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General relationships between pressure, weight and mass of a hydrostatic fluid
 

Summary: General relationships between pressure,
weight and mass of a hydrostatic fluid
BY MAARTEN H. P. AMBAUM*
Department of Meteorology, University of Reading, PO Box 243,
Reading RG6 6BB, UK
In curved geometries the hydrostatic pressure in a fluid does not equal the weight per
unit area of the fluid above it. General weight­pressure and mass­pressure relationships
for hydrostatic fluids in any geometry are derived. As an example of the mass­pressure
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.
Keywords: hydrostatic pressure; fluid dynamics; atmospheric science
1. Introduction
The textbook definition of the hydrostatic pressure p0 in terms of the weight W
or the mass M of the fluid aloft, per unit surface area A0, is
p0 Z
W
A0
Z

  

Source: Ambaum, Maarten - Department of Meteorology, University of Reading

 

Collections: Geosciences