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vortex

vortex

vortex Sentence Examples

  • Hence in any infinitesimal part of the fluid the circulation is zero round every small plane curve passing through the vortex line; and consequently the circulation round any curve drawn on the surface of a vortex filament is zero.

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  • Immediately afterwards Langton was drawn into the vortex of English politics.

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  • The earth, or other planet, does not actually move round the sun; yet it is carried round the sun in the subtle matter of the great vortex, where it lies in equilibrium, - carried like the passenger in a boat, who may cross the sea and yet not rise from his berth.

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  • The United States was, at this time, drawn into the vortex of European complications, and Adams, instead of taking advantage of the militant spirit which was aroused, patriotically devoted himself to securing peace with France, much against the wishes of Hamilton and of Hamilton's adherents in the cabinet.

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  • A single vortex will remain at rest, and cause a velocity at any point inversely as the distance from the axis and perpendicular to its direction; analogous to the magnetic field of a straight electric current.

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  • This finer matter which collects in the centre of each vortex is the first matter of Descartes - it constitutes the sun or star.

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  • In this year the short-lived federation of the five powers was shaken, and Italy was once more drawn into the vortex of Europe~n affairs.

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  • (7) Interchanging these values =m log r, 4, = mO, 4,+4,i =m log rei e (8) gives a state of vortex motion, circulating round Oz, called a straight or columnar vortex.

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  • At a time when the Cartesian system of vortices universally prevailed, he found it necessary to investigate that hypothesis, and in the course of his investigations he showed that the velocity of any stratum of the vortex is an arithmetical mean between the velocities of the strata which enclose it; and from this it evidently follows that the velocity of a filament of water moving in a pipe is an arithmetical mean between the velocities of the filaments which surround it.

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  • Jenn looked to where the vortex had been.

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  • Putting (12) a vortex line is defined to be such that the tangent is in the direction of w, the resultant of, n, called the components of molecular rotation.

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  • Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.

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  • If other vortices are present, any one may be supposed to move with the velocity due to the others, the resultant stream function being = gy m log r =log IIrm; (9) the path of a vortex is obtained by equating the value of 1P at the vortex to a constant, omitting the rm of the vortex itself.

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  • But in other cases the encrusted star settles in that portion of the revolving vortex which has a velocity equivalent to its own, and so continues to revolve in the vortex, wrapped in its own firmament.

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  • Hill's spherical vortex, advancing through the surrounding liquid with uniform velocity.

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  • When the liquid is bounded by a cylindrical surface, the motion of a vortex inside may be determined as due to a series of vorteximages, so arranged as to make the flow zero across the boundary.

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  • When the liquid is bounded by a cylindrical surface, the motion of a vortex inside may be determined as due to a series of vorteximages, so arranged as to make the flow zero across the boundary.

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  • The expression for w in (i) § 29 may be increased by the addition of the term im log z =-m0 + im log r, (1) representing vortex motion circulating round the annulus of liquid.

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  • If through every point of a small closed curve the vortex lines are drawn, a tube is obtained, and the fluid contained is called a vortex filament.

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  • So far these theorems on vortex motion are kinematical; but introducing the equations of motion of § 22, Du + dQ =o, Dv+dQ =o, Dw + dQ dt dx dt dy dt dz and taking dx, dy, dz in the direction of u, v, w, and dx: dy: dz=u: v: w, (udx + vdy + wdz) = Du dx +u 1+..

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  • The circulation being always zero round a small plane curve passing through the axis of spin in vortical motion, it follows conversely that a vortex filament is composed always of the same fluid particles; and since the circulation round a cross-section of a vortex filament is constant, not changing with the time, it follows from the previous kinematical theorem that aw is constant for all time, and the same for every cross-section of the vortex filament.

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  • A vortex filament must close on itself, or end on a bounding surface, as seen when the tip of a spoon is drawn through the surface of water.

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  • The effect of an external circulation of vortex motion on the motion of a cylinder has been investigated in § 29; a similar procedure will show the influence of circulation through a hole in a solid, taking as the simplest illustration a ring-shaped figure, with uniplanar motion, and denoting by the resultant axial linear momentum of the circulation.

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  • Thus the rotifer is, as it were, constantly drawn forward into the centre of this vortex ring.

