FLU
(6a)
FLU
$° In perpendicular Veffels of unequal Bafes t the Pref- fure on the 'Bottoms is in a Ratio compounded of the Sa- fes, and Altitudes.
From the proceeding Demonfiration it appears, that the Bottoms are prefs'd in the Ratio of the Gravities : And the Gravities of Fluids are as their Bulks; and their Bulks in a Ratio compounded of the Bafas and Altitudes. Confe- riuentiy, &c. , ,
io° If an inclined Veffel A B C D, Fig. 8. have the fame Safe and Altitude with a perpendicular one B £ F G, the Bottoms of each 'Bill he equally prefs'd.
For in the inclined Veffel A B C D, the Bottom C D, is prefs'd in the Direaion B D. But the Force of Gravity in the Direction B D, is to the abfolute Gravity, as B E to B D. See Gravity.
Confequently, the Bottom C D is prefs'd in the fame manner; as if it had been prefs'd perpendicularly by the Fluid under the Altitude B E. Therefore, the Bottoms of the perpendicular and inclined Veffels are equally prefs'd.
n« Fluids prefs upon fubjcBcd Bodies, according to their perpendicular Altitude, and not according to their Latitude.
Or, as others ftate it, thus : If a Veffel be taper, or un- equally big at Top and Bottom ; yet the Bottom will be prefs'd after the fame manner as if the Veffel were cylin- drical, and the Top and Bottom equal.
Or thus : The Preffure fuftain'd by the Bottom of a Vef- fel, whatever the Figure of the Veffel be, is ever equal to the Weight of a Column of the Fluid, whofe Bafe is the Bottomit felf, and Height, the vertical Diftance of the upper Surface of the Water from the Bottom.
Or, yet more explicitly, thus: If there be two Tubes or Veffels, having the fame Heights, and Bafes, both filled with Water ; but one of them made lb tapering upwards, that it mail contain but twenty Ounces of Water, whereas the other widening upwards, holds 200 Ounces: Yet, the Bottoms of the two Tubes fhall fuflain an equal Preffure of Water, vis. each of them, that of the Weight of 20CO Ounces.
This is a noble Paradox in Hydroftaticks, which it is well worth th" clearing and infilling on. It is found unexecptien- ably true from abundant Experiments : And may even be demonftrated and accounted for on Principles of Mecha- llicks.
Suppofe e. gr. the Bottom of a Veffel, C D ( Fig. 9. ) lefs than its Top, A B. Since the Fluid preffes the Bottom C D, which we fuppofc horizontal, in a perpendicular Di- rection E C, none but that Part within the Cylinder E C D F can prefs upon it ; the natural Tendency and Preffure of the reft being taken off by the Sides.
Again, fuppofing the Bottom, CDC Fig. 10. ) much big- ger than the Top F G. Or even, for the eafier Demon- stration, fuppofe a Tube F E fix'd in a Cylinder A B C D : And fuppote the Bottom C D rais'd to L ; that the Fluid may be moved through the Interval D L. Then will it have rifen through the Altitude G H, which is to D L, as the Bafe C D to that G F. The Velocity therefore of the Fluid F E, is to its Velocity in the Veffel A D ; as the Bafe C D to the Bafe F G.
Hence, we have the Momentum wherewith the Fluid in the Tubes tends downwards, by multiplying the Bafe of the Cylinder C D into its Altitude C K.
Consequently, the Bottom C D is prefs'd with the fame Force ; as it would be prefs'd by the Cylinder H C D I.
To confirm and illultrate this Doctrine of the Preffure of Fluids in the Ratio of the Bafe and Altitude, provide a me- tallick Veffel, A C D B {Fig. 11.) *° contrived, as that the Bottom C D may be moveable, and to that End fitted in the Cavity of the Veffel with a Rim of wet Leather, to Hide without letting any Water pafs. Then, thro' a Hole in the Top, A B, apply fuccefftvely feveral Tubes of equal A-Ititudes, but different Diameters. Laftly, fattening a String to the Beam of a Balance, and fixing the other End by a little Ring K. to the moveable Bottom ; put Weights in the other Scale, till they be fufficient to raife the Bottom C D : Then will you not only find, that the fame Weight is re-
by the whole Cylinder H C D I. —
ia° The moft folid and ponderous Body, which near the Surface of the Water would fink, with great Velocity, yet if placed at a greater Depth than twenty times its own Thicknefs, will not fink, unlefs affifted ly the Weight of the incumbent Water.
