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| {{hatnote|For the condensation cloud that forms around objects moving at transonic speeds, see [[vapor cone]].}}
| | Nice to meet you, I am Marvella Shryock. One of the things she loves most is to do aerobics and now she is attempting to make money with it. For many years he's been operating as a receptionist. California is exactly where I've always been living and I adore each day residing right here.<br><br>Here is my web site :: over the counter std test ([http://sanbird.com/xe/poll/149731 Home Page]) |
| {{Multiple issues|
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| {{technical|date=November 2011}}
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| {{expert-subject|date=November 2011}}
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| {{one source|date=November 2010}}
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| }}
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| [[File:FA-18_Hornet_breaking_sound_barrier_(7_July_1999).jpg|thumb|Example of a Jet producing a shockwave at transonic speeds. The Prandtl–Glauert singularity was incorrectly predicted to occur under these conditions. Jet [[F/A-18]].]]
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| The '''Prandtl–Glauert singularity''' is the prediction by the [[Prandtl–Glauert transformation]] that infinite pressures would be experienced by an aircraft as it approaches the [[speed of sound]]. Because it is invalid to apply the transformation at these speeds, the predicted singularity does not emerge. This is related to the early 20th century misconception of the impenetrability of the [[sound barrier]].
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| == Reasons of invalidity around Mach 1 ==
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| Near the sonic speed (''M=1'') the transformation features a [[mathematical singularity|singularity]], although this point is not within the area of validity. The singularity is also called the ''Prandtl–Glauert singularity'', and the aerodynamic forces are calculated to approach infinity. In reality, the aerodynamic and thermodynamic perturbations do get amplified strongly near the sonic speed, but they remain finite and a singularity does not occur. An explanation for this is that the Prandtl–Glauert transformation is a linearized approximation of compressible, inviscid potential flow. As the flow approaches sonic speed, the nonlinear phenomena dominate within the flow, which this transformation completely ignores for the sake of simplicity.
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| == Prandtl-Glauert transformation ==
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| {{Main|Prandtl–Glauert transformation}}
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| [[File:Prandtl-glauert-transform.png|thumb|Plot of the [[Prandtl-Glauert transformation]] as a function of [[Mach number]]. Notice the infinite limit at Mach 1.]]
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| The Prandtl-Glauert transformation is found by linearizing the potential equations associated with compressible, inviscid flow. For two-dimensional flow, the linearized pressures in such a flow are equal to those found from incompressible flow theory multiplied by a correction factor. This correction factor is given below:<ref>Erich Truckenbrodt: Fluidmechanik Band 2, 4. Auflage, Springer Verlag, 1996, p. 178-179
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| </ref>
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| :<math>c_{p} = \frac {c_{p0}} {\sqrt {|1-{M_{\infty}}^2|}}</math>
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| where | |
| * c<sub>p</sub> is the compressible [[pressure coefficient]]
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| * c<sub>p0</sub> is the [[incompressible]] [[pressure coefficient]]
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| * ''M<sub>∞</sub>'' is the freestream Mach number.
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| This formula is known as "Prandtl's rule", and works well up to low-transonic Mach numbers (M < ~0.7). However, note the limit:
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| <math>\lim_{M_{\infty} \to 1 }c_p = \infty</math> | |
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| This obviously nonphysical result (of an infinite pressure) is known as the Prandtl–Glauert singularity.
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| ==See also==
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| * [[Prandtl-Glauert transformation]]
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| * [[Compressible flow]]
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| * [[Sonic boom]]
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| == References ==
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| {{reflist}}
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| {{DEFAULTSORT:Prandtl-Glauert singularity}}
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| [[Category:Aerodynamics]]
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| [[Category:Physical phenomena]]
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| [[Category:Shock waves]]
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Nice to meet you, I am Marvella Shryock. One of the things she loves most is to do aerobics and now she is attempting to make money with it. For many years he's been operating as a receptionist. California is exactly where I've always been living and I adore each day residing right here.
Here is my web site :: over the counter std test (Home Page)