were directly sanctioned by the Republican government, including the Saint-Denis exhumations. Nonetheless, the Republican government also took steps to preserve historic artworks, notably by founding the Louvre museum to house and display the former royal art collection. This allowed the physical objects and national heritage to be preserved while stripping them of their association with the monarchy. Alexandre Lenoir saved many royal monuments by diverting them to preservation in a museum.

The statue of Napoleon on the column at Place Vendôme, Paris was also the target of iconoclasm several times: destroyed after the Bourbon Restoration, restored by Louis-Philippe, destroyed during the Paris Commune and restored by Adolphe Thiers.

Other examples

St. Helen's Gate in Cospicua, Malta, which had its marble coat of arms defaced during the French occupation of Malta
 
Statue of William of Orange formerly located on College Green, in Dublin. Erected in 1701, it was destroyed in 1929—one of several memorials installed during British rule which were destroyed after Ireland became independent.

Other examples of political destruction of images include:

In the Soviet Union

Demolition of the Cathedral of Christ the Saviour, Moscow, 5 December 1931

During and after the October Revolution, widespread destruction of religious and secular imagery in Russia took place, as well as the destruction of imagery related to the Imperial family. The Revolution was accompanied by destruction of monuments of tsars, as well as the destruction of imperial eagles at various locations throughout Russia. According to Christopher Wharton:

In front of a Moscow cathedral, crowds cheered as the enormous statue of Tsar Alexander III was bound with ropes and gradually beaten to the ground. After a considerable amount of time, the statue was decapitated and its remaining parts were broken into rubble.

The Soviet Union actively destroyed religious sites, including Russian Orthodox churches and Jewish cemeteries, in order to discourage religious practice and curb the activities of religious groups.

During the Hungarian Revolution of 1956 and during the Revolutions of 1989, protesters often attacked and took down sculptures and images of Joseph Stalin, such as the Stalin Monument in Budapest.

The fall of Communism in 1989-1991 was also followed by the destruction or removal of statues of Vladimir Lenin and other Communist leaders in the former Soviet Union and in other Eastern Bloc countries. Particularly well-known was the destruction of "Iron Felix", the statue of Felix Dzerzhinsky outside the KGB's headquarters. Another statue of Dzerzhinsky was destroyed in a Warsaw square that was named after him during communist rule, but which is now called Bank Square.

In the United States

During the American Revolution, the Sons of Liberty pulled down and destroyed the gilded lead statue of George III of the United Kingdom on Bowling Green (New York City), melting it down to be recast as ammunition. Similar acts have accompanied the independence of most ex-colonial territories. Sometimes relatively intact monuments are moved to a collected display in a less prominent place, as in India and also post-Communist countries.

In August 2017, a statue of a Confederate soldier dedicated to "the boys who wore the gray" was pulled down from its pedestal in front of Durham County Courthouse in North Carolina by protesters. This followed the events at the 2017 Unite the Right rally in response to growing calls to remove Confederate monuments and memorials across the U.S.

2020 demonstrations

During the George Floyd protests of 2020, demonstrators pulled down dozens of statues which they considered symbols of the Confederacy, slavery, segregation, or racism, including the statue of Williams Carter Wickham in Richmond, Virginia.

Further demonstrations in the wake of the George Floyd protests have resulted in the removal of:

Multiple statues of early European explorers and founders were also vandalized, including those of Christopher Columbus, George Washington, and Thomas Jefferson.

A statue of the African-American abolitionist statesman Frederick Douglass was vandalised in Rochester, New York, by being torn from its base and left close to a nearby river gorge. Donald Trump attributed the act to anarchists, but he did not substantiate his claim nor did he offer a theory on motive. Cornell William Brooks, former president of the NAACP, theorised that this was an act of revenge from white supremacists. Carvin Eison, who led the project that brought the Douglass statues to Rochester, thought it was unlikely that the Douglass statue was toppled by someone who was upset about monuments honoring Confederate figures, and added that "it's only logical that it was some kind of retaliation event in someone’s mind". Police did not find evidence that supported or refuted either claim, and the vandalism case remains unsolved.

