FREE SURFACE WA YES. Liquids differ from gases in having definite volumes: eonsequently, as noted hefore, if a liquid is poured into an open vessel, it will have a surface in contact with the atmosphere. This is called the `free surface.' if the liquid is in equilibrium, this surface mast he at right angles to the forces acting on it.
Thus a liquid at rest in an open vessel has a horizontal surface owing to the earth's force of gravity. If this surface is disturbed, e.g. by dropping in a stone, the displaced portion will return to its previous level owing to the action of gravity. but its inertia will cause it to eon thine its motion, making a displacement in the opposite direction; then it will return, ete., thus vibrating up and down and producing waves out over the surface. These gravitational surface waves on a liquid advance with a velocity which depends upon the nature and depth of the liquid and the wavelength of the waves. Thus, if the liquid is shallow compared with the wavelength, the velocity is given by the formula r where h is the depth of the liquid and 9 is the acceleration of a falling body. If the liquid is deep compared with the wave-length, the velocity of the waves is .9 X where X is the wavelength of any train of waves, and or = 3.1416. if the waves are ex tremely short—i.e. ripples—their motion is not due to gravitation, but to capillarity (q.v.), be cause the surface is increased in area by the ripples; and the eapillary forces are, in this case. large compared with the gravitation ones, the surface being so slightly elevated or de pressed. The velocity of these capillary waves IS = X p where T is the 'surface-tension' of the liquid. (See CAPILLARITY.) If the vessel containing the
liquid is cylindrical, and if this is set rotating rapidly about its axis, the free surface will'no longer be horizontal, la-cause now the surface is acted upon by both gravity and 'centrifugal force.' The shape of the surface will be such as to be :it right angles to their resultant, and will actually be it paraboloid of revolution.
If a liquid is poured into a vessel which con sists of several parts, the liquid will stand at the same height in all parts provided they are wide and open to the atmosphere; fur, as has been proved, all points at the same horizontal level in a fluid are at the same pressure. and conversely; and the points in the free surfaces are at the same pressure. viz. that of the atmosphere. lf, however, a liqui•is poured into a U-tube which stands civet. and then a lighter fluid. which does Lot mix with the first, is poured into one arm, the level of the surfaces of the liquids in the two arms is not the same. The pressure at points which lie in the horizontal plane passing through the surface I if separation of the two liquids must be the same, because they are all connected by one liquid. The pressure at the points in one arm in this level is p,gh, P, where (7 is the density of the liquid in that arm, h, is the verti cal height of its free surface above the level plane. and I' is the pressure of the atmosphere on the free surface; similarly the pressure at this level in the other arm is p.olL, P, where is the density of the liquid whose vertical height from the level to the free surface is There fore