Free surface

[2] An example of two such homogeneous fluids would be a body of water (liquid) and the air in the Earth's atmosphere (gas mixture).

[3] Fluidized/liquified solids, including slurries, granular materials, and powders may form a free surface.

On Earth, the flatness of a liquid is a function of the curvature of the planet, and from trigonometry, can be found to deviate from true flatness by approximately 19.6 nanometers over an area of 1 square meter, a deviation which is dominated by the effects of surface tension.

This calculation uses Earth's mean radius at sea level, however a liquid will be slightly flatter at the poles.

Momentum causes the wave to overshoot, thus oscillating and spreading the disturbance to the neighboring portions of the surface.

[4] Very minute waves or ripples are not due to gravity but to capillary action, and have properties different from those of the longer ocean surface waves,[4] because the surface is increased in area by the ripples and the capillary forces are in this case large compared with the gravitational forces.

If a liquid is contained in a cylindrical vessel and is rotating around a vertical axis coinciding with the axis of the cylinder, the free surface will assume a parabolic surface of revolution known as a paraboloid.

is the distance of the free surface from the bottom of the container along the axis of rotation.

If one integrates the volume of the paraboloid formed by the free surface and then solves for the original height, one can find the height of the fluid along the centerline of the cylindrical container: The equation of the free surface at any distance

from the center becomes If a free liquid is rotating about an axis, the free surface will take the shape of an oblate spheroid: the approximate shape of the Earth due to its equatorial bulge.