1096

THEORY AND PRACTICE OF ENGINEERING.

Book II.

400 kilogrammes; his Telocity at the ordinary pace without a load is T6 metres, his velocityin the machine is 0-8 metres; we have then

A —400 kilogrammes; v = 1 *6 metres ; w = 0‘8 metre.

The formula gives A'= 400 (1—^)*, or 100 kilogrammes, which is confirmed by experi-ment.

"We must remark that the formula of Euler , which determines with sufficient precisionthe pressure corresponding to the daily labour of animated movers as compared to water, isnot by any means satisfactory for the calculation of the effects of this fluid on the water-wheel. When treating of this fluid as a moving power we shall give another formula, whichaffords results approaching near to those observed.

CHAP. XVL

HYDROSTATICS.

Hydrostatics which teaches of the equilibrium of fluids, and that a fluid is composed ofmaterial particles, infinitely small, and move without friction on each other in every direction;this property it is which occasions it to communicate pressure equally in all directions:for the purpose of examining these qualities, it is necessary that we should leave out ofour consideration, all which relates cither to their expansibility or compressibility, theircohesion and capillary attraction. We must also view them as having a uniform densitythroughout.

One of the first laws which is apparent is that the surface of such a fluid, when at rest,assumes the horizontal : the face, however, always being perpendicular to the direction of allthe forces which act upon it, the power of gravitation having the effect upon the waters ofthe ocean, of occasioning it to lie in parallel lines with the earth’s curvature. We find alsothat when any part of a fluid is raised above the surface, it will quickly return to its level,from whence we learn that the pressure of a fluid on every particle of the vessel containingit, or any other surface in contact with it, is equal to the weight of a column of the fluid ofwhich the base is equal to that particle, and the height to its depth below the surface of thefiuid: so that in a cistern 10 feet deep, each square foot will sustain the weight of 10 cubefeet of the liquid, or 10,000 ounces; in a vessel filled with mercury, an inch in depth, eachsquare foot will sustain a pressure of 1130 ounces; the atmosphere has a pressure uponeach square foot of the earth’s surface of 34,000 ounces, which is equivalent to the weightof a column of mercury 30 inches high. It is therefore obvious that the pressure on everysquare foot of the bank of a river increases continually in descending towards the bottom.

Of the Level of Liquids and their Equilibrium. — Liquids, like other heavy bodies, tendalways towards the earth's centre, and descend as low as possible unless some obstacle pre-vents them. Water poured into a vessel and left to itself always assumes its level, for ifthere is at first one part of its surface more elevated than another, it will descend towardsthe lower as on an inclined plane, or as along several contiguous inclined planes, if it makea species of curve. If there be still some places higher than others, the same w ill happento each of them; the most elevated parts, if they can, will descend as low as possible, andwhen there is no longer any agitation on the surface, it will be found level, since all itspoints are equidistant from the earth's centre, and will always maintain themselves in tillsstate, if they are not put in motion.

"When the surface of a liquid is level , all the columns of which this liquid is composed are inequilibrio. — Suppose we pour water into the prismatic vessel BC, and that we supposethis water divided into columns of equal bases, that the surface A E of the first column 13 Eshould be level with the surface E F of the second; it is necessary that these two columnsshould counterbalance each other, and tend mutually to raise each other by an equal efforton their bases, otherwise if the first bore upon the second, the surface of this second, risingabove that of the first, could not maintain itself in this position, because, not being sustainedat the sides, it would fall on the first in order to assume its level. In like manner thesecond column, EM, could not by its own weight bear upon the third, M G, without thesurface of the latter mounting, and the former descending, but these two columns being ofan equal weight, there is no reason why one should bear upon the other; in like mannerall those which follow sustain each other reciprocally in equilibrio.

Hence when wc mix two liquids together, one of which is lighter than the other, as oiland water, the heaviest compels the lightest to rise to the surface ; nevertheless it appearsthat it is the oil which separates itself from the water.