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| == '''[[Choked flow]]''' ==
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| The '''choked flow''' (often referred to as '''critical flow''') of a flowing [[gas]] is a limiting point which occurs under specific conditions when a gas at a certain [[pressure]] and [[temperature]] flows through a restriction<ref>A [[valve]], a [[convergent-divergent nozzle]] such as a [[de Laval nozzle]], an [[orifice plate]] hole, a leak in a gas pipeline or other gas container, a [[rocket engine]] exhaust nozzle, etc.</ref> into a lower pressure environment.
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| As the gas flows through the smaller cross-sectional area of the restriction, its linear [[velocity]] must increase. The limiting point is reached when the linear gas velocity increases to the [[speed of sound]] ([[sonic velocity]]) in the gas. At that point, the [[mass]] flow rate (mass per unit of time) of the gas becomes independent of the downstream pressure, meaning that the mass flow rate can not be increased any further by further lowering of the downstream pressure. The physical point at which the choking occurs (i.e., the cross-sectional area of the restriction) is sometimes called the ''choke plane''. It is important to note that although the gas velocity becomes choked, the mass flow rate of the gas can still be increased by increasing the upstream pressure or by decreasing the upstream temperature.
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| The choked flow of gases is useful in many engineering applications because, under choked conditions, valves and calibrated orifice plates can be used to produce a particular mass flow rate. Choked flow in a [[de Laval nozzle]] as used in a [[rocket engine]] can be accelerated to [[supersonic]] linear velocities.
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| In the case of liquids, a different type of limiting condition (also known as choked flow) occurs when the [[Venturi effect]] acting on the liquid flow through the restriction decreases the liquid pressure to below that of the liquid [[vapor pressure]] at the prevailing liquid temperature. At that point, the liquid will partially "flash" into bubbles of vapor and the subsequent collapse of the bubbles causes [[cavitation]]. Cavitation is quite noisy and can be sufficiently violent to physically damage valves, pipes and associated equipment. In effect, the vapor bubble formation in the restriction limits the flow from increasing any further.<ref>[http://www.fisherregulators.com/technical/sizingcalculations/ Scroll to discussion of liquid flashing and cavitation]</ref><ref>[http://www.documentation.emersonprocess.com/groups/public/documents/book/cvh99.pdf Search document for "Choked"]</ref>
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| ===Conditions under which gas flow becomes choked===
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| All gases flow from upstream higher pressure sources to downstream lower pressure environments. Choked flow occurs when the ratio of the absolute upstream pressure to the absolute downstream pressure is equal to or greater than:
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| :<math>(1)</math> <font style="vertical-align:+15%;"><math>\big[(k+1)/2 \big]^{\,k/(k-1)}</math></font>
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| where <math>k</math> is the [[specific heat ratio]] of the discharged gas (sometimes called the [[isentropic expansion factor]] and sometimes denoted as <math>\gamma</math> ).
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| For many gases, <math>k</math> ranges from about 1.09 to about 1.41, and therefore the expression in '''(1)''' ranges from 1.7 to about 1.9, which means that choked velocity usually occurs when the absolute upstream vessel pressure is at least 1.7 to 1.9 times as high as the absolute downstream pressure.
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| ''[[Choked flow|.... (read more)]]''
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| {| class="wikitable collapsible collapsed" style="width: 90%; float: center; margin: 0.5em 1em 0.8em 0px;"
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| ! style="text-align: center;" | [[Choked flow#References|notes]]
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| {{reflist|2}} | | {{reflist|2}} |
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| | </small> |
Latest revision as of 10:19, 11 September 2020
Napoleon (Napoleon Bonaparte or, after 1804, Napoleon I, Emperor of the French) was a world historic figure and dictator of France from 1799 to 1814. He was the greatest general of his age--perhaps any age, with a sure command of battlefield tactics and campaign strategies, As a civil leader he played a major role in the French Revolution, then ended it when he became dictator in 1799 and Emperor of France in 1804 He modernized the French military, fiscal, political legal and religious systems. He fought an unending series of wars against Britain with a complex, ever-changing coalition of European nations on both sides. Refusing to compromise after his immense defeat in Russia in 1812, he was overwhelmed by a coalition of enemies and abdicated in 1814. In 1815 he returned from exile, took control of France, built a new army, and in 100 days almost succeeded--but was defeated at Waterloo and exiled to a remote island. His image and memory are central to French national identity, but he is despised by the British and Russians and is a controversial figure in Germany and elsewhere in Europe.
Rise to Power
Once the Revolution had begun, so many of the aristocratic officers turned against the Revolutionary government, or were exiled or executed, that a vacuum of senior leadership resulted. Promotions came very quickly now, and loyalty to the Revolution was as important as technical skill; Napoleon had both. His demerits were overlooked as he was twice reinstated, promoted, and allowed to collect his back pay. Paris knew him as an intellectual soldier deeply involved in politics. His first test of military genius came at Toulon in 1793, where the British had seized this key port. Napoleon, an acting Lieutenant-Colonel, used his artillery to force the British to abandon the city. He was immediately promoted by the Jacobin radicals under Robespierre to brigadier-general, joining the ranks of several brilliant young generals. He played a major role in defending Paris itself from counter-revolutionaries, and became the operational planner for the Army of Italy and planned two successful attacks in April 1794. He married Josephine (Rose de Beauharnais) in 1796, after falling violently in love with the older aristocratic widow.[1]
- ↑ Englund pp 63-73, 91-2, 97-8
