# Free surface

In physics a free surface is the surface of a body that is subject to neither perpendicular normal stress nor parallel shear stress, such as the boundary between two homogenous fluids, for example liquid water and the air in the Earth's atmosphere. Unlike liquids, gases cannot form a free surface on their own.

A liquid in a gravitational field will form a free surface if unconfined from above. Under mechanical equilibrium this free surface must be perpendicular to the forces acting on the liquid; if not there would be a force along the surface, and the liquid would flow in that direction. Thus, on the surface of the Earth, all free surfaces of liquids are horizontal unless disturbed (except near solids dipping into them, where surface tension distorts the surface locally).

In a free liquid at rest, that is one subject to internal attractive forces only and not affected by outside forces such as a gravitational field, its free surface will assume the shape with the least surface area for its volume — a perfect sphere. This can be demonstrated experimentally by observing a large globule of oil placed below the surface of a mixture of water and alcohol having the same density so the oil has neutral buoyancy.

## Waves

If the free surface of a liquid is disturbed, waves are produced on the surface. These waves are not elastic waves due to any elastic force; they are gravity waves caused by the force of gravity tending to bring the surface of the disturbed liquid back to its horizontal level, but due to momentum, it overshoots. Thus it oscillates and spreads the disturbance to the neighboring portions of the surface. The velocity of the surface waves varies as the square root of the wavelength if the liquid is deep; therefore long waves on the sea go faster than short ones. 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, because the surface is increased in area by the ripples and the capillary forces are in this case large compared with the gravitational forces.

## Rotation

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. The free surface at each point is at a right angle to the force acting at it, which is the resultant of the force of gravity and the centrifugal force from the motion of each point in a circle.

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.

## Related terms

• In hydrodynamics, the free surface is defined mathematically by the the free-surface condition:
$\ \frac{Dp}{Dt} = 0.$

• In hydraulic engineering a free-surface jet is one where the entrainment of the fluid outside the jet is minimal, as opposed to submerged jet where the entrainment effect is significant. A liquid jet in air approximates a free surface jet.
• In fluid mechanics a free surface flow, also called open channel flow, is the gravity driven flow of a fluid under a free surface, typically water flowing under air in the atmosphere.