Abstract
In the first chapter we introduced the perfect fluid as a fluid that does not conduct heat and for which the fluid elements interact only through pressure.
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Notes
- 1.
On condition, of course, that the functions are continuous, i.e. that the fluid particles do not cross a shock wave.
- 2.
H. Pitot (1695–1771) was a French physicist who invented this device around 1732 in order to measure the velocity of water in a river or the speed of a ship.
- 3.
That are paths which cannot be reduced from one to the other by a continuous deformation within the space occupied by the fluid or, equivalently, the surface bounded by the two paths does not belong entirely to this space.
- 4.
A harmonic function is a solution of Laplace’s equation.
- 5.
We just need to project the equation on Legendre’s polynomials and to use their orthogonality with respect to the scalar product \(\int _{0}^{\pi }P_{\ell}(\cos \theta )P_{k}(\cos \theta )d\cos \theta \propto \delta _{\ell k}\).
- 6.
Point on the solid where the fluid’s velocity is zero.
- 7.
This condition was also found independently by Joukovski in 1906 and is also called sometimes Joukovski’s Condition.
References
Batchelor, G. K. (1967). An introduction to fluid dynamics. Cambridge: Cambridge University Press.
Magarvey, R. & MacLatchy, C. (1964) The formation and structure of vortex rings Can. J. Phys. 42, 678–683
Saffman, P. (1992). Vortex dynamics. Cambridge: Cambridge University Press.
Ting, L., & Klein, R. (1991). Viscous vortical flows. Lecture Notes in Physics. Berlin: Springer.
Zeytounian, R. (1991). Mécanique des fluides fondamentale. Lecture Notes in Physics. Berlin: Springer.
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Rieutord, M. (2015). Flows of Perfect Fluids. In: Fluid Dynamics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-09351-2_3
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DOI: https://doi.org/10.1007/978-3-319-09351-2_3
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