Defining local pressures is pivotal to understanding phenomena such as buoyancy and atmospheric physics, which always require space-varying pressure fields to be considered. Such fields have precise definitions within the frameworks of hydro-thermodynamics and the kinetic theory of gases, but a pedagogical approach based on standard statistical mechanics techniques is still lacking. In this paper, we propose a new microscopic definition of local pressure inside a classical fluid, relying upon a local barometer potential that is built into the many-particle Hamiltonian. This setup allows pressure to be locally defined as an ensemble average of the radial force exerted by the barometer potential on the gas' particles. Moreover, this same framework is also employed in a microscopic derivation of buoyancy of immersed bodies in the presence of arbitrary external fields. As instructive examples, buoyant forces are calculated for ideal fluids in the presence of a uniform force field, in the presence of a spherical harmonic confinement field and in rotation with a constant angular velocity.
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March 2022
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March 01 2022
A new microscopic look into pressure fields and local buoyancy
S. Meneses João
;
S. Meneses João
a)
Centro de Física das Universidades do Minho e Porto and Faculty of Sciences, University of Porto
, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
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J. P. Santos Pires
;
J. P. Santos Pires
Centro de Física das Universidades do Minho e Porto and Faculty of Sciences, University of Porto
, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
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J. M. Viana Parente Lopes
J. M. Viana Parente Lopes
b)
Centro de Física das Universidades do Minho e Porto and Faculty of Sciences, University of Porto
, Rua do Campo Alegre 687, 4169-007 Porto, Portugal
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a)
Electronic mail: simao.joao@fc.up.pt
b)
Electronic mail: jlopes@fc.up.pt
Am. J. Phys. 90, 179–186 (2022)
Article history
Received:
June 18 2021
Accepted:
January 12 2022
Citation
S. Meneses João, J. P. Santos Pires, J. M. Viana Parente Lopes; A new microscopic look into pressure fields and local buoyancy. Am. J. Phys. 1 March 2022; 90 (3): 179–186. https://doi.org/10.1119/5.0060479
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