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Inside this Book – This means that we are missing one equation, which is coming with the last conservation principle, namely the conservation of energy (iii). The absence of heat exchange between the different parts of the fluid implies that the motion is adiabatic: thus the motion of an ideal fluid is by definition considered as adiabatic. In other words, the entropy of any fluid particle remains constant as that particle moves in space inside the fluid. We label the entropy per unit mass as s. We can easily write the condition for an adiabatic motion as:

Inside this book –**Lecture notes in fluid mechanics From basics to the millennium problem PDF Book **by Laurent Schoeffel – We continue the argument assuming the flow is steady. We consider a steady flow past a material body with the much reasonable hypothesis that the incident flow is uniform at infinity. This means that its velocity is constant at infinity, and thus its vorticity is zero at infinity. Following the previous statement, we conclude that the vorticity is zero along all streamlines and thus in all space. In fact, this is not exactly correct as the proof that vorticity is zero along a streamline is invalid for a line which lies on the surface of the solid body, since the presence of the surface makes it impossible to draw a closed contour encircling such a streamline! Of course, the physical problem of flow past a given body has a well-defined solution. The key point is that ideal fluids do not really exist: any real fluid has a certain viscosity, even small.

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## Lecture notes in fluid mechanics From basics to the millennium problem by Laurent Schoeffel PDF : eBook Information

**Full Book Name**– Lecture notes in fluid mechanics From basics to the millennium problem**Author of this Book**– Laurent Schoeffel**Language –**English**Book Genre –**Non Fiction, Novel, mechanics, millennium,**Download Format –**PDF**Size**– 950 KB**eBook Pages –**67**Price –**Free

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