FLU
(61 )
FLU
Corel, i. Hence, the Altitudes of Waters, A B, and CD, difcharged thro' equal Apertures E and F ; are in a duplicate Ratio of the Waters difcharged in the fame time. And as the Quantities of Water are as the Velocities ; the Velocities are likewife in a fubduplicate Ratio of their Altitudes;
z. Hence, the Ratio of the Waters difcharged by two Tubes A B, and C D, together with the Altitude of one of them being given j we have a Method of finding the Altitude of the other, viz. by finding a fourth Proportional to the three given Quantities ■ which Proportional multi- plied by it felf, gives the Altitude of CD, required.
3. Hence alfo, the Ratio of the Altitudes of two Tubes of equal Apertures being given ; as alfo the Quantity of Water difcharged by one of them ; We have a Method of determining the Quantity the other fliall difcharge in the fame time. Thus, to the given Altitudes, and the Square of the Quantity of Water difcharged at one Aperture, find a -fourth Proportional. The fquare Root of this will be the Quantity of Water required.
Suppofe e.gr. the Heights of the Tubes as 9 to 25 ; and the Quantity of Water difcharged at one of them, three Inches: That difcharged by the other, will be =r jJ (9.2.5:9)
— V I! = 5.
7 c If the Altitudes of two tubes A S, and C D be un- equal ; and the Apertures, E and F like-wife unequal : the Quantities of Water difcharged in the fame twie t will be in a Ratio compounded of the fimple Ratio of the Aper- tures ; and the fubduplicate one of the Altitudes.
Corol. Hence, if the Quantities of Water difcharged in the fame time by two Tubes, whole Apertures and Altitudes arc unequal, be equal 5 the Apertures are reciprocally as the Roots of the Altitudes : and the Altitudes in a reciprocal Ratio of the Squares of the Apertures.
8° If the Altitudes of two "tubes be equal, the Water will flow out with equal Velocity, however unequal the Apertures be.
9 If the Altitudes of two tubes, A S, and C D (Fig;i 9.) as alfo their Apertures E, and Fbe zinequal^ the Velocities of the Waters difcharged are in a fubduplicate Ratio of their Altitudes,
Corol. 1. Hence, as the Velocities of Waters flowing out at equal Apertures, when the Altitudes arc unequal, are alfo in a fubduplicate Ratio of the Altitudes - y and, as this Ratio is equal, if the Altitudes be equal ; it appears, in the general, that the Velocities of Waters flowers out of Tubes is in a lubdupHcate Ratio of the Altitudes.
2. Hence alfo, the Squares of the Velocities aire as the Altitudes.
Mariotte found from repeated Experiments, that if a Veffcl A B C D have a Tube E F fitted to it, there will more Water be evacuated through the Tube, than there could have been in the fame time, through the Aperture of the Veffel E, without the Tube : And that the Motion of the Fluid is accelerated fo much the more, as the Tube E F is the longer.
E.gr. The Altitude of a Veflel A C being one Foot, that of the Tube E F three Feet, and the Diameter of the A- pcrture three Lines ; 6{- Septiers of Water were difcharged in the Space of one Minute; whereas- upon taking off" the Tube, only four Septiers were difcharged. Again, when the Length of the Tube E F was fix Feet, and the Dia- meter of the Aperture F, an Inch 5 the whole Quantity of Water run out in 57 Seconds: But, cutting off half the Tube F H, the Veffel was not evacuated in lefs than 4.5 Se- conds ; and taking it quite away, in lefs than 95 Seconds.
9° the Altitudes and Apertures of two Cylinders full of Water, being the fame : One of them will difcharge double the Quantity of Water difcharged in the fame time by the other , if the firfl be kept continually full, while the other runs it fclf empty.
For the Velocity of the full Veffcl will be equable 5 and that of the other continually retarded. Now, 'tis demon- ilrated, that, if two Bodies be impell'd by the fame Force, and the one proceeds equably, and the fecond is equably re- tarded : By that time they have loft all their Motion, the one has moved double the fpace ot the other.
io° If two tubes have the fame Altitudes, and equal A- fcrtures ■ the times wherein they will empty themfelves, will be in the Ratio of their Safes.
ii° Cyiindric, and Trifmatic Vejfcls , as A S C D (Fig. 14.) empty themfelves by this Law, that the Quanti- ties of Water difcharged in equal times, decreafe according to the uneven. Numbers, 1. 3- 5- 7-9- <kc. taken backwards.
For the Velocity of the defcending Level F G is conti' nually decreafing in the fubduplicate Ratio of the decreaf- ing Altitudes: But the Velocity of a heavy Body defcend- ing, incrcafes 'in the fubduplicate Ratio of the incrcafing Altitudes. The Motion, therefore, of the Level F G in its Defccnt from G to B, is the fame, as if it were to defcend in the inverfe Ratio, from B to G. But if it defcend from B to G, the Spaces, in equal times, would incrcale accor- ding to the Progreilion of the uneven Numbers. Conle-
quently, the Altitudes of the Level F G in equal times decreafe according to the fame Progrcffion inverfely taken.
