Abstract
Our goal is to present a very brief introduction to the basics of Hydrodynamics. Namely, we will introduce the notions of ideal fluid, Pascal’s law and the continuity equation. Furthermore, we shall obtain Euler’s equation as an analog of Newton’s second law for the ideal fluid and consider some consequences, such as Bernoulli’s equation, which can be seen as the continuous version of energy conservation. Finally, we will discuss the equation for sound waves, representing a propagating perturbation of density and pressure.
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Notes
- 1.
This problem was already considered in Chap. 3, but here we treat it in a little bit different way.
- 2.
In this chapter we will denote all multiple integrals by a unique symbol, as is common in Physics literature. For example, a volume integral is \(\int \limits _{(V )}\rho dV\) instead of \(\int\int\int \limits _{(V )}\rho dV\).
- 3.
References
G.K. Batchelor, An Introduction to Fluid Dynamics (Cambridge Mathematical Library, Cambridge University Press,Cambridge/New York, 2000)
R.A. Granger, Fluid Mechanics. Dover Books on Physics (Dover, New York, 1995)
L.D. Landau, E.M. Lifshitz, Hydrodynamics. Course of Theoretical Physics Series, vol. 6, 2nd edn. (Butterworth-Heinemann, 1987)
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Shapiro, I.L., de Berredo-Peixoto, G. (2013). Basic Notions of Hydrodynamics. In: Lecture Notes on Newtonian Mechanics. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7825-6_10
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DOI: https://doi.org/10.1007/978-1-4614-7825-6_10
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