Abstract
This chapter of the book introduces the basic elements of fluid mechanics constituting the essential background for understanding the blood flow phenomena in the cardiovascular system. It discusses the physics of flow and its implications. This chapter is aimed to provide an intuitive understanding, accompanied by an essential mathematical formulation that ensures a rigorous reference ground.
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Notes
- 1.
The generalization of equations in three dimensions often makes use of the vector-operator Ñ, called nabla, for simpler compact writing. Nabla is a three-component derivative operator that can be seen as a vector of derivatives whose components in Cartesian coordinates, are given by [∂/∂x, ∂/∂y, ∂/∂z].
- 2.
This equation is also valid in presence of gravity (or any other conservative force).
- 3.
This intuitive result is somehow simplified: the viscous term should include variations along all directions about the streamline. In particular for three-dimensional flow, it should include the other direction perpendicular to both the streamline and to n. It was simplified here to avoid unnecessary symbolic complications.
References
Fung YC. Biomechanics: circulation. New York: Springer; 1997.
Panton RL. Incompressible flow. 3rd ed. Hoboken: Wiley; 2005.
Pedley TJ. The fluid mechanics of large blood vessels. Cambridge: Cambridge University Press; 1980.
Schlichting H, Gersten K. Boundary layer theory. 8th ed. Berlin Heidelberg: Springer; 2000.
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Kheradvar, A., Pedrizzetti, G. (2012). Fundamental Fluid Mechanics. In: Vortex Formation in the Cardiovascular System. Springer, London. https://doi.org/10.1007/978-1-4471-2288-3_1
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DOI: https://doi.org/10.1007/978-1-4471-2288-3_1
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