I am trying to decipher if an error occurred in a calculation given in this paper.(adsbygoogle = window.adsbygoogle || []).push({});

It is understandable that if two compressible fluids of different uniform densities have a common interface (e.g. Figure 1), then to be in equilibrium and supported against gravity, there must be a pressure gradient across the boundary of the two fluids. Thus on either side of the boundary is a different pressure (i.e. pressure discontinuity). Based on reading the authors' assumptions, each fluid has a constant density and pressure (and thus sound speed) at equilibrium, but these values differ between the two fluids. Using simply (16) from the paper, I have calculated that the pressure difference across the boundary in equilibrium is given by: ##p_2 - p_1 = \frac {c^2}{4}(\rho_{01} - \rho_{02}) > 0## (where ##g## is a constant acceleration given by a static field) and thus non-zero.

In the paper, the authors solve the problem and essentially derive equations (21) and (25) which are evaluated on either side of the boundary. When plugging (21) into (25), what I fail to understand is why the pressure can be taken outside of the summation/difference across the boundary as indicated in (26)? They now treat the pressure, ##p##, as a given value yet it only has meaning on either side of the boundary as ##p_1## or ##p_2## to my knowledge. Thus is there an error in the paper? What is the definition of this ##p##? In the ensuing equations, the authors distinguish between the densities on either side of the boundary (i.e. ##\rho_{01}## and ##\rho_{02}##), but make no such distinctions about the pressure, which is now simply ##p## instead of ##p_1## and/or ##p_2## and I am failing to recognize the obvious reason(s) why.

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# A Boundary conditions errantly applied to pressure across flui

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