Pressure

From Wikipedia, the free encyclopedia

Pressure
Common symbols
p, P
SI unitpascal [Pa]
In SI base unitsN/m2, 1 kg/(m·s2), or 1 J/m3
Derivations from
other quantities
p = F / A
DimensionM L−1 T−2
A figure showing pressure exerted by particle collisions inside a closed container. The collisions that exert the pressure are highlighted in red.
Pressure as exerted by particle collisions inside a closed container

Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled gage pressure) is the pressure relative to the ambient pressure.

Various units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the SI unit of pressure, the pascal (Pa), for example, is one newton per square metre (N/m2); similarly, the pound-force per square inch (psi) is the traditional unit of pressure in the imperial and U.S. customary systems. Pressure may also be expressed in terms of standard atmospheric pressure; the atmosphere (atm) is equal to this pressure, and the torr is defined as 1760 of this. Manometric units such as the centimetre of water, millimetre of mercury, and inch of mercury are used to express pressures in terms of the height of column of a particular fluid in a manometer.

Definition

Pressure is the amount of force applied perpendicular to the surface of an object per unit area. The symbol for it is "p" or P. The IUPAC recommendation for pressure is a lower-case p. However, upper-case P is widely used. The usage of P vs p depends upon the field in which one is working, on the nearby presence of other symbols for quantities such as power and momentum, and on writing style.

Formula

Pressure force area.svg

Mathematically:

where:

is the pressure,
is the magnitude of the normal force,
is the area of the surface on contact.

Pressure is a scalar quantity. It relates the vector area element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors:

The minus sign comes from the convention that the force is considered towards the surface element, while the normal vector points outward. The equation has meaning in that, for any surface S in contact with the fluid, the total force exerted by the fluid on that surface is the surface integral over S of the right-hand side of the above equation.

It is incorrect (although rather usual) to say "the pressure is directed in such or such direction". The pressure, as a scalar, has no direction. The force given by the previous relationship to the quantity has a direction, but the pressure does not. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.

Pressure is distributed to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics, and it is conjugate to volume.

Units

Mercury column

The SI unit for pressure is the pascal (Pa), equal to one newton per square metre (N/m2, or kg·m−1·s−2). This name for the unit was added in 1971; before that, pressure in SI was expressed simply in newtons per square metre.

Other units of pressure, such as pounds per square inch (lbf/in2) and bar, are also in common use. The CGS unit of pressure is the barye (Ba), equal to 1 dyn·cm−2, or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre (g/cm2 or kg/cm2) and the like without properly identifying the force units. But using the names kilogram, gram, kilogram-force, or gram-force (or their symbols) as units of force is expressly forbidden in SI. The technical atmosphere (symbol: at) is 1 kgf/cm2 (98.0665 kPa, or 14.223 psi).

Since a system under pressure has the potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume. It is therefore related to energy density and may be expressed in units such as joules per cubic metre (J/m3, which is equal to Pa). Mathematically:

Some meteorologists prefer the hectopascal (hPa) for atmospheric air pressure, which is equivalent to the older unit millibar (mbar). Similar pressures are given in kilopascals (kPa) in most other fields, except aviation where the hecto- prefix is commonly used. The inch of mercury is still used in the United States. Oceanographers usually measure underwater pressure in decibars (dbar) because pressure in the ocean increases by approximately one decibar per metre depth.

The standard atmosphere (atm) is an established constant. It is approximately equal to typical air pressure at Earth mean sea level and is defined as 101325 Pa.

Because pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g., centimetres of water, millimetres of mercury or inches of mercury). The most common choices are mercury (Hg) and water; water is nontoxic and readily available, while mercury's high density allows a shorter column (and so a smaller manometer) to be used to measure a given pressure. The pressure exerted by a column of liquid of height h and density ρ is given by the hydrostatic pressure equation p = ρgh, where g is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely. When millimetres of mercury (or inches of mercury) are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units. One millimetre of mercury is approximately equal to one torr. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These manometric units are still encountered in many fields. Blood pressure is measured in millimetres of mercury in most of the world, and lung pressures in centimetres of water are still common.

