General relationships between pressure, weight, and mass of a hydrostatic fluid
Ambaum, M. H.P. (2008) General relationships between pressure, weight, and mass of a hydrostatic fluid. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464 (2092). pp. 943-950. ISSN 1364-5021
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To link to this article DOI: 10.1098/rspa.2007.0148
In curved geometries the hydrostatic pressure in a fluid does not equal the weight per unit area of the fluid above it. General weight–pressure and mass–pressure relationships for hydrostatic fluids in any geometry are derived. As an example of the mass–pressure relationship, we find a geometric reduction in surface pressure as large as 5 mbar on Earth and 39 mbar on Titan. We also present a thermodynamic interpretation of the geometric correction which, as a corollary, provides an independent proof of the hydrostatic relationship for general geometries.
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