second considerably larger at top than at bottom, the third considerably less at top than at bottom, and with the sides of the two latter either regularly or irregularly sloped, have their bottoms moveable, but kept close by the action of a weight upon a lever; then it will be found, that when the same weight acts at the same distance upon the lever, water must be poured in to the same height in each vessel before its pressure will force open the bottom. 3. Let a glass tube, open at both ends (whether cylindrical or not, does not signify), have a piece of bladder tied over one end, so as to be capable of hanging below that end, or of rising up within it, when pressed from the outside. Pour into this tube some water tinged red, so as to stand at the depth of seven or eight inches; and then immerse the tube with its coloured water vertically into a larger glass vessel nearly full of colourless water, the bladder being downwards serving as a flexible bottom to the tube. Then, it will be observed that when the depth of the water in the tube exceeds that in the larger vessel, the bladder will be forced below the tube, by the excess of the interior over the exterior pressure: but when the exterior water is deeper than the interior, the bladder will be thrust up within the tube, by the excess of exterior pressure: and when the water in the tube and that in the larger vessel, have their upper surfaces in the same horizontal plane, then the bladder will adjust itself into a flat position just at the bottom of the tube. The success of this experiment does not depend upon the actual depth of the water in the tube, but upon the relation between the depths of that and the exterior water; and proves that in all cases, the deeper water has the greater pressure at its bottom, tending equally upward and downward. 4. The hydrostatical paradox, as it is usually denominated, results from the principle that any quantity of a non-elastic fluid, however small, may be made to balance another quantity; or any weight, as large as we please. It may be illustrated by the hydrostatic bellows, consisting of two thick boards DC, F E, each about 16 or 18 inches dia meter, more or less, covered or connected A E as three hundred weights, be laid upon the upper board, bv pouring the water in at the pipe till it be full, it will sustain all the weights, though the water in the pipe should not weigh a quarter of a pound: for the pipe or tube may be as small as we please, provided it be but long enough, the whole effect depending upon the height, and not at all on the width of the pipe for the proportion is always this, As the area of the orifice of the pipe is to the area of the bellows board, so is the weight of water in the pipe, above D C, 5. In lieu of the bellows part of the apparatus, the leather of which would be incapable of resisting any very considerable pressure, the late Mr. Joseph Bramah used a very strong metal cylinder, in which a piston moved in a perfectly air and water tight manner, by passing through leather collars, and as a substitute for the high column of water, he adopted a very small forcing pump to which any power can be applied; and thus the pressing column becomes indefinitely long, although the whole apparatus is very compact, and takes but little room. The marginal figure is a section of one of these presses, in which c is the piston of the large cylinder, formed of a solid piece of metal turned truly cylindrical, and carrying the lower board v of the press upon it: u is the piston of the small forcing pump, being also a cylinder of solid metal moved up and down by the handle or lever . The whole lower part of the press is sometimes made to stand in a case xx, containing more than sufficient water as at y, to fill both the cylinders; and the suction pipe of the forcing pump u dipping into this water will be constantly supplied. Whenever, therefore, the handle w is moved upwards, the water will rise through the conical metal valve z, opening upwards into the bottom of the pump u; and when the handle is depressed, that water will be forced through another similar valve a, opening in an opposite direction in the pipe of communication between the pump and the great cylinder &, which will now receive the water by which the piston rod t will be elevated at each stroke of the pump u. Another small conical valve c is applied by means of a screw to an orifice in the lower part of the large cylinder, the use of which is to release the pressure whenever it may be necessary; for, on opening this valve, any water which was previously contained in the large cylinder b, will run off into the reservoir y by the passage d, and the piston t will descend; so that the same water may be used over and over again. The power of such a machine is enormously great; for, supposing the hand to be applied at the end of the handle w, with a force of only 10 pounds, and that this handle or lever be so constructed as to multiply that force but 5 times, then the force with which the piston u descends will be equal to 50 pounds: let us next suppose that the magnitude of the piston t is such, that the area of its horizontal section shall contain a similar area of the smaller piston u 50 times, then 50 multiplied by 50 gives 2500 pounds, for the force with which the piston t and the presser v will rise. A man can, however, exert ten times this force for a short time, and could therefore raise 25,000 pounds; and would do more if a greater disproportion existed between the two pistons