Underwater divers use the metre sea water (msw or MSW) and foot sea water (fsw or FSW) units of pressure, and these are the standard units for pressure gauges used to measure pressure exposure in diving chambers and personal decompression computers. A msw is defined as 0.1 bar (= 100000 Pa = 10000 Pa), is not the same as a linear metre of depth. 33.066 fsw = 1 atm (1 atm = 101325 Pa / 33.066 = 3064.326 Pa). Note that the pressure conversion from msw to fsw is different from the length conversion: 10 msw = 32.6336 fsw, while 10 m = 32.8083 ft.

Gauge pressure is often given in units with "g" appended, e.g. "kPag", "barg" or "psig", and units for measurements of absolute pressure are sometimes given a suffix of "a", to avoid confusion, for example "kPaa", "psia". However, the US National Institute of Standards and Technology recommends that, to avoid confusion, any modifiers be instead applied to the quantity being measured rather than the unit of measure. For example, "pg = 100 psi" rather than "p = 100 psig".

Differential pressure is expressed in units with "d" appended; this type of measurement is useful when considering sealing performance or whether a valve will open or close.

Presently or formerly popular pressure units include the following:

  • atmosphere (atm)
  • manometric units:
    • centimetre, inch, millimetre (torr) and micrometre (mTorr, micron) of mercury,
    • height of equivalent column of water, including millimetre (mm H
      2
      O
      ), centimetre (cm H
      2
      O
      ), metre, inch, and foot of water;
  • imperial and customary units:
  • non-SI metric units:
    • bar, decibar, millibar,
      • msw (metres sea water), used in underwater diving, particularly in connection with diving pressure exposure and decompression,
    • kilogram-force, or kilopond, per square centimetre (technical atmosphere),
    • gram-force and tonne-force (metric ton-force) per square centimetre,
    • barye (dyne per square centimetre),
    • kilogram-force and tonne-force per square metre,
    • sthene per square metre (pieze).

Examples

The effects of an external pressure of 700 bar on an aluminum cylinder with 5 mm (0.197 in) wall thickness

As an example of varying pressures, a finger can be pressed against a wall without making any lasting impression; however, the same finger pushing a thumbtack can easily damage the wall. Although the force applied to the surface is the same, the thumbtack applies more pressure because the point concentrates that force into a smaller area. Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. Unlike stress, pressure is defined as a scalar quantity. The negative gradient of pressure is called the force density.

Another example is a knife. If we try to cut with the flat edge, force is distributed over a larger surface area resulting in less pressure, and it will not cut. Whereas using the sharp edge, which has less surface area, results in greater pressure, and so the knife cuts smoothly. This is one example of a practical application of pressure.

For gases, pressure is sometimes measured not as an absolute pressure, but relative to atmospheric pressure; such measurements are called gauge pressure. An example of this is the air pressure in an automobile tire, which might be said to be "220 kPa (32 psi)", but is actually 220 kPa (32 psi) above atmospheric pressure. Since atmospheric pressure at sea level is about 100 kPa (14.7 psi), the absolute pressure in the tire is therefore about 320 kPa (46 psi). In technical work, this is written "a gauge pressure of 220 kPa (32 psi)". Where space is limited, such as on pressure gauges, name plates, graph labels, and table headings, the use of a modifier in parentheses, such as "kPa (gauge)" or "kPa (absolute)", is permitted. In non-SI technical work, a gauge pressure of 32 psi (220 kPa) is sometimes written as "32 psig", and an absolute pressure as "32 psia", though the other methods explained above that avoid attaching characters to the unit of pressure are preferred.

Gauge pressure is the relevant measure of pressure wherever one is interested in the stress on storage vessels and the plumbing components of fluidics systems. However, whenever equation-of-state properties, such as densities or changes in densities, must be calculated, pressures must be expressed in terms of their absolute values. For instance, if the atmospheric pressure is 100 kPa (15 psi), a gas (such as helium) at 200 kPa (29 psi) (gauge) (300 kPa or 44 psi [absolute]) is 50% denser than the same gas at 100 kPa (15 psi) (gauge) (200 kPa or 29 psi [absolute]). Focusing on gauge values, one might erroneously conclude the first sample had twice the density of the second one.

