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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. | ||
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. | |||
The | 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. | ||
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> | |||
''[[ | ===Conditions under which gas flow becomes choked=== | ||
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: | |||
:<math>(1)</math> <font style="vertical-align:+15%;"><math>\big[(k+1)/2 \big]^{\,k/(k-1)}</math></font> | |||
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> ). | |||
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. | |||
''[[Choked flow|.... (read more)]]'' | |||
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Revision as of 07:09, 20 April 2012
Choked flow
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[1] into a lower pressure environment.
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.
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.
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.[2][3]
Conditions under which gas flow becomes choked
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:
![{\displaystyle {\big [}(k+1)/2{\big ]}^{\,k/(k-1)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/77260f95002ed270cad1fcf26435d242240c4d38)
where is the specific heat ratio of the discharged gas (sometimes called the isentropic expansion factor and sometimes denoted as ).
For many gases, 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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