1374:
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.
38:
437:
1373:
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
823:
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:
1524:
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
300:. 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. Since the main mirror in a telescope must be parabolic, this principle is used to create
707:
112:
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
317:
1031:
905:
791:
1156:
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.
265:, because the surface is increased in area by the ripples and the capillary forces are in this case large compared with the gravitational forces. Capillary ripples are damped both by sub-surface
1396:
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
591:
1106:
292:
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
520:
583:
821:
480:
432:{\displaystyle {\frac {\partial P}{\partial r}}=\rho r\omega ^{2},\quad {\frac {\partial P}{\partial \theta }}=0,\quad {\frac {\partial P}{\partial z}}=-\rho g,}
928:
544:
500:
460:
249:, thus oscillating and spreading the disturbance to the neighboring portions of the surface. The velocity of the surface waves varies as the square root of the
1218:
1645:
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.
1606:
1685:
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…
144:. It 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
1537:
936:
128:
In a free liquid that is not affected by outside forces such as a gravitational field, internal attractive forces only play a role (e.g.
1622:
The free-surface vortex (whirlpool) that occurs during the draining of a basin has received different interpretations along its history;
1387:
282:
1714:
1678:
1587:
1303:
830:
718:
1545:
1515:
1497:
1364:
1454:
BĂĽnnagel, R.; Oehring, H.-A.; Steiner, K. (1968), "Fizeau interferometer for measuring the flatness of optical surfaces",
1068:
1193:
1138:
occurs when liquids or granular materials under a free surface in partially filled tanks or holds shift when the vessel
1360:
1338:
1243:
547:
1173:, is the gravity driven flow of a fluid under a free surface, typically water flowing under air in the atmosphere.
241:
caused by the force of gravity tending to bring the surface of the disturbed liquid back to its horizontal level.
1739:
1610:
1203:
1634:
1594:
A simple example of irrotational flow is a whirlpool, which is known as a potential vortex in fluid mechanics.
702:{\displaystyle dP=\rho r\omega ^{2}dr-\rho gdz\to {\frac {dz_{\text{isobar}}}{dr}}={\frac {r\omega ^{2}}{g}}.}
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301:
1330:
109:
1146:
293:
70:
1549:
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1334:
234:
129:
195:. Over large distances or planetary scale, the surface of an undisturbed liquid tends to conform to
1213:
1183:
1134:
1062:
262:
105:
1129:
257:
on the sea go faster than short ones. Very minute waves or ripples are not due to gravity but to
246:
216:
58:
136:). Its free surface will assume the shape with the least surface area for its volume: a perfect
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1471:
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553:
270:
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220:
196:
114:
1721:
The term open channel flow denotes the gravity-driven flow of a liquid with a free surface.
799:
465:
1188:
1160:
1037:
184:
141:
118:
1467:
1425:
1259:
Surface of a body with no normal stress perpendicular or shear stresses parallel to it…
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1208:
1111:
1036:
If a free liquid is rotating about an axis, the free surface will take the shape of an
913:
529:
485:
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200:
133:
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1054:
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66:
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31:
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1496:
Gilman, Daniel Coit; Peck, Harry
Thurston; Colby, Frank Moore, eds. (1903).
1270:
266:
176:
168:
17:
1483:
1441:
167:'s free surface. On Earth, the flatness of a liquid is a function of the
242:
149:
94:
1475:
1607:"Ricerca Italiana - PRIN - Global stability of three-dimensional flows"
145:
46:
1117:
164:
137:
98:
90:
74:
1026:{\displaystyle z_{s}=h_{0}-{\frac {\omega ^{2}}{4g}}(R^{2}-2r^{2}).}
307:
Consider a cylindrical container filled with liquid rotating in the
311:
direction in cylindrical coordinates, the equations of motion are:
175:, can be found to deviate from true flatness by approximately 19.6
280:
204:
62:
36:
1703:
The CRC Handbook of
Thermal Engineering (Mechanical Engineering)
1667:
The CRC Handbook of
Thermal Engineering (Mechanical Engineering)
226:
27:
Surface of a fluid that is subject to zero parallel shear stress
1412:
Dew, G.D. (March 1966), "The measurement of optical flatness",
191:
at sea level, however a liquid will be slightly flatter at the
117:
unless disturbed (except near solids dipping into them, where
78:
1121:, also known as a potential vortex or whirlpool, forms in an
900:{\displaystyle h_{c}=h_{0}-{\frac {\omega ^{2}R^{2}}{4g}}.}
786:{\displaystyle z_{s}={\frac {\omega ^{2}}{2g}}r^{2}+h_{c},}
53:
is the surface of a fluid that is subject to zero parallel
1574:
Schaum's outline of theory and problems of fluid dynamics
261:, and have properties different from those of the longer
108:
will form a free surface if unconfined from above. Under
1522:. New York: D. Appleton and company. 1880. p. 123.
