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1 - The Fundamentals of Hydrodynamics

from Part I - 1-D MHD in Ten Weeks

Published online by Cambridge University Press:  05 June 2025

David Alan Clarke
Affiliation:
Saint Mary's University, Nova Scotia
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Summary

This chapter begins with a formal definition of a fluid (what it means to be a continuum rather than an ensemble of particles) followed by a review of kinetic theory of gases where the connections between pressure and particle momentum and between specific energy (temperature) and average particle kinetic energy are made. A distinction is made between extensive and intensive variables, from which the Theorem of Hydrodynamics is postulated and proven. From this theorem, the basic equations of ideal hydrodynamics (zero-field limit of MHD) are derived including continuity, total energy equation, and the momentum equation. Alternate equations of HD such as the internal energy, pressure, and Euler’s equations are also introduced. The equations of HD are then assembled into two sets–conservative and primitive–with the distinction between the two explained.

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Publisher: Cambridge University Press
Print publication year: 2025

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