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  • A vortex filament must close on itself, or end on a bounding surface, as seen when the tip of a spoon is drawn through the surface of water.

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  • and as we prove subsequently (§ 37) that the vortex lines are composed of the same fluid particles throughout the motion, the surface m and satisfies the condition of (6) § 23; so that K is uniform throughout the fluid at any instant, and changes with the time only, and so may be replaced by F(t).

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  • 35 A circular vortex, such as a smoke ring, will set up motion symmetrical about an axis, and provide an illustration; a half vortex ring can be generated in water by drawing a semicircular blade a short distance forward, the tip of a spoon for instance.

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  • The vortex advances with a certain velocity; and if an equal circular vortex is generated coaxially with the first, the mutual influence can be observed.

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  • The first vortex dilates and moves slower, while the second contracts and shoots through the first; after which the motion is reversed periodically, as if in a game of leap-frog.

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  • The analytical treatment of such vortex rings is the same as for the electro-magnetic effect of a current circulating in each ring.

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  • Flow, Circulation, and Vortex Motion.-The line integral of the tangential velocity along a curve from one point to another, defined by s v as + u'a s) ds =f (udx+vdy-}-zdz), (I) is called the " flux " along the curve from the first to the second point; and if the curve closes in on itself the line integral round the curve is called the " circulation " in the curve.

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  • Trans., 1890); the solution is given by ch nS2=sn w, shnS2=i cn w (II) so that, round the boundary of the polygon, ik = K', sin n8 =o; and on the surface of the vortex 1P= o, q = Q, and cos n8=sn4p,nB= Zit -am sic, (12) the intrinsic equation of the curve.

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  • Various analogies of this sort are open to us to follow up: for example, the way in which a fluid medium transmits pressure from one immersed solid to another - or from one vortex ring belonging to the fluid to another, which is a much wider and more suggestive case; or the way in which an elastic fluid like the atmosphere transmits sound; or the way in which an elastic solid transmits waves of transverse as well as longitudinal displacement.

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  • The other course is to consider matter as formed of ultimate atoms, each the nucleus or core of an intrinsic modification impressed on the surrounding region of the aether; this might conceivably be of the nature of vortical motion of a liquid round a ring-core, thus giving a vortex atom, or of an intrinsic strain of some sort radiating from a core, which would give an electric atom.

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  • FitzGerald) from a structure of tangled or interlaced vortex filaments pervading its substance, which might conceivably arrange themselves into a stable configuration and so resist deformation.

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  • We can obtain a pertinent illustration from the motion of a vortex ring in a fluid; if the circular core of the ring is thin compared with its diameter, and the vorticity is not very great, it is the vortical state of motion that travels across the fluid without transporting the latter bodily with it except to a slight extent very close to the core.

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  • Trans., 1890); the solution is given by ch nS2=sn w, shnS2=i cn w (II) so that, round the boundary of the polygon, ik = K', sin n8 =o; and on the surface of the vortex 1P= o, q = Q, and cos n8=sn4p,nB= Zit -am sic, (12) the intrinsic equation of the curve.

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  • Various analogies of this sort are open to us to follow up: for example, the way in which a fluid medium transmits pressure from one immersed solid to another - or from one vortex ring belonging to the fluid to another, which is a much wider and more suggestive case; or the way in which an elastic fluid like the atmosphere transmits sound; or the way in which an elastic solid transmits waves of transverse as well as longitudinal displacement.

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  • Projected perpendicularly against a plane boundary, the motion is determined by an equal opposite vortex ring, the optical image; the vortex ring spreads out and moves more slowly as it approaches the wall; at the same time the molecular rotation, inversely as the cross-section of the vortex, is seen to increase.

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  • If at any points of a vortex line the cross-section ABC, A'B'C' is drawn of the vortex filament, joined by the vortex line AA', then, since the flow in AA' is taken in opposite directions in the complete circuit ABC AA'B'C' A'A, the resultant flow in AA' cancels, and the circulation in ABC, A'B'C' is the same; this is expressed by saying that at all points of a vortex filament wa is constant where a is the cross-section of the filament and w the resultant spin (W.

