Statics Reference

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    Hydrostatic Fluid Pressure

    Pascal's Law: A fluid at rest creates a pressure point p at a point that is the same in all directions.

    Fluid Pressure

    For an incompressible fluid (density \( \rho \)) at rest, the pressure \( p \) varies linearly with fluid depth \( z \). This means that the pressure along a horizontal plane (at a certain depth \( z \) is constant.
    Derivation of the pressure \( P(z) \) at the bottom of a cylinder of liquid with cross-sectional area \( A \)
    The fluid pressure \( P(z) \) can be written as:
    $$ P(z) = \rho*g*z\ $$
    Derivation:
    Derivation of the pressure \( P(z) \) at the bottom of a cylinder of liquid with cross-sectional area \( A \)

    Buoyancy

    Archimedes' Principle: Any object that is either partially or totally immersed in a fluid has a buoyancy force equal to the weight of the fluid displaced by the object.