Many of the fundamental pieces of calculus are related to fluid mechanics: total derivative, gradient, divergence, and rotation, among others. This chapter explores this connection and the application of differential operators in fluid mechanics. Before deriving the important continuity and Navier‐Stokes equations, the chapter considers a mathematical tool necessary in the Eulerian description of fluid flows. The Nabla operator is very useful in fluid mechanics because it significantly simplifies notation and makes the meaning of individual terms more transparent; however, by itself it has no physical meaning. The rotation of the velocity vector plays an important role in the definition of potential flows and finds application in lifting flows. The linear, homogeneous, second order partial differential equation forms the foundation of potential theory. The Laplace equation expresses conservation of mass for potential flow, a specific class of inviscid flows. Besides fluid mechanics, potential theory is also used in the field of magneto‐electrodynamics.
Fluid Mechanics and Calculus
2019-05-06
9 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
SPECIAL SECTION: THEORETICAL FLUID MECHANICS - Theoretical Fluid Mechanics
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