Scalar nature

In a static gas, the gas as a whole does not appear to move. The individual molecules of the gas, however, are in constant random motion. Because we are dealing with an extremely large number of molecules and because the motion of the individual molecules is random in every direction, we do not detect any motion. If we enclose the gas within a container, we detect a pressure in the gas from the molecules colliding with the walls of our container. We can put the walls of our container anywhere inside the gas, and the force per unit area (the pressure) is the same. We can shrink the size of our "container" down to a very small point (becoming less true as we approach the atomic scale), and the pressure will still have a single value at that point. Therefore, pressure is a scalar quantity, not a vector quantity. It has magnitude but no direction sense associated with it. Pressure force acts in all directions at a point inside a gas. At the surface of a gas, the pressure force acts perpendicular (at right angle) to the surface.

A closely related quantity is the stress tensor σ, which relates the vector force to the vector area via the linear relation .

This tensor may be expressed as the sum of the viscous stress tensor minus the hydrostatic pressure. The negative of the stress tensor is sometimes called the pressure tensor, but in the following, the term "pressure" will refer only to the scalar pressure.

According to the theory of general relativity, pressure increases the strength of a gravitational field (see stress–energy tensor) and so adds to the mass-energy cause of gravity. This effect is unnoticeable at everyday pressures but is significant in neutron stars, although it has not been experimentally tested.

Types

Fluid pressure

Fluid pressure is most often the compressive stress at some point within a fluid. (The term fluid refers to both liquids and gases – for more information specifically about liquid pressure, see section below.)

Water escapes at high speed from a damaged hydrant that contains water at high pressure

Fluid pressure occurs in one of two situations:

  1. An open condition, called "open channel flow", e.g. the ocean, a swimming pool, or the atmosphere.
  2. A closed condition, called "closed conduit", e.g. a water line or gas line.

Pressure in open conditions usually can be approximated as the pressure in "static" or non-moving conditions (even in the ocean where there are waves and currents), because the motions create only negligible changes in the pressure. Such conditions conform with principles of fluid statics. The pressure at any given point of a non-moving (static) fluid is called the hydrostatic pressure.

Closed bodies of fluid are either "static", when the fluid is not moving, or "dynamic", when the fluid can move as in either a pipe or by compressing an air gap in a closed container. The pressure in closed conditions conforms with the principles of fluid dynamics.

The concepts of fluid pressure are predominantly attributed to the discoveries of Blaise Pascal and Daniel Bernoulli. Bernoulli's equation can be used in almost any situation to determine the pressure at any point in a fluid. The equation makes some assumptions about the fluid, such as the fluid being ideal and incompressible. An ideal fluid is a fluid in which there is no friction, it is inviscid (zero viscosity). The equation for all points of a system filled with a constant-density fluid is

where:

p, pressure of the fluid,
= ρg, density × acceleration of gravity is the (volume-) specific weight of the fluid,
v, velocity of the fluid,
g, acceleration of gravity,
z, elevation,
, pressure head,
, velocity head.

Applications

Explosion or deflagration pressures

Explosion or deflagration pressures are the result of the ignition of explosive gases, mists, dust/air suspensions, in unconfined and confined spaces.

Negative pressures

Low-pressure chamber in Bundesleistungszentrum Kienbaum, Germany

While pressures are, in general, positive, there are several situations in which negative pressures may be encountered:

  • When dealing in relative (gauge) pressures. For instance, an absolute pressure of 80 kPa may be described as a gauge pressure of −21 kPa (i.e., 21 kPa below an atmospheric pressure of 101 kPa). For example, abdominal decompression is an obstetric procedure during which negative gauge pressure is applied intermittently to a pregnant woman's abdomen.
  • Negative absolute pressures are possible. They are effectively tension, and both bulk solids and bulk liquids can be put under negative absolute pressure by pulling on them. Microscopically, the molecules in solids and liquids have attractive interactions that overpower the thermal kinetic energy, so some tension can be sustained. Thermodynamically, however, a bulk material under negative pressure is in a metastable state, and it is especially fragile in the case of liquids where the negative pressure state is similar to superheating and is easily susceptible to cavitation. In certain situations, the cavitation can be avoided and negative pressures sustained indefinitely, for example, liquid mercury has been observed to sustain up to −425 atm in clean glass containers. Negative liquid pressures are thought to be involved in the ascent of sap in plants taller than 10 m (the atmospheric pressure head of water).
  • The Casimir effect can create a small attractive force due to interactions with vacuum energy; this force is sometimes termed "vacuum pressure" (not to be confused with the negative gauge pressure of a vacuum).
  • For non-isotropic stresses in rigid bodies, depending on how the orientation of a surface is chosen, the same distribution of forces may have a component of positive pressure along one surface normal, with a component of negative pressure acting along another surface normal.
    • The stresses in an electromagnetic field are generally non-isotropic, with the pressure normal to one surface element (the normal stress) being negative, and positive for surface elements perpendicular to this.
  • In cosmology, dark energy creates a very small yet cosmically significant amount of negative pressure, which accelerates the expansion of the universe.