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  • If at any points of a vortex line the cross-section ABC, A'B'C' is drawn of the vortex filament, joined by the vortex line AA', then, since the flow in AA' is taken in opposite directions in the complete circuit ABC AA'B'C' A'A, the resultant flow in AA' cancels, and the circulation in ABC, A'B'C' is the same; this is expressed by saying that at all points of a vortex filament wa is constant where a is the cross-section of the filament and w the resultant spin (W.

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  • d - K dK dK _ dK dK dK ?dx n dyd °, udx dz - ° and K=fdp/o+V+2q 2 =H (3) is constant along a vortex line, and a stream line, the path of a fluid particle, so that the fluid is traversed by a series of H surfaces, each covered by a network of stream lines and vortex lines; and if the motion is irrotational H is a constant throughout the fluid.

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  • For example, a pair of equal opposite vortices, moving on a line parallel to a plane boundary, will have a corresponding pair of images, forming a rectangle of vortices, and the path of a vortex will be the Cotes' spiral r sin 20 = 2a, or x-2+y-2=a-2; (io) this is therefore the path of a single vortex in a right-angled corner; and generally.

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  • As the small filings produced by friction seek to pass through the interstices between the rapidly revolving spherical particles in the vortex, they are detained and become twisted and channelled in their passage, and when they reach the edge of the inner ocean of solar dust they settle upon it as the froth and foam produced by the agitation of water gathers upon its surface.

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  • For a plane boundary the image is the optical reflection of the vortex.

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  • Another explanation may be given of the sidelong force, arising from the velocity of liquid past a cylinder, which is encircled by a vortex.

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  • The resultant hydrostatic thrust across any diametral plane of the cylinder will be modified, but the only term in the loss of head which exerts a resultant thrust on the whole cylinder is 2mU sin Olga, and its thrust is 27rpmU absolute units in the direction Cy, to be counteracted by a support at the centre C; the liquid is streaming past r=a with velocity U reversed, and the cylinder is surrounded by a vortex.

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  • Michell has discussed also the hollow vortex stationary inside a polygon (Phil.

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  • 192, resembling the trochoidal curves, which can be looped, investigated in § 29 for the motion of a cylinder under gravity, when surrounded by a vortex.

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  • When A is held still, and B rotated, centrifugal action sets up vortex currents in the water in the pockets; thus a continuous circulation is caused between B and A, and the consequent changes of momentum give rise to oblique reactions.

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  • Then following into the pocketed chambers V,, V2, it is caught into the vortex, and finally escapes at the circumference, flowing away at F.

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  • lating the water are connected to the casing, so that any tilting automatically regulates the flow, and therefore the thickness of the film in the vortex.

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  • But the hydrodynamical discovery of Helmholtz that a vortex in a perfect liquid possesses certain permanent characteristics has been applied by Sir W.

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  • Thomson (Lord Kelvin) to form a theory of vortex atoms in a homogeneous, incompressible and frictionless liquid."

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  • We might thus examine a structure formed of an aggregation of very thin vortex rings, which would move across the fluid without sensibly disturbing it; on the other hand, if formed of stronger vortices, it may transport the portion of the fluid that is within, or adjacent to, its own structure along with it as if it were a solid mass, and therefore also push aside the surrounding fluid as it passes.

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  • The motion of the well-known steady spherical vortex is an example of the latter case.

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  • It is true that the theory of vortex rings in hydrodynamics is of a simpler type; but electric currents cannot be likened to permanent vortex rings, because their circuits can be broken and the element of cyclic steadiness on which the simplicity depends is thereby destroyed.

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  • In addition to a large number of publications in the Proceedings of the Royal Society and the Philosophical Magazine, he has published A Treatise on the Motion of Vortex Rings (1884); The Application of Dynamics to Physics and Chemistry (1886); Recent Researches in Electricity and Magnetism (1892); Elements of the Mathematical Theory of Electricity and Magnetism (18 95, 5th ed.

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  • From these contests of rival nobles, in which the names of Spinola and Doria stand forth with greatest prominence, Genoa was soon drawn into the great vortex of the Guelph and Ghibelline factions; but its recognition of foreign authority - successively German, Neapolitan and Milanese - gave way to a state of greater independence in 1339, when the government assumed a more permanent form with the appointment of the first doge, an office held at Genoa for life, in the person of Simone Boccanera.

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  • In the famous typhoon of the 10th of October 1882, the vortex of which passed over Manila, an immense amount of damage was done in the city.

