12 to 1, and the diameter of the pump, or plunger, ths of an inch. 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.) 82 48×32×62.5 2000 48 tons net. 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 1.11; 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. Deductions from the preceding Experiments. 1. That the quantities of water discharged in equal times by the same orifice, from the same head of water, are nearly as the areas of the orifices. 2. That the quantities of water discharged in equal times by the same orifices, under different heads, are nearly as the square roots of the corresponding heights of the water in the reservoir, above the surface of the orifices. 3. That the quantities of water discharged during the same time by different apertures, under different heights of water in the reservoir, are to one another in the compound ratio of the areas of the apertures, and of the square roots of the heights in the reservoir. 4. That, on account of the friction, small orifices discharge proportionally less fluid than those which are larger and of similar figure, under the same altitude of fluid in the reservoir. 5. That, in consequence of a slight augmentation which the contraction of the fluid vein undergoes, in proportion as the height of the fluid in the reservoir increases, the expenditure ought to be a little diminished. 6. That circular apertures are most advantageous, as they have less rubbing surface under the same area. 7. That the discharge of a fluid through a cylindrical horizontal tube, the diameter and length of which are equal to one another, is the same as through a simple orifice. 8. That if the cylindrical horizontal tube be of greater length than the extent of the diameter, the discharg discharge of water is much increased, and may be increased with advantage to four times the diameter of the orifice. TABLE Of Comparison of the Theoretic with the Real Discharges per Minute through an Constant altitude of the Theoretical discharges Real discharges in the Paris Feet. Real discharges in the same time by a cylindrical tube, one inch in diameter, and two inches long. Cubic Inches. eter. Of the Heights corresponding to different Velocities, in French Metres, per Second. NOTE. The metre equals 39-37023 inches, or 3.281 English feet. BY M. MORIN. To obtain the velocity due to a given height of water, above the center or middle of an orifice, or the height due to a given velocity, Rule. Multiply the height of the water above the center of the |