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MATHEMATICAL CONSIDERATION For a volume of a fluid which is not in motion, Newton's Laws state that it must have zero net force on it - the forces up must equal the forces down. For a Cuboid volume element of a fluid, the force downwards on the top of the fluid from the Pressure , P, of the fluid above it on the top surface area of the volume element, A, is : And on the volume element from the fluid below is : The minus sign comes from the directon: this force supports the volume element, rather than pull it down. Finally, the Weight of the volume element must be considered. If the density is ρ, the volume V and the Acceleration Due To Gravity g, then: : We can split volume into the area of the top or bottom, times the height. : By balancing these forces: : This is zero if the gas isn't moving. If we divide by A, : Or, : By saying that the change in h is very small, which means the change in P is very small, we can write this in Differential notation: : Points to note:
APPLICATIONS Fluids The ''Hydrostatic equilibrium'' pertains to Hydrostatics and the Principles Of Equilibrium of Fluid s. A Hydrostatic Balance is a particular balance for weighing substances in water. Hydrostatic balance allows the Discovery of their Specific Gravities . Physics In . In Physics , Hydrostatic equilibrium also explains why Earth 's atmosphere does not collapse to a very thin layer on the ground and how the Tyre s on a car or bicycle are able to support the weight of the vehicle. SEE ALSO REFERENCE Strobel, Nick. (May, 2001). Nick Strobel's Astronomy Notes. |
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