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  • Unfortunately, she, in common with the rest of South Africa, was subsequently swept into the seething vortex of contemporary politics and controversy.

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  • It is impossible within brief limits to convey more than a general idea of the work of a philosopher who published more than three hundred original papers bearing upon nearly every branch of physical science; who one day was working out the mathematics of a vortex theory of matter on hydrodynamical principles or discovering the limitations of the capabilities of the vortex atom, on another was applying the theory of elasticity to tides in the solid earth, or was calculating the size of water molecules, and later was designing an electricity meter, a dynamo or a domestic water-tap. It is only by reference to his published papers that any approximate conception can be formed of his life's work; but the student who had read all these knew comparatively little of Lord Kelvin if he had not talked with him face to face.

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  • Jenn looked to where the vortex had been.

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  • annulus flow leads to increased vortex strength within the cavity.

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  • Vortex Dynamics Dr. A.M. Campbell The project is investigating the role of surface currents in the critical current of BSCCO crystals.

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  • Ted was ideally placed to make use of neutron diffraction to study the nature of the vortex state.

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  • EUROMECH Colloquium 491: " vortex dynamics from quantum to geophysical scales " EUROMECH Colloquium 491 home page.

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  • Another vortex phenomenon case involved a group of young hippies who were camped out inside Stonehenge when the stones were struck by lightning.

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  • Peter Lynn Vortex is a twin skin closed cell foil kite from the Peter Lynn stable.

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  • Thus there is no vortex lattice, indeed no vortices at all.

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  • The big blocky " starring " credits, reminiscent of the Superman films, seemed to make the vortex less mysterious I thought.

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  • neutron diffraction to study the nature of the vortex state.

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  • polar vortex.

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  • These results showed that the vortex breakdown is a very sensitive technique to study polymer rheology.

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  • The vortex establishes itself in the middle to lower stratosphere.

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  • Striking graphics confusing ANYONE who has seen 3-D Tunnel will find Vortex for the 16K Spectrum familiar.

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  • upside down cone shape as the vortex moved out across the lake.

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  • Most of the game consists of rounding up rabbits or other vermin into the swirling vortex of your vacuum vehicle machine.

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  • Dynamics of the vortex wakes of swimming and flying vertebrates.

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  • The Vortex dampens the vibration caused by the rapidly spinning motors in the hard drive, reducing noise and shock.

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  • The Gilkes Vortex turbine was manufactured in Kendal and drove a 6kw dynamo generating 110 volts.

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  • vortex of energy.

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  • At the blade tip, a similar leakage induces a vortex about the blade tip.

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  • The changes in wind speed then create a vortex.

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  • On the highest surface all intrusions are governed by the location of the polar vortex.

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  • Lee, A. M., et al., The impact of the mixing properties within the Antarctic stratospheric vortex on ozone loss in spring.

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  • Most of the game consists of rounding up rabbits or other vermin into the swirling vortex of your vacuum vehicle machine.

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  • Air Cannon Target our air cannons at a target and push the plunger to send a spinning vortex of air across the room.

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  • vortex shedding - hillwalkers included.

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  • vortex lattice, indeed no vortices at all.

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  • vortex generators to aircraft.

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  • vortex dynamics to determine the development of simple three-dimensional flows.

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  • vortex wake is then all concentrated in two trails.

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  • vortex tube work?

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  • The periodic shedding of the tip vortex at the blade tip is also observed in vorticity contour plots measured at the of axial planes.

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  • The vortex patterns correspond to the intersection of the laser sheet with the trailing, helical vortices from the turbine blades.

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  • WISY Vortex Filters Vortex filters connect to standard storm water pipes below ground.

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  • A vortex is a rapidly whirling spiral, a body of fluid or gas rotating around its own center.

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  • The earth, or other planet, does not actually move round the sun; yet it is carried round the sun in the subtle matter of the great vortex, where it lies in equilibrium, - carried like the passenger in a boat, who may cross the sea and yet not rise from his berth.

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  • p their corners pared off by rubbing against each other; and two species of matter thus arise, - one consisting of small globules which continue their circular motion with a (centrifugal) tendency to fly off from the centre as they swing round the axis of rotation, while the other, consisting of the fine dust--the filings and parings of the original particles - gradually becoming finer and finer, and losing its velocity, tends (centripetally) to accumulate in the centre of the vortex, which has been gradually left free by the receding particles of globular matter.

