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The Prandtl–Glauert transformation or Prandtl–Glauert rule (also Prandtl–Glauert–Ackeret rule) is an approximation function which allows to compare aerodynamical processes occurring at different Mach numbers.
## Mathematical expression

## History

## Singularity

## References

Even in subsonic flow the compressibility of the fluid (often air) is getting more and more influential with increasing velocity. Thus characteristic values of the flow can be multiplied with a correction factor to account for this influence; this is called the Prandtl–Glauert transformation. As an example following equation shows this for the pressure coefficient c_{p}, given as a function of the c_{p0} of an incompressible flow and the Mach number M :

- $c\_\{p\}\; =\; frac\; \{c\_\{p0\}\}\; \{sqrt$
>}

The equation is not valid for velocities between M=0.7 and M=1.3.

Ludwig Prandtl had been teaching this transformation in his lectures for a while, however the first publication was in 1928 by Hermann Glauert. The introduction of this relation allowed the design of aircraft which were able to operate in higher subsonic speed areas . Subsequently the equation was extended by Jakob Ackeret to the common form used today, which is also valid in the supersonic region.

Near the sonic speed (M=1) the discussed equation features a singularity, although this point is not within the area of validity. The singularity is also called the Prandtl–Glauert singularity, and the flow resistance is approaching infinity here. In reality aerodynamic and thermodynamic perturbations get amplified strongly near the sonic speed, however a singularity does not occur.

Besides this the theoretical singularity is often - however not correctly – used to explain phenomena near the sonic speed, e.g. see Prandtl–Glauert singularity.

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Last updated on Friday October 10, 2008 at 18:57:28 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Friday October 10, 2008 at 18:57:28 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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