FLU (t%
Hydrojlatical Laius of F l u i d s.
FLU
I. Of the Preffure and Equilibrium of F l u i D s.
i° The upper Tarts of all Fluids, as Water, &c. do prefs upon the lower : Or, as fome Philofophers ftate it; ^//Flu- ids do gravitate in proprio loco.
The Contrary of this was a Principle in the School-Philo- ophy; but the Certainty of fuch Preffure is now demon- ftrated by a thoufand Experiments : It will be fufficient to initance one or two.
Immcrge a Tube, open at both Ends, and half filled with Oil of Turpentine, in a Veffel of Water, the upper End of the Tube being ttopp'd with the Finger : If now the upper Surface of the Oil lie as low as that of the Water; the Oil, upon removing the Finger, will not run out at the lower End of. the Tube : Nay, and if the Tube be thrult a little lower, the Water will rile up in it, and bear the Oil above it : But if the upper Surface of the Oil be confider- ably higher than chat of the Water; the Oil will drop out of the Tube. Whence it follows, that the Column of Oil in one cafe preffes or gravitates lefs on the Plane imagined to pafs under its lower Surface, than a Column of Water 5 and in the other cafe, more.
Or thus; an empty Vial, clofe fhut, being immerfed in Water, and fufpended by a Horfe Hair to the Ecam of a Balance, with a Weight at the other End exactly counter- poiling it : Upon unltopping the Vial, and letting it fill with Water, it will preponderate, and bear down the End of the Balance; without having any Communication with the external Air.
Which two Experiments abundantly prove the Propofi- tion, that the upper Parts of Fluids prels, or gravitate on the lower. See Pressure, and Gravitation.
Corel'. From this Gravity it follows, that the Surfaces of ifagnant Fluids are plain, and parallel to the Horizon; or rather that they are Segments of a Sphere concentrical with the Earth.
For, as the Particles are fuppofed to yield to any Force imprefs'd, they will be moved by the Action of Gravity, till fuch time as none of them can defcend any lower. And this Situation once attained, the Fluid mult remain at reft, unleis put in Motion by fome foreign Cauie; inafmuch as none of the Particles can now move without afcending; contrary to their natural Tendency.
2 If a Body be immerfed in a Fluid, either wholly, or in part, its lower Surface will he prefs'd upward by the Water underneath it.
The Truth of this Proposition is evident from the Ex- periment above mention'd; where the Oil of Turpentine was lufpended, nay and made to mount up in the Tube by the Preffiire of the Water upwards on its lower Parts.
The Law, or Quantity of this Preffure is this, that a "Body immerged in a Fluid, lofes juft fo much of the Weight it would have in Air; as fo much of the Fluid as is equal to it in "Bulk, if weigh'd in the Air, would amount to.
This Preffure of Fluids on the lower Parts of an immerfed Body is farther confirm'd, by attending to the Reafon why Bodies fpecifically lighter than Fluids afcend therein. The Effect, is owing to this, that there is a greater Preffure or Weight on every other Part of the Plane or Surface of the Fluid imagined to pais under the lower Surface of the Body, than there is on that whereon the emerging Body in- fills. Conlequently, to produce an Equilibrium in the Fluid, the Parts immediately under the riling Body being prols'd by the reft every way, do continually force it up- wards.
In effect, the emerging Body is continually prefs'd on by two Columns of Water, one bearing againft its upper; and the other againft its lower Parrs : The length of both which Columns being to be accounted from the Top of the Water; that which preffes on the lower Part, will be the longer, by the Thicknels of the afcending Body, and conlequently overbalance it by the Weight of as much Water as will till the Space that Body takes up. See Specific Gravity.
Corel. 1. Hence we are furnifti'd with one Reafon, why very minute Corpufcles, either heavier, or lighter than the Liquor they are mingled with, will be fuftain'd therein a good while, without either emerging to the Top, or pre- cipitating to the Bottom : The Difference between the two Columns of the Fluid being here inconiiderable.
Carol, z. Hence alfo, if a Body A be fpecifically lighter than B, an equal Portion of the Fluid in which it is immerged; it will rife with a Force proportionable to the Exccfs of Gravity ofB above A: And if A be fpecifically heavier than B; it gtavitatcs and defcends with the Excels only of its Weight above that of B.
- ° The 'Preffure of the upper Tarts of a Fluid, on the
lower, exerts it felf every way, and every way equally; laterally, horizontally ■, and obliquely as well as perpendicu- larly.