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  • This finer matter which collects in the centre of each vortex is the first matter of Descartes - it constitutes the sun or star.

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  • The spherical particles are the second matter of Descartes, and their tendency to propel one another from the centre in straight lines towards the circumference of each vortex is what gives rise to the phenomenon of light radiating from the central star.

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  • As the small filings produced by friction seek to pass through the interstices between the rapidly revolving spherical particles in the vortex, they are detained and become twisted and channelled in their passage, and when they reach the edge of the inner ocean of solar dust they settle upon it as the froth and foam produced by the agitation of water gathers upon its surface.

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  • velocity of the decaying star be greater than that of any part of the vortex which has swept it up, it will ere long pass out of the range of that vortex, and continue its movement from one to another.

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  • But in other cases the encrusted star settles in that portion of the revolving vortex which has a velocity equivalent to its own, and so continues to revolve in the vortex, wrapped in its own firmament.

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  • In this year the short-lived federation of the five powers was shaken, and Italy was once more drawn into the vortex of Europe~n affairs.

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  • The United States was, at this time, drawn into the vortex of European complications, and Adams, instead of taking advantage of the militant spirit which was aroused, patriotically devoted himself to securing peace with France, much against the wishes of Hamilton and of Hamilton's adherents in the cabinet.

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  • At a time when the Cartesian system of vortices universally prevailed, he found it necessary to investigate that hypothesis, and in the course of his investigations he showed that the velocity of any stratum of the vortex is an arithmetical mean between the velocities of the strata which enclose it; and from this it evidently follows that the velocity of a filament of water moving in a pipe is an arithmetical mean between the velocities of the filaments which surround it.

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  • Putting (12) a vortex line is defined to be such that the tangent is in the direction of w, the resultant of, n, called the components of molecular rotation.

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  • d o, dx dy dz dx dy dz so that, at any instant, the surfaces over which tk and m are constant intersect in the vortex lines.

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  • and as we prove subsequently (§ 37) that the vortex lines are composed of the same fluid particles throughout the motion, the surface m and satisfies the condition of (6) § 23; so that K is uniform throughout the fluid at any instant, and changes with the time only, and so may be replaced by F(t).

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  • d - K dK dK _ dK dK dK ?dx n dyd °, udx dz - ° and K=fdp/o+V+2q 2 =H (3) is constant along a vortex line, and a stream line, the path of a fluid particle, so that the fluid is traversed by a series of H surfaces, each covered by a network of stream lines and vortex lines; and if the motion is irrotational H is a constant throughout the fluid.

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  • Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.

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  • (7) Interchanging these values =m log r, 4, = mO, 4,+4,i =m log rei e (8) gives a state of vortex motion, circulating round Oz, called a straight or columnar vortex.

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  • A single vortex will remain at rest, and cause a velocity at any point inversely as the distance from the axis and perpendicular to its direction; analogous to the magnetic field of a straight electric current.

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  • If other vortices are present, any one may be supposed to move with the velocity due to the others, the resultant stream function being = gy m log r =log IIrm; (9) the path of a vortex is obtained by equating the value of 1P at the vortex to a constant, omitting the rm of the vortex itself.

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  • For a plane boundary the image is the optical reflection of the vortex.

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  • For example, a pair of equal opposite vortices, moving on a line parallel to a plane boundary, will have a corresponding pair of images, forming a rectangle of vortices, and the path of a vortex will be the Cotes' spiral r sin 20 = 2a, or x-2+y-2=a-2; (io) this is therefore the path of a single vortex in a right-angled corner; and generally.

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  • (II) A single vortex in a circular cylinder of radius a at a distance c from the centre will move with the velocity due to an equal opposite image at a distance a 2 /c, and so describe a circle with velocity mc/(a 2 -c 2)in the periodic time 21r(a 2 -c 2)/m.

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  • The expression for w in (i) § 29 may be increased by the addition of the term im log z =-m0 + im log r, (1) representing vortex motion circulating round the annulus of liquid.

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  • Considered by itself, with the cylinders held fixed, the vortex sets up a circumferential velocity m/r on a radius r, so that the angular momentum of a circular filament of annular cross section dA is pmdA, and of the whole vortex is pm7r(b2-a2).

