 
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