For, as the Parts of a Fluid yield to' any Impreflion, and are eafily moved, 'tis impoffible any Drop fhou a reman in its Place : If while it is prefs'd by the fuper-incurhbenc Fluid, it be not equally prels'd on every fide.
The fame is confirm'd from Experiments : For fevcral Tubes of divers Forms, flraight, curved, annular gV. fad- ing immerfed in the fame Fluid; tho' the Apertures, 'thro' which the Fluid enters, be differently pofited to the Surface or Plane, fome being perpendicular, others parallel, and others varioufiy inclined; yet will the Fluid rife to an eoual Height in all.
Carol. 1. Hence, all the Particles of -Fluids being thus 1 equally prefs'd on all Sides, 'tis argued that they mull be at reft, and not in continual Motion; as has been ufually fuppos'd. — ■ — •
Corel, 2. Hence alfo a Body being immerfed in a Fluid, fuilams a lateral Preffure from the Fluid; which is alfo in- creased as the Body is placed deeper beneath the Surface of the Fluid. ■
4 ' In Tubes that have a Communication with each other, whatever their Magnitude be, whether equal, or unequal 3 and whatever their Form, whether freight, angular, or crooked : Still, Fluids rife in them to the fame Height.
5" If a Fluid rife to the fame Altitude in two Tubes that communicate with each other; the Fluid in one Tube is at Balance, or equal in weight, to that in the other.
If the Tubes be of equal Diameters, the Columns ot the Fluid having the fame Bafe and Altitude, are equal, and confequently their Gravities equal; fo that they prefs and gravitate againft each other with equal Force.
the Space of an Inch, as from L toO; it will then rife in the other the Space of four Inches, as from M to N. Where- fore the Velocity wherewith the Fluid moves in the Tube H K, is to that wherewith it moves in G I; as the Bafe of the Tube G I to the Bafe of the other, H K. But the Altitude of the Fluid being fuppofed the fame in both Tubes, the Quantity of the Fluid in the Tube G I, will be to that in the other Tube H K as the Bafe of the Tube G I to the Bafe of the other, H K.
Confequently, the Momentum of the Fluid in the Tube G I, is to that in the Tube H K, as the Product of the Bafe of the Tube G I into the Bafe of the other H K; to the Factum of the Tube H K into the Bafe of the other G I. Wherefore, the Products being equal; the Momenta muff be equal.
The fame is eafily demonftrated where one of the Tubes is inclined, and the other perpendicular, gfc.
Corel. Hence in Tubes that communicate, the Fluid preponderates in that where its Altitude is the greateft.
6" In Communicating Tubes, Fluids, of different fpecific Gravities, will equiponderate, if their Altitudes be in the Ratio of their fpecific Gravities.
Corel. Hence we have a Way of finding the Specific Gravities of Fluids, viz* by pouring one Fluid into one of the communicating Tubes, as A B [Fig 7.) and another, into the other Tube C D; and meafuring the Altitudes E B and F D, at which they ftand when balanced.
For the fpecific Gravity of the Fluid in A B, is to that • in D C; as D H, to B G. If the Fluids be apt to mix; it may be proper to fill the Horizontal Tube B D with Mer- cury, to ptevent the Mixture.
Corel. Since the Denudes of Fluids, are as their fpe- cific Gravities; the Denfities will likewiie be as the Alti- tudes of the Fluids D H and B G : So that we have hence likewiie a Method of determining the "Denfities of Fluids. See Density;
7° The Bottoms, and Sides of Veffels, are prefs' din the fame manner, and by the fame Laws as the Liquids, con- tained in them.
Corel. Hence as Action and Re-action are equal; the Fluids fhemfelves, fuftain an equal Preffure from the Bot- toms and Sidesi And as the Preffton of Fluids is equal every way, the Bottom and Sides are prefs'd as much as the neighbouring Parts of the Fluids: And confequently this Action increafes in proportion to the Height of the Fluid ■ and is equal every way at the fame Depth '; as depending al- together on the Height, and not at all on the Quantity of the Fluid.
8° In perpendicular Veffels of equal Safes, the <Pref- furcs of Fluids on the Bottoms, is in the Ratio of their AltitudeSi
This is evident, in that the Veffels being perpendicular, the Bottoms are horizontal : Confequently the Tendency of Fluids by the Action of Gravity will be in Lines perpendi- cular to the Bottom; fo that they will prels with all their Weight : The Bottoms therefore are prefs'd in the Ratio of the Gravities. But the Gravities are as the Bulks; and the Bulks here are as the Altitudes : Therefore the Pref- fures on the Bottoms are as the Altitude*.
»° I?