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  • Any circular filament can be started from rest by the application of a circumferential impulse 7rpmdr at each end of a diameter; so that a mechanism attached to the cylinders, which can set up a uniform distributed impulse rpm across the two parts of a diameter in the liquid, will generate the vortex motion, and react on the cylinder with an impulse couple-pmira 2 and pm7rb 2, having resultant pm7r(b 2 -a 2), and this couple is infinite when b = oo, as the angular momentum of the vortex is infinite.

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  • Round the cylinder r=a held fixed in the U current the liquid streams past with velocity q' =2U sin 0+m/a; (2) and the loss of head due to this increase of velocity from U to q' is q' 2 -U 2 - (2U sin e to space filled with liquid, and at rest at infinity, the cylinder will experience components of force per unit length (i.) -27rpmV, 27rpmU, due to the vortex motion; 2 dU 2dV (ii.) -71-pa 2 w,, -7rpa dt, due to the kinetic reaction of the liquid; (iii.) o, -7r(a-p)a 2 g, due to gravity, taking Oy vertically upward, and denoting the density of the cylinder by a; so that the equations of motion are 71-0-a 2 - di r = - 7pa2- -- 22rpmV, (4) aa 2 - = -7rpa 2 dV +27rpmV - 7r(cr - p) a2g, (5) 7r or, putting m = a 2 w, so that the vortex velocity is due to an angular velocity w at a radius a, (o+p)dU/dt+2pwV =o, (6) (a+ p) dV /dt - 2 pwU + (v - p)g = o.

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  • Another explanation may be given of the sidelong force, arising from the velocity of liquid past a cylinder, which is encircled by a vortex.

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  • The resultant hydrostatic thrust across any diametral plane of the cylinder will be modified, but the only term in the loss of head which exerts a resultant thrust on the whole cylinder is 2mU sin Olga, and its thrust is 27rpmU absolute units in the direction Cy, to be counteracted by a support at the centre C; the liquid is streaming past r=a with velocity U reversed, and the cylinder is surrounded by a vortex.

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  • 35 A circular vortex, such as a smoke ring, will set up motion symmetrical about an axis, and provide an illustration; a half vortex ring can be generated in water by drawing a semicircular blade a short distance forward, the tip of a spoon for instance.

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  • The vortex advances with a certain velocity; and if an equal circular vortex is generated coaxially with the first, the mutual influence can be observed.

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  • The first vortex dilates and moves slower, while the second contracts and shoots through the first; after which the motion is reversed periodically, as if in a game of leap-frog.

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  • Projected perpendicularly against a plane boundary, the motion is determined by an equal opposite vortex ring, the optical image; the vortex ring spreads out and moves more slowly as it approaches the wall; at the same time the molecular rotation, inversely as the cross-section of the vortex, is seen to increase.

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  • The analytical treatment of such vortex rings is the same as for the electro-magnetic effect of a current circulating in each ring.

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  • Flow, Circulation, and Vortex Motion.-The line integral of the tangential velocity along a curve from one point to another, defined by s v as + u'a s) ds =f (udx+vdy-}-zdz), (I) is called the " flux " along the curve from the first to the second point; and if the curve closes in on itself the line integral round the curve is called the " circulation " in the curve.

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  • If through every point of a small closed curve the vortex lines are drawn, a tube is obtained, and the fluid contained is called a vortex filament.

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  • Hence in any infinitesimal part of the fluid the circulation is zero round every small plane curve passing through the vortex line; and consequently the circulation round any curve drawn on the surface of a vortex filament is zero.

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  • So far these theorems on vortex motion are kinematical; but introducing the equations of motion of § 22, Du + dQ =o, Dv+dQ =o, Dw + dQ dt dx dt dy dt dz and taking dx, dy, dz in the direction of u, v, w, and dx: dy: dz=u: v: w, (udx + vdy + wdz) = Du dx +u 1+..

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  • The circulation being always zero round a small plane curve passing through the axis of spin in vortical motion, it follows conversely that a vortex filament is composed always of the same fluid particles; and since the circulation round a cross-section of a vortex filament is constant, not changing with the time, it follows from the previous kinematical theorem that aw is constant for all time, and the same for every cross-section of the vortex filament.

