In a fluid resting in a gravitational field, the pressure increases downward. The change of pressure with depth is independent of the size and shape of the "container" (tank, bath tub, atmosphere, lake, see…) for the fluid.

The change of pressure with depth (or height in the case of an atmosphere) only depends upon the density of the fluid and the strength of the gravitational field.

If the density and the gravitational field are constant (such as in the case of a lake at the surface of the Earth):

     p(z) = p_o + rho·g·z

z: depth (z = 0 at the surface of the liquid); [z] = m, rho: density of liquid; [rho] = kg/m^3, g: strength of gravitational field; [g] = N/kg, p_o: pressure at z = 0 (in the case of a lake: atmospheric pressure)

If density and strength of gravitational field are variable (such as in the case of our atmosphere):

     dp/dz = – rho·g

(z measured opposite to the direction of g)

pressure, pressure gradient, gravitational pressure difference,

The pressure of a liquid in a gravitational field only depends upon the depth (measured from the top down). It does not dpeend upon the size or shape of the container.

hydrostatischer Druck