By R. J. Knops
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Extra resources for Nonlinear Analysis & Mechanics: Heriot-Watt Symposium, Volume II (Research Notes in Mathematics)
Example text
Taylor and Walton, London (1807) Chapter 2 Hydrostatics 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.
23); because the two reference points are at the same height, their pressures are the same so, ρgh 1 = ρgh 2 ⇒ h1 = h2. 25) In other words: a density preserving fluid in two communicating vessels is only in equilibrium, if both free surfaces are at the same level. Incidentally, this argument can easily be extended to a whole series of communicating vessels. 4 To explain it, consider Fig. 10, in which three vessels, symmetric to their mid plumb line and with the same basal surface but different volumes are shown.
4 Pressure Distribution in a Density Preserving Heavy Fluid 27 Fig. 7 Force onto a wall of a container. Arbitrary vessel with surface element d A and exterior unit normal vector n of the wall of the vessel. The pressure inside is given by p, that outside is given by p0 d Fig. 8 Communicating vessel. In a communicating vessel the free surfaces of its arms are at the same height The resultant of the elementary pressure forces acting on a given partial area A is obtained by reducing all these forces to a single force and possibly a moment in an arbitrary point.