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  • Hill's spherical vortex, advancing through the surrounding liquid with uniform velocity.

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  • Michell has discussed also the hollow vortex stationary inside a polygon (Phil.

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  • The effect of an external circulation of vortex motion on the motion of a cylinder has been investigated in § 29; a similar procedure will show the influence of circulation through a hole in a solid, taking as the simplest illustration a ring-shaped figure, with uniplanar motion, and denoting by the resultant axial linear momentum of the circulation.

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  • 192, resembling the trochoidal curves, which can be looped, investigated in § 29 for the motion of a cylinder under gravity, when surrounded by a vortex.

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  • When A is held still, and B rotated, centrifugal action sets up vortex currents in the water in the pockets; thus a continuous circulation is caused between B and A, and the consequent changes of momentum give rise to oblique reactions.

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  • Then following into the pocketed chambers V,, V2, it is caught into the vortex, and finally escapes at the circumference, flowing away at F.

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  • lating the water are connected to the casing, so that any tilting automatically regulates the flow, and therefore the thickness of the film in the vortex.

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  • But the hydrodynamical discovery of Helmholtz that a vortex in a perfect liquid possesses certain permanent characteristics has been applied by Sir W.

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  • Thomson (Lord Kelvin) to form a theory of vortex atoms in a homogeneous, incompressible and frictionless liquid."

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  • (i) Let R and S be the vortex and the base of a pyramid.

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  • The other course is to consider matter as formed of ultimate atoms, each the nucleus or core of an intrinsic modification impressed on the surrounding region of the aether; this might conceivably be of the nature of vortical motion of a liquid round a ring-core, thus giving a vortex atom, or of an intrinsic strain of some sort radiating from a core, which would give an electric atom.

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  • FitzGerald) from a structure of tangled or interlaced vortex filaments pervading its substance, which might conceivably arrange themselves into a stable configuration and so resist deformation.

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  • We can obtain a pertinent illustration from the motion of a vortex ring in a fluid; if the circular core of the ring is thin compared with its diameter, and the vorticity is not very great, it is the vortical state of motion that travels across the fluid without transporting the latter bodily with it except to a slight extent very close to the core.

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  • We might thus examine a structure formed of an aggregation of very thin vortex rings, which would move across the fluid without sensibly disturbing it; on the other hand, if formed of stronger vortices, it may transport the portion of the fluid that is within, or adjacent to, its own structure along with it as if it were a solid mass, and therefore also push aside the surrounding fluid as it passes.

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  • The motion of the well-known steady spherical vortex is an example of the latter case.

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  • It is true that the theory of vortex rings in hydrodynamics is of a simpler type; but electric currents cannot be likened to permanent vortex rings, because their circuits can be broken and the element of cyclic steadiness on which the simplicity depends is thereby destroyed.

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  • An effect similar to drift is observable at tennis, golf, base-ball and cricket; but this effect is explainable by the inequality of pressure due to a vortex of air carried along by the rotating ball, and the deviation is in the opposite direction of the drift observed in artillery practice, so artillerists are still awaiting theory and crucial experiment.

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  • Thus the rotifer is, as it were, constantly drawn forward into the centre of this vortex ring.

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  • In addition to a large number of publications in the Proceedings of the Royal Society and the Philosophical Magazine, he has published A Treatise on the Motion of Vortex Rings (1884); The Application of Dynamics to Physics and Chemistry (1886); Recent Researches in Electricity and Magnetism (1892); Elements of the Mathematical Theory of Electricity and Magnetism (18 95, 5th ed.

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  • From these contests of rival nobles, in which the names of Spinola and Doria stand forth with greatest prominence, Genoa was soon drawn into the great vortex of the Guelph and Ghibelline factions; but its recognition of foreign authority - successively German, Neapolitan and Milanese - gave way to a state of greater independence in 1339, when the government assumed a more permanent form with the appointment of the first doge, an office held at Genoa for life, in the person of Simone Boccanera.

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  • In the famous typhoon of the 10th of October 1882, the vortex of which passed over Manila, an immense amount of damage was done in the city.

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  • Immediately afterwards Langton was drawn into the vortex of English politics.

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  • Unfortunately, she, in common with the rest of South Africa, was subsequently swept into the seething vortex of contemporary politics and controversy.