1275:
McGraw-Hill
Dictionary of Scientific and Technical Terms
712:
Integrating, the equation for the free surface becomes
65:. An example of two such homogeneous fluids would be a
1071:
939:
916:
833:
802:
721:
594:
556:
532:
508:
488:
468:
448:
320:
1057:, the free surface is defined mathematically by the
1705:. Berlin: Springer-Verlag and Heidelberg. pp.
1669:. Berlin: Springer-Verlag and Heidelberg. pp.
285:Free surface of a liquid in a rotating vessel is a
183:, a deviation which is dominated by the effects of
1571:
1100:
1025:
922:
899:
815:
785:
701:
577:
538:
514:
494:
474:
454:
431:
41:Disturbed free surface of a sea, viewed from below
910:The equation of the free surface at any distance
229:are produced on the surface. These waves are not
1040:: the approximate shape of the Earth due to its
1570:Brighton, John A.; Hughes, William T. (1999).
225:If the free surface of a liquid is disturbed,
140:. Such behaviour can be expressed in terms of
8:
1125:flow, for example when a bathtub is drained.
121:distorts the surface in a region called the
1219:Computational methods for free surface flow
1659:"3.2.2 Forced Convection - External Flows"
1520:Appletons' Cyclopædia of Applied Mechanics
1400:liquid will then assume a spherical form.
1325:
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321:
319:
81:cannot form a free surface on their own.
550:. Taking a surface of constant pressure
1289:
1287:
1235:
1504:. Dodd, Mead and Company. p. 739.
1635:"The Free Surface Effect - Stability"
1578:. Boston, Mass: McGraw Hill. p.
1365:"161. Shape assumed by a free liquid"
1277:. McGraw-Hill Companies, Inc., 2003.
7:
1388:"92. Shape Assumed by a Free Liquid"
1298:. New York: McGraw-Hill. p. 4.
1371:. Ginn & company. p. 114.
1345:. American Book Co. pp. 70–71.
1101:{\displaystyle {\frac {Dp}{Dt}}=0.}
1502:The New International Encyclopædia
405:
397:
375:
367:
332:
324:
25:
1414:Journal of Scientific Instruments
253:if the liquid is deep; therefore
1546:American Meteorological Society
585:the total differential becomes
502:is the radius of the cylinder,
393:
363:
1017:
988:
641:
572:
557:
1:
1657:Suryanarayana, N. V. (2000).
1386:Dull, Charles Elwood (1922).
482:is the density of the fluid,
1392:Essentials of Modern Physics
1194:Laser-heated pedestal growth
69:(liquid) and the air in the
1250:. Vishay Measurements Group
1756:
1701:. In Kreith, Frank (ed.).
1434:10.1088/0950-7671/43/7/301
1281:. Retrieved on 2007-12-02.
548:gravitational acceleration
214:
203:follows approximately the
29:
1369:A First Course in Physics
1339:"Free Surface of Liquids"
1065:on the pressure is zero:
163:refers to the shape of a
101:may form a free surface.
1697:White, Frank M. (2000).
1357:Millikan, Robert Andrews
1244:"Glossary: Free Surface"
1204:Splash (fluid mechanics)
930:from the center becomes
302:liquid-mirror telescopes
187:. This calculation uses
171:of the planet, and from
61:between two homogeneous
30:Not to be confused with
1699:"2.5 Open Channel Flow"
1542:Glossary of Meteorology
1331:Rowland, Henry Augustus
1132:and marine safety, the
515:{\displaystyle \omega }
199:surfaces; for example,
148:so the oil has neutral
1102:
1059:free-surface condition
1027:
924:
901:
817:
787:
703:
579:
578:{\displaystyle (dP=0)}
540:
516:
496:
476:
456:
433:
289:
110:mechanical equilibrium
73:(gas mixture). Unlike
42:
1394:. New York: H. Holt.
