a elliptical cylinder in a constant flow. Then a coordinate transform to cylindrical coordinates would effectively give a circle in a constant flow. This has now reduced to a problem that has been significantly studied in fluid dynamics.

The transform described above is a conformal transform of the coordinate system. In an incompressible regime, such a conformal transform would automatically give the correct result, but in a compressible regime, where nonlinearity is important, the velocity will not be completely accurate. The smaller the eccentricity and the fast-mode Mach number, the more accurate the coordinate transform will be.

Derivation of equations to determine a prominence’s plasma $\beta$
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Here we use a classic result from fluid dynamics to define a set of equations that can be used to interpret prominence observations and determine physical parameters relating to that prominence. First, we describe the thought process behind the method, followed by a derivation of the equations used to determine the plasma $\beta$ of the prominence.

The derivation presented here is analogous to that presented in @VD1975 for a compressible flow around a circular cylinder in a steady state. Here the derivation is altered to include a magnetic field that is perpendicular to 