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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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| ! 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 09:19, 11 September 2020
Paramhansa Yogananda circa 1920.
Paramhansa Yogananda (5 Jan 1893–7 Mar 1952) was one of the first Indian teachers from the Hindu spiritual tradition to reside permanently in the West, and in particular, he was the first to teach yoga to Americans. He emphasized the universality of the great religions, and ceaselessly taught that all religions, especially Hinduism and Christianity, were essentially the same in their essence. The primary message of Yogananda was to practice the scientific technique of kriya yoga to be released from all human suffering.
He emigrated from India to the United States in 1920 and eventually founded the Self-Realization Fellowship there in Los Angeles, California. He published his own life story in a book called Autobiography of a Yogi, first published in 1946. In the book, Yogananda provided some details of his personal life, an introduction to yoga, meditation, and philosophy, and accounts of his world travels and encounters with a wide variety of saints and colorful personalities, including Therese Neumann, Mohandas K. Gandhi, Luther Burbank, and Jagadis C. Bose.
Paramhamsa, also spelled Paramahamsa, is a Sanskrit title used for Hindu spiritual teachers who have become enlightened. The title of Paramhansa originates from the legend of the swan. The swan (hansa) is said to have a mythical ability to sip only the milk from a water-and-milk mixture, separating out the more watery part. The spiritual master is likewise said to be able to live in a world like a supreme (param) swan, and only see the divine, instead of all the evil mixed in there too, which the worldly person sees.
Yogananda is considered by his followers and many religious scholars to be a modern avatar.
In 1946, Yogananda published his Autobiography of a Yogi. It has since been translated into 45 languages, and in 1999 was designated one of the "100 Most Important Spiritual Books of the 20th Century" by a panel of spiritual authors convened by Philip Zaleski and HarperCollins publishers.
Awake: The Life of Yogananda is a 2014 documentary about Paramhansa Yogananda, in English with subtitles in seventeen languages. The documentary includes commentary by George Harrison and Ravi Shankar, among others.[1][2]