1294:White, Frank (2003).
1147:hydraulic engineering
1103:
1028:
925:
902:
818:
816:{\displaystyle h_{c}}
788:
704:
580:
541:
517:
497:
477:
475:{\displaystyle \rho }
457:
434:
294:surface of revolution
284:
215:Further information:
40:
1335:Joseph Sweetman Ames
1069:
937:
914:
831:
800:
719:
592:
554:
530:
506:
486:
466:
446:
318:
130:Van der Waals forces
1476:10.1364/AO.7.000331
1468:1968ApOpt...7..331B
1426:1966JScI...43..409D
1343:Elements of Physics
1214:Riabouchinsky solid
1184:Free surface effect
1135:free surface effect
1063:material derivative
263:ocean surface waves
245:causes the wave to
189:Earth's mean radius
106:gravitational field
1361:Gale, Henry Gordon
1130:naval architecture
1098:
1023:
920:
897:
813:
783:
699:
575:
536:
512:
492:
472:
452:
429:
290:
217:Ocean surface wave
179:over an area of 1
89:solids, including
71:Earth's atmosphere
43:
1248:Interactive Guide
1171:open-channel flow
1166:free surface flow
1090:
986:
923:{\displaystyle r}
892:
755:
694:
669:
657:
539:{\displaystyle g}
524:angular frequency
495:{\displaystyle r}
462:is the pressure,
455:{\displaystyle P}
412:
382:
339:
16:(Redirected from
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1618:
1609:. Archived from
1603:
1597:
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1558:
1557:
1548:. Archived from
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1042:equatorial bulge
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271:surface rheology
259:capillary action
221:Airy wave theory
197:equigeopotential
21:
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1740:Fluid mechanics
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1296:Fluid mechanics
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1237:
1232:
1189:Surface tension
1180:
1161:fluid mechanics
1082:
1074:
1067:
1066:
1061:, that is, the
1050:
1038:oblate spheroid
1007:
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978:
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185:surface tension
158:
142:surface tension
119:surface tension
97:materials, and
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23:
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15:
12:
11:
5:
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1598:
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1562:
1538:"Free surface"
1529:
1516:"Hydrostatics"
1507:
1498:"Hydrostatics"
1488:
1462:(2): 331–335,
1456:Applied Optics
1446:
1420:(7): 409–415,
1404:
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1304:
1283:
1263:
1234:
1233:
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1228:
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1221:
1216:
1211:
1209:Slosh dynamics
1206:
1201:
1196:
1191:
1186:
1179:
1176:
1175:
1174:
1169:, also called
1157:
1143:
1126:
1112:fluid dynamics
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1080:
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201:mean sea level
157:
154:
134:hydrogen bonds
104:A liquid in a
57:, such as the
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1752:
1741:
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1735:
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1718:
1716:3-540-66349-5
1712:
1708:
1704:
1700:
1693:
1690:
1686:
1682:
1680:3-540-66349-5
1676:
1672:
1668:
1664:
1663:Kreith, Frank
1660:
1653:
1650:
1646:
1636:
1630:
1627:
1623:
1613:on 2012-02-09
1612:
1608:
1602:
1599:
1595:
1591:
1589:0-07-031118-8
1585:
1581:
1576:
1575:
1566:
1563:
1552:on 2007-12-09
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1307:
1305:0-07-240217-2
1301:
1297:
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1276:
1272:
1267:
1264:
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1249:
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1225:
1224:Water current
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1151:free-surface
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1116:free-surface
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1055:hydrodynamics
1052:
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1048:Related terms
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1279:Answers.com
296:known as a
237:; they are
233:due to any
1640:2007-12-02
1617:2007-12-02
1556:2007-11-27
1254:2007-12-02
1230:References
298:paraboloid
287:paraboloid
255:long waves
251:wavelength
177:nanometers
115:horizontal
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