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Fluid statics

31 bytes added, 14:13, 19 December 2016
Tidied up maths formatting
===Pressure variation in a static Fluid===
Applying [[Isaac Newton|Newton]]'s [[Newton's Laws of Motion|laws of motions]] to a fluid at rest, it can be determined that the sum of forces must equal zero throughout the fluid, which means any arbitrary element of the fluid is subjected to forces that sums to zero. Since the fluid is not deforming while it is at rest, the only forces acting on the fluid are those due to gravity and pressure.
:<math>\rho\mathbf{g} =\nabla P</math>
where <math>\rho</math> is the density of the fluid, '''<math>g''' </math> is the gravitational acceleration (vector), and <math>P </math> is the pressure at the fluid element.
For small changes in altitude, '''<math>g''' </math> can be assumed to be constant (A more accurate description for large change in altitude can be found [[Gravitation|here]]). Simplifications can also be made for constant [[density]], and reducing the analysis to only the y dimension:
:<math>P-P_0=\rho g\left( y-y_0\right)</math>