Thus, immcrge the lower End of a flender Glafs Tube in a Veffel of Mercury : Then, (topping the upper End with your Finger, you will by that means keep about half an Inch of that ponderous Fluid, fufpended in the Tube. Laftly, keeping the Finger thus; immerge the Tube in a long Glals of Water, till the little Column of Mercury be more than <3 or 14 times its Length under Water. Then, removiug
the Finger, you will find that the Mercury will be kept fuf- pended in the Tube by the Preffure of the Water upwards: But if you raife the Tube a very little above the former Station ; the Mercury will immediately run out : Whereas if before you had removed the Finger from the Top, you had funk the Pipe fo low, as that the Mercury were 12 or 14 Inches, &c. below the Surface of the Water ; the Mer- cury would be violently forced up, and make feveral Afcents and Delcents in the Tube, till it had gain'd its proper Sta- tion, according to the Laws of fpecific Gravity.
Corel. Hence we have a Solution of the Phenomenon of two polifh'd Marbles, or other Planes, adhering fo ftrong- ly together: In that the Atmofphere preffes or gravitates with its whole Weight on the under Surface and Sides of the lower Marble ; but cannot do fo at all on its upper Sur- face, which is clofely contiguous to the upper, and fufpended Marble.
II. For the Laws of the 'Preffure and Gravitation in Flu- ids specifically heavier, or lighter than the Bodies im- merged, fee Specific Gravity.
For the Laws of the Refinance of Fluids, or the Re- tardation of foitd Bodies, moving in Fluids, fee Resist- ance.
For the Jfcent of Fluids in Capillary Tubes, or be- tween Glafs Planes, fee Ascent.
The Motions of Fluids, and particularly Water, make the Subject of Hydrulicks. See Hydrulicks.
Hydrulich Laivs of Fluids.
i p ihe Velocity of a Fluid, as Water, moved ly the Pref- fure of a fuper-incumhent Fluid, as Air, is equal at equal "Depths ; and unequal, at unequal ones.
For the Preffure being equal at equal Depths, the Velo- city arifing thence muft be fo too ; and vice verfa : Yet does not the Velocity follow the fame Proportion, as the Depth ; notwithstanding that the Preffure, whence the Ve- locity arifes, does increafe in the Proportion of the Depth. But here the Quantity of the Matter is concern 'd : And the Quantity of Motion, which is compounded of the Ra- tio of the Velocity and Quantity of Matter, is increafed in equal times as the Square of the Velocities.
2° The Velocity of a Fluid arifing from the 'Preffure of a fuper-incumhent Fluid, at any Depth, is the fame as that which a Body would acquire in falling from a Height, e- qual to the Depth. As is demonftrated both from Mecha- nicks and Experiments. See Descent.
3° Jf two Tithes of equal Diameters, full of any Fluid, he placed any how, cither ereff, or inclined ; provided they he of the fame Altitude, they will difcharge equal Quanti- ties of the Fluid in equal times.
That Tubes, every way equal, mould, under the fame Circumftances, empty theriifclvcs equally, is evident ; and that the Bottom of a perpendicular Tube is prefs'd with the fame Force, as that of an inclined one, when their Al- titudes arc equal, has already been fhewn. Whence it eafily follows, that they muft yield equal Quantities of Water, ££c.
4 Jf two Tubes of equal Altitudes, hut unequal jlper- tures or Diameters, be kept constantly full of Water, the Quantities of Water they yield in the fame Time, will be as the Diameters : And this, whether they be erctJ, or any how inclined.
Corel . If the Apertures or Diameters be circular, the Quantities of Water emptied in the fame time, are in a du- plicate Ratio of the Diameters*
This Law, Mariotte obferves, is not perfectly agreeable to Experiment. If one Diameter be double the other, the Water flowing out of the lefs is found more than a Fourth of what flows out of the greater. But this muft be owing to fome accidental Irregularities in making the Experi- ments.
Wolfius afcribes it principally to this, that the Column of Water direct ly over the Aperture is fhorter than that next the Sides or Parietes of the Veffel : For the Water, in its Efflux forms a kind of Cavity over the Aperture ; that Part immediately over it being evacuated firft, and the other Water not running faft enough from the Sides to fupply it. Now, this Cavity, or Diminution of Altitude being greater in the greater Tube, than the lefs; hence the Preffure or Endeavour to pafs out, becomes proportionably lefs in the greater Tube, than the lefs.
5° If the Apertures E and F of two fubes A B and C 2>(Fig. iz) be equal,the Quantities of Water 'difcharged in the fame time are as the Velocities.
6° If two "Tubes have equal Apertures E and F, and unequal Altitudes A B and C D ; the Quantity of Water difcharged from the greater A B, will be to that dij- charged from C D, in the fame time ; in a fubduplicate Ratio of the Altitudes A 8 and C D.
Corel.