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  • It is impossible within brief limits to convey more than a general idea of the work of a philosopher who published more than three hundred original papers bearing upon nearly every branch of physical science; who one day was working out the mathematics of a vortex theory of matter on hydrodynamical principles or discovering the limitations of the capabilities of the vortex atom, on another was applying the theory of elasticity to tides in the solid earth, or was calculating the size of water molecules, and later was designing an electricity meter, a dynamo or a domestic water-tap. It is only by reference to his published papers that any approximate conception can be formed of his life's work; but the student who had read all these knew comparatively little of Lord Kelvin if he had not talked with him face to face.

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  • These results showed that the vortex breakdown is a very sensitive technique to study polymer rheology.

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  • Vortex dynamics in strongly stratified flow over three-dimensional obstacles.

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  • For the first time, the phenomenon of vortex merger has been identified in the stratosphere of the southern hemisphere (Lahoz et al.

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  • The vortex establishes itself in the middle to lower stratosphere.

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  • Striking graphics confusing ANYONE who has seen 3-D Tunnel will find Vortex for the 16K Spectrum familiar.

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  • Noticed a perfect upside down cone shape as the vortex moved out across the lake.

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  • Most of the game consists of rounding up rabbits or other vermin into the swirling vortex of your vacuum vehicle machine.

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  • Dynamics of the vortex wakes of swimming and flying vertebrates.

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  • The Vortex dampens the vibration caused by the rapidly spinning motors in the hard drive, reducing noise and shock.

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  • The Gilkes Vortex turbine was manufactured in Kendal and drove a 6kw dynamo generating 110 volts.

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  • Then I felt drawn into what seemed like a vortex of energy.

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  • At the blade tip, a similar leakage induces a vortex about the blade tip.

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  • The vortex patterns correspond to the intersection of the laser sheet with the trailing, helical vortices from the turbine blades.

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  • The changes in wind speed then create a vortex.

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  • Lee, A. M., et al., The impact of the mixing properties within the Antarctic stratospheric vortex on ozone loss in spring.

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  • Air Cannon Target our air cannons at a target and push the plunger to send a spinning vortex of air across the room.

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  • On the hill there are a lot of objects that are quite capable of causing vortex shedding - hillwalkers included.

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  • Part 3: examples of applications of vortex generators to aircraft.

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  • Use vortex dynamics to determine the development of simple three-dimensional flows.

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  • The vortex wake is then all concentrated in two trails.

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  • What is the status of your vortex tube work?

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  • The periodic shedding of the tip vortex at the blade tip is also observed in vorticity contour plots measured at the of axial planes.

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  • WISY Vortex Filters Vortex filters connect to standard storm water pipes below ground.

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  • A vortex is a rapidly whirling spiral, a body of fluid or gas rotating around its own center.

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  • Canari Vortex Lyte Lycra Cycling Shorts made from nylon and lycra.

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  • Even the names of the shades evoke power, sophistication, and superior performance: Lightning, Thunder, Legacy, Heat, Warrior, Speed, Inferno, Vortex, Equinox, and Hurricane are all Gargoyle styles.

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  • Another B&M designed ride, the Vortex is a standing coaster featuring a loop and a corkscrew.

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  • While it isn't pink, the LG Vortex is available in a violet color.

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  • The blender uses a proprietary vortex mixing mechanism and a clover-shaped carafe to increase efficiency and decrease blending time.

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  • LD: Miele's ultra-quiet Vortex Motor System™ delivers the powerful suction and airflow necessary to remove stubborn pet hair and is tested to last an incredible 20 years.

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  • The site lists the Braun Series 7 760cc electric razor as the best all around shaver, the Philips Norelco Arcitec 1050X as the best rotary shaver and the Panasonic Vortex HydraClean ES8109S as the best wet/dry foil shaver.

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  • Jewelry Vortex: The Jewelry Vortex offers more affordable versions of the baguette diamond wedding bands.

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  • Jewelry Vortex has matching textured bands in a variety of styles, including braids, checked patterns and waves.

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  • Vortex Shadow lists tables from which you'll select various prefixes and suffixes to create unique elven names.

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  • d o, dx dy dz dx dy dz so that, at any instant, the surfaces over which tk and m are constant intersect in the vortex lines.

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  • (i) Let R and S be the vortex and the base of a pyramid.

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