t and u, and the lever w were made more favourable to the exertion of his strength. This machine not only acts as a press, but is capable of many other useful applications, such as a jack for raising heavy loads, or even buildings; to the purpose of drawing up trees by their roots, or the piles used in bridge-building. To find the thickness of the metal in Bramah's press, to resist certain pressures, Mr. Barlow gives this theorem, pr where p 1 = = pressure in lbs. per square inch, r = radius of the cylinder, tits thickness, and c = 18000 lbs. the cohesive power of a square inch of cast iron. Ex. Suppose it were required to determine the thickness of metal in two presses, each of 6 inches radius, in one of which the pressure may extend to 4278 pounds, in the other to 8556 pounds per square inch. t = t = Here in the first case, The usual rules, explained below (art. 10) would make the latter thickness double the former extensive experiments are necessary to tell which method deserves the preference. 6. If the breadth, and d the depth of a rectangular gate, or other surface exposed to the pressure of water from top to bottom; then the entire pressure is equal to the weight of a prism of water whose content is b d2. Or, if b and d be in feet, then the whole pressure b d', in cwts. = 31 b d2, in lbs. or nearly = 7. If the gate be in form of a trapezoid, widest at top, then, if B and b be the breadths at the top and bottom respectively, and d the depth. = b) + b] d2 131 [3 (B — b) + b] d2, nearly. whole pressure in lbs. =314 [} (B whole pressure in cwts. 8. The weight of a cubic foot of rain or river water, is nearly equal to cwt. The pressure on a square inch, at the depth of THIR-ty feet is very nearly THIR-teen pounds. Pressure on a square foot, nearly a ton at the depth of thirty-six feet. [The true depth is 35.84 feet.] The weight of an ale gallon of rain water is nearly 10 lbs. that of an imperial gallon 10 lbs. The weight of a cubic foot of sea-water is nearly of a cwt. These are all useful approximations. Thus, the pressure of rain water upon a square inch at the depth of 3000 feet, is 1300 lbs. And the pressure upon a square foot at the depth of 108 feet is nearly three tons. E 9. In the structure of dykes or embankments, both faces or slopes should be planes, and the exterior and interior slopes should make an angle of not less than 90°. For if A D' be the exterior slope, and the angle D' A B be acute, E D' perpendicular to A B is the direction of the pressure upon it; and the portion D' A E will probably be torn off. But when DA is the exterior face, making with A в an obtuse angle, the direction of the pressure falls within the base, and therefore augments its stability. DF D' B 10. The strength of a circular bason confining water, requires the consideration of other principles. The perpendicular pressure against the wall depends merely on the altitude of the fluid, without being affected by the volume. But, as professor Leslie remarks, the longitudinal effort of the thrust, or its tendency to open the joints of the masonry, is measured by the radius of the circle. To resist that action in very wide basons, the range or course of stones along the inside of the wall, must be proportionally thicker. On the other hand, if any opposing surface present some convexity to the pressure of water, the resulting longitudinal strain will be exerted in closing the joints and consolidating the building. Such reversed incurvation is, therefore, often adopted in the construction of dams. с In like manner, the thickness of pipes to convey water h d must vary in proportion to, where h is the height of the head of water, d the diameter of the pipe, and c the measure of the cohesion of a bar of the same material as the pipe, and an inch square. A pipe of cast iron, 15 inches diameter, and of an inch thick, will be strong enough for a head of 600 feet. A pipe of oak of the same diameter, and 2 inches thick, would sustain a head of 180 feet. Where the cohesion is the same, t varies as hd or as HDT hd: t, in the comparison of two cases.* * Example.-What, then, must be the respective thicknesses of pipes of cast iron and oak, each 10 inches diameter, to carry water from a head of 360 feet? Here, 1st. for cast iron: HD (= 600 × 15) : т (= 1) :: hd ( = of an inch. 360 x 10) t = 2dly. for oak: = = 180 x 15 SECTION II.-Floating Bodies. 1. If any body float on a fluid, it displaces a quantity of the fluid equal to itself in weight. 2. Also, the centres of gravity of the body and of the fluid displaced must, when the body is at rest, be in the same vertical line. 3. If a vessel contain two fluids that will not mix (as water and mercury), and a solid of some intermediate specific gravity be immersed under the surface of the lighter fluid and float on the heavier; the part of the solid immersed in the heavier fluid, is to the whole solid as the difference between the specific gra • To ascertain whether or not a pipe is strong enough to sustain a proposed pressure, it is a good custom amongst practical men to employ a safety valve, usually of an inch in diameter, and load it with the proposed weight, and a surplus determined by practice. Then, if the proposed pressure be applied interiorly, by a forcing pump, or in any other way, if the pipe remain sound in all its parts after the safety-valve has yielded, such pipe is regarded as sufficiently strong." The actual pressures upon a pipe of any proposed diameter and head, may evidently be determined by a similar method. |