Corel. Hence, the Level of Water F G, defcends by the fame Law, as, by an equal Force imprefs'd, it Would, afcend thro' an Altitude equal to F G.
From this Principle, might many other particular Law3 of the Motion of Fluids be demonstrated, which for Bre- vity fake we here omit.
To divide a Cylindrical Veffel into Tarts, which floall be evacuated in certain Tarts, or Divifions of time, fee Clepsidra.
i2° If Water defcending thro" a tube II E (Fig. 1 5.) fpout up at the Aperture G, whofc Direction is vertical, it will rife to the fame Altitude G I, at which the Level of the Water L M, in the Vcjfcl A $ CD does Jland.
For fince the Water is driven thro' the Aperture G, by the Force of Gravity of the Column E IC ; its Velocity will be the fame as that of a Body by the fame Force imprefs'd, would rife to the Altitude F I. Wherefore, fince the Di- rection of the Aperture is vertical ; the Direction of the Water fpouting thro' it, will be fo too. Confequcntly, the Water muft rife to the Height of the Level of the Water .L M in the Veflel.
Indeed, by the Experiment it appears, that the Water does not rife quite fo high as I : Befide, that the Aperture G mould be fmaller, as the Height of the Level of the Water is lefs : And even (mailer, when Mercury is to be fpouted, than when Water. But this is no Objection to the Truth of the Theorem ; it only fliews that there are cer- tain external Inpediments, which diminifh the Afcent.
Such arc the Refinance of the Air; the Friction of the Tube, and the Gravity of the afcending Fluid.
1 3 Water defcending thro' an inclined Tube, or a Tube bent in any manner; will fpout up through a perpendicular Aperture to the Height at which the Level of the Water in the Veffcl ftands.
14 the Lenghts or Di fiances 2) E.and 2> F, or 1 11, and /G(Fig.itf.) to which Water will fpout either thro* an in- clined, or a horizontal Aperture 2), are in a fubduplicate Ra- tio of the Altitudes in the Vcjfel or tube A % and A 2>.
For, fince Water fpouted out thro' the Aperture D, en- deavours to proceed in the horizontal Line DF; and at the fame time, by the Power of Gravity, tends downwards in Lines perpendicular to the lame ; nor can the one Power hinder the other, in as much as the Directions are not con- trary : It follows, that the Water by the Direction B A will arrive at the Line I G, in the fame tithe wherein it would have arrived at it, had there been no horizontal Impulfe at all. Now the Right-lines I H and I G are the Spaces which the fame Water would have defcribed in the mean time by the horizontal Impetus : But the Spaces IH and I G, inafmuch as the Motion is uniform, are as the Velo- cities. Confequently, the Velocities are in a fubduplicate Ratio of the Altitudes A B and A D. And therefore, the Lengths or Diflances to which the Water will fpout in A- pertures cither horizontal or iuclined, are in a fubduplicate Ratio of the Altitudes.
Corol. Hence, as every Body projected cither hori- zontally, or obliquely, in an unre filling Medium, delcribes a Parabola: Water projected either through, a vertical or inclined Spout, will defcribc a Parabola.
Hence we have a way of making a delightful kind of Water Arbours, or Arches, viz. by placing fcveral inclined Tubes in the fame Ri^ht-line.
On thefe Principles are form'd various Hydraulic En- gines for the raifing, &c. of Fluids, as Pumps, Syphcns, Fountains, or Jets de Eau, &c. Which fee defcribed under their proper Articles, Pump, Syphon, Fountain, Smp.al Screw, &c.
For the Laws of the Motion of Fluids, by their own Gravity, along open Channels, ike. fee Rivep., and Wave. ■ For the Laws of Tre/fure and Motion of Air, confi- defd as a Fluid, fee Air, and Wind.
FLUMMERY, A wholefome Jelly, made of Oatmeal.
The manner of preparing it in the Weftern Parts of England, is to take half a Peck of Wheat Bran, which muit be (baked in cold Water three or four Days; then ftrain out the Oil and Milk-water of it, and boil it to a Jelly : After- wards leafon it with Sugar, Rofe and Orange-flower Water, and let it fiand till cold, and thickened again ; and then ear it with White or Rhenilli Wine, or Milk-cream.
FLUOR, in Phyfick, &c. a Fluid ; or more properly, the State of a Body, which was before hard, or folid, but is now redue'd by Fu'fion or Fire into a State of Fluidity. See Fluidity.
Gold and Silver will remain a long time in a Fluor, kept to it by the intenfeft Heat, without lofing any thing ot their Weight. See Fixity.
Fluor is alfo us'd by the modern^ Mineral Writers for fuch foft, tranfparent, {tarry kinds of mineral Concretions, as are frequently found amongll Oars, and Stones, in Mines and Quarries.
- Q_ Fluor