Stagnation pressure

Stagnation pressure is the pressure a fluid exerts when it is forced to stop moving. Consequently, although a fluid moving at higher speed will have a lower static pressure, it may have a higher stagnation pressure when forced to a standstill. Static pressure and stagnation pressure are related by:

where

is the stagnation pressure,
is the density,
is the flow velocity,
is the static pressure.

The pressure of a moving fluid can be measured using a Pitot tube, or one of its variations such as a Kiel probe or Cobra probe, connected to a manometer. Depending on where the inlet holes are located on the probe, it can measure static pressures or stagnation pressures.

Surface pressure and surface tension

There is a two-dimensional analog of pressure – the lateral force per unit length applied on a line perpendicular to the force.

Surface pressure is denoted by π:

and shares many similar properties with three-dimensional pressure. Properties of surface chemicals can be investigated by measuring pressure/area isotherms, as the two-dimensional analog of Boyle's law, πA = k, at constant temperature.

Surface tension is another example of surface pressure, but with a reversed sign, because "tension" is the opposite to "pressure".

Pressure of an ideal gas

In an ideal gas, molecules have no volume and do not interact. According to the ideal gas law, pressure varies linearly with temperature and quantity, and inversely with volume:

where:

p is the absolute pressure of the gas,
n is the amount of substance,
T is the absolute temperature,
V is the volume,
R is the ideal gas constant.

Real gases exhibit a more complex dependence on the variables of state.

Vapour pressure

Vapour pressure is the pressure of a vapour in thermodynamic equilibrium with its condensed phases in a closed system. All liquids and solids have a tendency to evaporate into a gaseous form, and all gases have a tendency to condense back to their liquid or solid form.

The atmospheric pressure boiling point of a liquid (also known as the normal boiling point) is the temperature at which the vapor pressure equals the ambient atmospheric pressure. With any incremental increase in that temperature, the vapor pressure becomes sufficient to overcome atmospheric pressure and lift the liquid to form vapour bubbles inside the bulk of the substance. Bubble formation deeper in the liquid requires a higher pressure, and therefore higher temperature, because the fluid pressure increases above the atmospheric pressure as the depth increases.

The vapor pressure that a single component in a mixture contributes to the total pressure in the system is called partial vapor pressure.

Liquid pressure

When a person swims under the water, water pressure is felt acting on the person's eardrums. The deeper that person swims, the greater the pressure. The pressure felt is due to the weight of the water above the person. As someone swims deeper, there is more water above the person and therefore greater pressure. The pressure a liquid exerts depends on its depth.

Liquid pressure also depends on the density of the liquid. If someone was submerged in a liquid more dense than water, the pressure would be correspondingly greater. Thus, we can say that the depth, density and liquid pressure are directly proportionate. The pressure due to a liquid in liquid columns of constant density or at a depth within a substance is represented by the following formula:

where:

p is liquid pressure,
g is gravity at the surface of overlaying material,
ρ is density of liquid,
h is height of liquid column or depth within a substance.

Another way of saying the same formula is the following:

The pressure a liquid exerts against the sides and bottom of a container depends on the density and the depth of the liquid. If atmospheric pressure is neglected, liquid pressure against the bottom is twice as great at twice the depth; at three times the depth, the liquid pressure is threefold; etc. Or, if the liquid is two or three times as dense, the liquid pressure is correspondingly two or three times as great for any given depth. Liquids are practically incompressible – that is, their volume can hardly be changed by pressure (water volume decreases by only 50 millionths of its original volume for each atmospheric increase in pressure). Thus, except for small changes produced by temperature, the density of a particular liquid is practically the same at all depths.

