OF PRACTICAL FORMULA, By which to determine the Amount of Weigh a Column of given dimensions will support in lbs. Example 1.-A rectangular column of oak, 6 inches on the side, and 12 feet in length. What weight will it support? Example 2.-What weight will a cast iron cylinder support, whose diameter is 4 inches, and length 10 feet? Diameter. Weight Weight Weight Weight Weight Weight Weight Weight Weight in cwts. in cwts, in cwts. in cwts, in cwts. in cwts.in cwts. in cwts. in ewts. TABLE. MR. BARLOW furnishes the following as some of the results obtained by him, upon the Deflection of Beams. The science of HYDRODYNAMICS embraces Hydrostatics and Hydraulics, the former of which treats of the properties and equilibrium of liquids in a state of rest, and the latter of liquids in motion, as conducting water in pipes, raising liquids by pumps, &c. 1. The peculiar distinguishing properties of liquids or fluids in general are, capability of flowing, and constant tendency to press outwards in every direction. 2. Fluids are of two kinds, aëriform and liquid, or elastic and nonelastic; that is, bodies which are easily compressed into a smaller bulk, and bodies which are scarcely susceptible of compression. Atmospheric air, steam, or vapor of water, and all other gaseous bodies, are of the first kind; and water, alcohol, mercury, &c., are of the second. Compression of Liquids, in Millionth Parts per Atmosphere. 3. The weight of water or other fluid is as the quantity, but the pressure exerted is as the vertical height. 4. Fluids press equally in all directions; hence, any vessel containing a fluid sustains a pressure equal to as many times the weight of the column of greatest height of that fluid, as the area of the vessel is to the sectional area of the column. 5. The hydraulic press is of this principle. A jet of water is thrown into a cavity by means of a force pump; the action and noncompressible property of the liquid repels a piston or ram, the force of which equals the product of the effective power or pressure exerted on the fluid in the pump, multiplied by the number of times the area of the base of the ram exceeds the sectional area of the pump. Example.-Required the repulsive force of a six-inch ram, when power of 50 lbs. is applied to the end of the lever, which is as 12 to 1, and the diameter of the pump, or plunger, ths of an inch. Area of pump = *6013 and 50 × 12×47=28200 lbs., or 12 tons, nearly. 6. The lateral pressure of a fluid on the sides of any vessel in which it is contained is equal to the product of the length multiplied by half the square of the depth, and by the weight of the fluid in cubic unity of dimensions. Example.-A cistern 12 feet square and 8 feet deep is filled with water: required the whole amount of lateral pressure. (Weight of a cubic foot of water, 62.5 lbs.) 12×4=48 feet, the whole length of sides, 82 48 × 32 × 62.5 and =32; then -48 tons net. 2000 2 7. Fluids always tend to a natural level, or curve similar to the earth's convexity, every point of which is equally distant from the center of the earth, the apparent level, or level taken by any instrument for that purpose, being only a tangent to the earth's circumference: hence, in leveling for canals, &c., the difference caused by the earth's curvature must be deducted from apparent level to obtain the true level. To find the Difference between True and Apparent Level. If the distance is considerable, and refraction must be attended to, diminish the distance in respect to calculation by th. Example.-What is the difference between true and apparent level at a distance of 18 chains, when refraction is taken into account? 18 12 =15, and 18-1.5=16·52×00125=3403 inches. 8. When a body is partly or wholly immersed in a fluid, the vertical pressure of the fluid tends to raise the body with a force equal to the weight of the fluid displaced: hence, the weight of any displaced quantity of a fluid by a buoyant body equal the weight of that body. 9. The center of pressure, and also the center of percussion in a fluid, is two-thirds the depth from the surface. 10. The resistance by which a moving body is opposed in passing through a liquid is as the square of its velocity: hence, if a body be propelled at a certain velocity by a known power, to double that velocity will require four times the power; to triple it, nine times the power, &c. The flowing of water through pipes, or in natural channels, is liable to be materially affected by friction. Water flows smoothly and with least retardation when the course is perfectly smooth and straight. Every little inequality which is presented to the liquid tends to retard its motion, and so likewise does every bend or angle in its path. Thus, suppose equal quantities of water to be discharged through pipes of equal diameters and lengths, but of the following forms: and the time that the quantity discharged through the first is 1; the time that will be required to discharge an equal quantity through the second is 111; and the time for the same quantity through the third, 1.55. Hence, the necessity of avoiding as much as possible any bends or angles in pipes or channels for the conduction of fluids. 1. When water issues out of a circular aperture in a thin plate on the bottom or side of a reservoir, the issuing stream tends to converge to a point at the distance of about half its diameter outside the orifice, and this contraction of the stream reduces the area of its section from 1 to 666, according to Bossut; to 631, according to Venturi; and to 64, according to Eytelwein. But, from more accurate experiments, it is found that the quantity discharged is not sufficient to fill this section with the velocity due or corresponding to the height, and that the orifice must be diminished to 619, or nearly ths. 2. When water issues through a short tube, the vein of the stream is less contracted than in the former case, in the proportion of 16 to 13; and if it issues through an aperture which is the frustrum of a cone, whose greater base is the aperture, the height of the frustrum, half the diameter of the aperture, and the area of the small end to the area of the large end as 10 to 16, there will be no contraction of the vein. Hence, when the greatest possible supply of water is required, this form of orifice ought to be employed. 3. The quantity of water that flows out of a vertical rectangular aperture that reaches as high as the surface is ds of the quantity that would flow out of the same aperture placed horizontally at the depth of the base. To determine the quantity of water discharged by a small vertical or horizontal orifice, the time of discharge and height of the fluid in the vessel being known: Let A represent the area of the orifice, Q the quantity of water discharged, T the time of discharge, H the height of fluid in the vessel, and g=16.087 feet per second; then By means of these formulæ, the quantity of water discharged in the same time from any other vessel, in which A is the area of the orifice, and H the altitude of the fluid; for, since T and g are constant, we shall have Q: Q = A √H: A' √H. TABLE, Showing the Quantity of Water discharged per Minute by Experiments with Orifices differing in Form and Position |