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,cite web |url=http://www.vishay.com/company/brands/measurements-group/guide/glossary/freesurf.htm |title=Glossary: Free Surface |accessdate=2007-12-02 |format= | publisher = Vishay Measurements Group |work= Interactive Guide | quote = Surface of a body with no normal stress perpendicular or shear stresses parallel to it…] such as the boundary between two homogenous fluids, [ [http://www.answers.com/topic/free-surface Free surface] . "McGraw-Hill Dictionary of Scientific and Technical Terms". McGraw-Hill Companies, Inc., 2003. Answers.com. Retrieved on 2007-12-02.] 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.cite book |author=White, Frank |title=Fluid mechanics |publisher=McGraw-Hill |location=New York |year=2003 |pages= p. 4 |isbn=0-07-240217-2 |oclc= |doi=] 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. [cite book | chapterurl=http://books.google.com/books?id=yqkLAAAAYAAJ&dq=%22free+surface%22+liquid&as_brr=1&vq=free%20surface&pg=PA114&ci=56,675,889,771&source=bookclip|title = A First Course in Physics| chapter = 161. Shape assumed by a free liquid | first = Robert Andrews | last = Millikan | authorlink = Robert Andrews Millikan | coauthors = Henry Gordon Gale | pages = p. 114| year = 1906 | publisher = Ginn & company|quote= Since, then, every molecule of a liquid is pulling on every other molecule, any body of liquid which is free to take its natural shape that is which is acted on only by its own cohesive forces, must draw itself together until it has the smallest possible surface compatible with its volume; for, since every molecule in the surface is drawn toward the interior by the attraction of the molecules within, it is clear that molecules must continually move toward the center of the mass until the whole has reached the most compact form possible. Now the geometrical figure which has the smallest area for a given volume is a sphere. We conclude, therefore, that if we could relieve a body of liquid from the action of gravity and other outside forces, it would at once take the form of a perfect sphere.] [cite book|chapter=92. Shape Assumed by a Free Liquid |quote = Since the molecules of liquids slide over one another readily, the force of gravity causes the surface of liquids to become level. If the force of gravity can be nullified, a small portion of "free" liquid will then assume a spherical form. |chapterurl = http://books.google.com/books?id=dD0AAAAAYAAJ&dq=%22Shape+assumed+by+a+free+liquid%22&pg=PA77&ci=87,959,680,215&source=bookclip | title = Essentials of Modern Physics | first = Charles Elwood |last = Dull | year = 1922 | publisher = H. Holt | location = New York]

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.cite book|chapterurl=http://books.google.com/books?id=ImlMAAAAMAAJ&dq=%22free+surface%22+liquid&as_brr=1&pg=PA731&ci=499,532,396,57&source=bookclip | title = The New International Encyclopædia | editor = Gilman, Daniel Coit; Peck, Harry Thurston; Colby, Frank Moore|pages = p. 739|chapter = Hydrostatics|year = 1903| publisher =Dodd, Mead and Company ]

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.cite book | chapterurl= http://books.google.com/books?id=m9oXAAAAIAAJ&dq=%22free+surface%22&as_brr=1&pg=PA70&ci=101,317,865,1066&source=bookclip | title = Elements of Physics| chapter = Free Surface of Liquids | first = Henry Augustus | last = Rowland | authorlink = Henry Augustus Rowland | coauthors = Joseph Sweetman Ames| pages = pp. 70-71| year = 1900 | publisher = American Book Co.]

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. [cite book|chapterurl=http://books.google.com/books?id=RkkOAAAAYAAJ&dq=%22free+surface%22+liquid&as_brr=1&pg=PA123&ci=64,1063,791,78&source=bookclip|title = Appletons' Cyclopædia of Applied Mechanics| chapter = Hydrostatics| pages = p. 123 | publisher = D. Appleton and company | year = 1880 | city = New York|quote=If a perfectly homogeneous mass of liquid be acted upon by a force which varies directly as the distance from the centre of the mass, the free surface will be of spherical form; if the mass rotates about an axis, the form assumed will be that of an oblate spheroid, which is the shape of the earth.]

Related terms

*In hydrodynamics, the free surface is defined mathematically by the free-surface condition:cite web |url=http://amsglossary.allenpress.com/glossary/search?id=free-surface1 |work=Glossary of Meteorology | publisher = American Meteorological Society| title = Free surface |accessdate=2007-11-27 ]

::$frac\{Dp\}\{Dt\}\; =\; 0.$

*In fluid dynamics, a "free-surface vortex", also known as a potential vortex or whirlpool, forms in an irrotational flow,cite book |author=Brighton, John A.; Hughes, William T. |title=Schaum's outline of theory and problems of fluid dynamics |publisher=McGraw Hill |location=Boston, Mass |year=1999 |pages= p. 51|isbn=0-07-031118-8 |quote = A simple example of irrotational flow is a whirlpool, which is known as a potential vortex in fluid mechanics.] for example when a bathtub is drained.cite web |url=http://www.ricercaitaliana.it/prin/dettaglio_completo_prin_en-2005092015.htm |title=Ricerca Italiana - PRIN - Global stability of three-dimensional flows |accessdate=2007-12-02 |format= |work=| quote = The free-surface vortex (whirlpool) that occurs during the draining of a basin has received different interpretations along its history;]

*In naval architecture and marine safety, the "free surface effect" occurs when liquids or granular materials under a free surface in partially filled tanks or holds shift when the vessel heels.cite web |url=http://www.tc.gc.ca/MarineSafety/TP/Tp10038/27-stab-free-surface-effect.htm |title=The Free Surface Effect - Stability | TP 10038 | Marine Safety |accessdate=2007-12-02 |format= |work= |quote = In a partly filled tank or fish hold, the contents will shift with the movement of the boat. This "free surface" effect increases the danger of capsizing.]

*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.cite book |editor=Kreith, Frank |title=The CRC Handbook of Thermal Engineering (Mechanical Engineering)|first = N. V. | last = Suryanarayana | chapter = 3.2.2 Forced Convection - External Flows |publisher=Springer-Verlag and Heidelberg |location= Berlin |year= 2000|pages= p. 3-44 |isbn=3-540-66349-5 | quote = In free-surface jets — a liquid jet in an atmosphere of air is a good approximation to a free-surface jet — the entrainment effect is usually negligible…]

*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.cite book | author = White, Frank M. | chapter = 2.5 Open Channel Flow|editor=Kreith, Frank |title=The CRC Handbook of Thermal Engineering (Mechanical Engineering) |publisher=Springer-Verlag and Heidelberg |location= Berlin|year= 2000|pages= p. 2-61 |isbn=3-540-66349-5 | quote = The term open channel flow denotes the gravity-driven flow of a liquid with a free surface.]

ee also

*Splash (fluid mechanics)
*Riabouchinsky solid

References