Atmospheric pressure pressing on the surface of a liquid must be taken into account when trying to discover the total pressure acting on a liquid. The total pressure of a liquid, then, is ρgh plus the pressure of the atmosphere. When this distinction is important, the term total pressure is used. Otherwise, discussions of liquid pressure refer to pressure without regard to the normally ever-present atmospheric pressure.

The pressure does not depend on the amount of liquid present. Volume is not the important factor – depth is. The average water pressure acting against a dam depends on the average depth of the water and not on the volume of water held back. For example, a wide but shallow lake with a depth of 3 m (10 ft) exerts only half the average pressure that a small 6 m (20 ft) deep pond does. (The total force applied to the longer dam will be greater, due to the greater total surface area for the pressure to act upon. But for a given 5-foot (1.5 m)-wide section of each dam, the 10 ft (3.0 m) deep water will apply one quarter the force of 20 ft (6.1 m) deep water). A person will feel the same pressure whether their head is dunked a metre beneath the surface of the water in a small pool or to the same depth in the middle of a large lake. If four vases contain different amounts of water but are all filled to equal depths, then a fish with its head dunked a few centimetres under the surface will be acted on by water pressure that is the same in any of the vases. If the fish swims a few centimetres deeper, the pressure on the fish will increase with depth and be the same no matter which vase the fish is in. If the fish swims to the bottom, the pressure will be greater, but it makes no difference what vase it is in. All vases are filled to equal depths, so the water pressure is the same at the bottom of each vase, regardless of its shape or volume. If water pressure at the bottom of a vase were greater than water pressure at the bottom of a neighboring vase, the greater pressure would force water sideways and then up the narrower vase to a higher level until the pressures at the bottom were equalized. Pressure is depth dependent, not volume dependent, so there is a reason that water seeks its own level.

Restating this as energy equation, the energy per unit volume in an ideal, incompressible liquid is constant throughout its vessel. At the surface, gravitational potential energy is large but liquid pressure energy is low. At the bottom of the vessel, all the gravitational potential energy is converted to pressure energy. The sum of pressure energy and gravitational potential energy per unit volume is constant throughout the volume of the fluid and the two energy components change linearly with the depth. Mathematically, it is described by Bernoulli's equation, where velocity head is zero and comparisons per unit volume in the vessel are

Terms have the same meaning as in section Fluid pressure.

Direction of liquid pressure

An experimentally determined fact about liquid pressure is that it is exerted equally in all directions. If someone is submerged in water, no matter which way that person tilts their head, the person will feel the same amount of water pressure on their ears. Because a liquid can flow, this pressure isn't only downward. Pressure is seen acting sideways when water spurts sideways from a leak in the side of an upright can. Pressure also acts upward, as demonstrated when someone tries to push a beach ball beneath the surface of the water. The bottom of a boat is pushed upward by water pressure (buoyancy).

When a liquid presses against a surface, there is a net force that is perpendicular to the surface. Although pressure doesn't have a specific direction, force does. A submerged triangular block has water forced against each point from many directions, but components of the force that are not perpendicular to the surface cancel each other out, leaving only a net perpendicular point. This is why water spurting from a hole in a bucket initially exits the bucket in a direction at right angles to the surface of the bucket in which the hole is located. Then it curves downward due to gravity. If there are three holes in a bucket (top, bottom, and middle), then the force vectors perpendicular to the inner container surface will increase with increasing depth – that is, a greater pressure at the bottom makes it so that the bottom hole will shoot water out the farthest. The force exerted by a fluid on a smooth surface is always at right angles to the surface. The speed of liquid out of the hole is , where h is the depth below the free surface. This is the same speed the water (or anything else) would have if freely falling the same vertical distance h.

Kinematic pressure

is the kinematic pressure, where is the pressure and constant mass density. The SI unit of P is m2/s2. Kinematic pressure is used in the same manner as kinematic viscosity in order to compute the Navier–Stokes equation without explicitly showing the density .

Navier–Stokes equation with kinematic quantities

Equality (mathematics)

From Wikipedia, the free encyclopedia https://en.wikipedia.org/wiki/Equality_...