page_title: Prandtl–Glauert singularity
section_title: Prandtl–Glauert transformation
hierarchical_section_title: Prandtl–Glauert singularity / Prandtl–Glauert transformation
context_page_description: The Prandtl–Glauert singularity is a theoretical construct in flow physics, often incorrectly used to explain vapor cones in transonic flows.
  It 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. The incorrect association is related to the early-20th-century misconception of the impenetrability of the sound barrier.
context_section_description: 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:
  where
  cₚ is the compressible pressure coefficient
  cₚ₀ is the incompressible pressure coefficient
  M∞ is the freestream Mach number.
  This formula is known as "Prandtl's rule", and works well up to low-transonic Mach numbers  (M < ~0.7).  However, note the limit:
  This obviously nonphysical result (of an infinite pressure) is known as the Prandtl–Glauert singularity.
caption: Plot of the Prandtl–Glauert transformation as a function of Mach number.  Notice the infinite limit at Mach 1.
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