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| [[Image:Prandtl meyer function.png|thumb|300px|Varition in the Prandtl–Meyer function (<math>\nu</math>) with Mach number (<math>M</math>) and ratio of specific heat capacity (<math>\gamma</math>). The dashed lines show the limiting value <math> \nu_\text{max} </math> as Mach number tends to infinity.]] | | Friends contact her Claude Gulledge. One of extended auto [http://www.dmv.org/buy-sell/auto-warranty/extended-warranty.php warranty] the issues I love car warranty most is greeting card gathering but [http://www.consumerreports.org/cro/magazine/2014/04/extended-warranties-for-cars-are-an-expensive-game/ I don't] have the time recently. The occupation I've been occupying for years is a bookkeeper but I've already applied for another 1. I presently reside in Arizona but [http://der-erste-clan.de/index.php?mod=users&action=view&id=11094 auto warranty] now I'm contemplating other options.<br><br>Also visit my page - [http://sociallyunitingnetworks.de/index.php?mod=users&action=view&id=14420 extended car warranty] ([http://demonknights.madrealms.net/index.php?mod=users&action=view&id=13883 what google did to me]) |
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| '''Prandtl–Meyer function''' describes the angle through which a flow can turn [[Isentropic process#Isentropic flow|isentropically]] for the given initial and final [[Mach number]]. It is the maximum angle through which a sonic ([[Mach number|M]] = 1) flow can be turned around a convex corner. For an [[ideal gas]], it is expressed as follows,
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| : <math>\begin{align} \nu(M)
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| & = \int \frac{\sqrt{M^2-1}}{1+\frac{\gamma -1}{2}M^2}\frac{\,dM}{M} \\
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| & = \sqrt{\frac{\gamma + 1}{\gamma -1}} \cdot \arctan \sqrt{\frac{\gamma -1}{\gamma +1} (M^2 -1)} - \arctan \sqrt{M^2 -1} \\
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| \end{align} </math>
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| where, <math>\nu \,</math> is the Prandtl–Meyer function, <math>M</math> is the Mach number of the flow and <math>\gamma</math> is the [[heat capacity ratio|ratio of the specific heat capacities]].
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| By convention, the constant of integration is selected such that <math>\nu(1) = 0. \,</math>
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| As Mach number varies from 1 to <math>\infty</math>, <math>\nu \,</math> takes values from 0 to <math>\nu_\text{max} \,</math>, where
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| : <math>\nu_\text{max} = \frac{\pi}{2} \bigg( \sqrt{\frac{\gamma+1}{\gamma-1}} -1 \bigg)</math>
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| {|
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| |-
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| |For isentropic expansion,
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| |<math>\nu(M_2) = \nu(M_1) + \theta \,</math>
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| |-
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| |For isentropic compression,
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| |<math>\nu(M_2) = \nu(M_1) - \theta \,</math>
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| |-
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| |}
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| where, <math>\theta </math> is the absolute value of the angle through which the flow turns, <math>M</math> is the flow Mach number and the suffixes "1" and "2" denote the initial and final conditions respectively.
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| == See also == | |
| * [[Gas dynamics]]
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| * [[Prandtl–Meyer expansion fan]]
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| == References ==
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| * {{cite book
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| | last = Liepmann | first = Hans W. | coauthors = Roshko, A.
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| | title = Elements of Gasdynamics | origyear = 1957
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| | publisher = [[Dover Publications]] | year = 2001
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| | isbn = 0-486-41963-0 }}
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| {{DEFAULTSORT:Prandtl-Meyer function}}
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| [[Category:Aerodynamics]]
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| [[Category:Fluid dynamics]]
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| {{fluiddynamics-stub}}
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