Abstract
Fluid pressure is introduced based on the formulation of the equilibrium equations (force and moment balances). This gives rise to the introduction of body and surface specific forces and the definition of normal shear tractions on surfaces. Liquids in equilibrium are based on the assumption that shear tractions vanish, which, through the equilibrium conditions, yield a unique definition of the concept of ‘hydrostatic pressure’. This leads, naturally, to the fundamental equation of hydrostatics, which subsequently is applied to various examples of density preserving liquids: among these are communicating vessels, Pascal’s paradoxon, manometers, hydraulic heavers, buoyancy and stability of floating bodies. Two sections extend this to hydrostatics in accelerated reference systems and pressure distribution in a still atmosphere.
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- 1.
It is assumed that the reader is familiar with the concepts of the mechanics of rigid bodies as commonly taught in elementary mechanics courses at universities in compendia treating ‘statics, dynamics and strength of materials’.
- 2.
Traction is equivalent to vector. At a surface element the traction is decomposed into normal traction and shear traction.
- 3.
Jean le Rond d’Alembert (1717–1783), mathematician, physicist and philosopher. In mechanics he is best known for his principle, according to which mass times acceleration can be replaced by the inertial force as stated above.
- 4.
Blaise Pascal (1623–1662), French mathematician and physicist. He is known for his paradox and the ‘Pascal triangle’. For his short biography see Fig. 2.9
- 5.
Note \(I_{\xi _1}\) for a circle is half of the polar moment of inertia, which is given by \(I_{0} = \int _{A}r^{2}r\mathrm {d}r\mathrm {d}\phi = 2\pi \int _{A}r^{3}\mathrm {d}r = {\frac{1}{2}}\pi \,r^{4} \).
- 6.
Archmedes (\(\sim \)287 B.C.–212 B.C.) ancient Greek mathematician, physicist and engineer, founder of hydrostatic and geometric statics. For his short biography see Fig. 2.19 .
- 7.
The computations for this example are a bit involved. In a first reading a reader may wish to simply concentrate on the physical implications of the computations.
- 8.
In the English literature \({\varvec{v}}_{f}\) is not separately defined; it is that rigid body velocity, which agrees in each body point with the velocity of the same geometric point that performs the motion of the accelerated reference frame.
Reference
Fachlexikon: Forscher und Erfinder. 3. Auflage. Harri Deutsch Verlag, Thun-Frankfurt (1992)
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© 2016 Springer International Publishing Switzerland
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Hutter, K., Wang, Y. (2016). Hydrostatics. In: Fluid and Thermodynamics. Advances in Geophysical and Environmental Mechanics and Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-33633-6_2
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DOI: https://doi.org/10.1007/978-3-319-33633-6_2
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