The pressure upon a number of surfaces is found by multiplying the sum of the surfaces into the depth of their common centre of gravity, below the surface of the fluid. CONSTRUCTION OF BANKS. A bank, constructed of a given quantity of materials, will just resist the pressure of the water when the square of its thickness at the base is to the square of its perpendicular height, as the weight of a given bulk of water is to the weight of the same bulk of the material the bank is made of, increased by twice the aforesaid weight of the given bulk of water. Thus, if the bank is made of a stone 2 times heavier than water, the thickness of the base should be to the height, as 3 to 6. If the height, compared to the thickness of the base, be as 10 to 7, stability is always ensured, whatever the specific gravity of the material may be. The bottom of a conical, pyramidal, or cylindrical vessel, or of one the section of which is that of an inverted frustrum of a cone or pyramid, sustains a pressure equal to the area of the bottom and the depth of the fluid. FLOOD GATES. To find the Strain which a Fluid will exert to make it turn upon its Hinges, or open. RULE.-Multiply of the square of the height by the square of the breadth, and take a bulk of water equal to the product. EXAMPLE. If the gate is 6 feet square, To find the Strain the Water exerts upon its Hinges. RULE.-Multiply of the breadth by the cube of the height, and take a bulk of water equal to the product. RULE.-Multiply the height of the head of the fluid in feet by the diameter of the pipe in inches, and divide their product by the cohesion of one square inch of the material of which the pipe is composed. By experiment it has been found that a cast iron pipe, 15 inches in diameter, and of an inch thick, will support a head of water of 600 feet; and that one of oak, of the same diameter, and 2 inches thick, will support a head of 180 feet. The cohesive power of cast iron, then, would be 12,000 lbs.; of oak, 1350 lbs. That of lead is 750 lbs.; and wrought iron boiler plates, riveted together, is from 25 to 30,000 lbs. In conduit pipes, lying horizontal, and made of lead, their thickness, compared to their diameter, should be, As 24, 3, 4, 5, 6, 7, 8 lines, The tenacity of lead is increased to 3000 by the addition of 1 part of zinc in 8. HYDROSTATIC PRESS. To find the Thickness of the Metal to resist a Given Pressure. Let p pressure per square inch in pounds, r-radius of cylinder, and c cohesion of the metal per square inch. Then = pr thickness of metal. The cohesive force of a square inch of cast iron is frequently estimated at 18000 lbs., but 16000 is preferable. A cylindrical ring, the diameters of which were 5.3 and 10.8 inches, burst at a pressure of 9000 lbs. per square inch. These dimensions by the above rule would give HYDRAULICS AND HYDRODYNAMICS. HYDRAULICS treats of the motion of non-elastic fluids, and Hydrodynamics of the force with which they act. Descending water is actuated by the same laws as falling bodies. Water will fall through 1 foot in of a second, 4 feet in of a second, and through 9 feet in of a second, and so on. The velocity of a fluid, spouting through an opening in the side of a vessel, reservoir, or bulkhead, is the same that a body would acquire by falling through a perpendicular space equal to that be tween the top of the water and the middle of the aperture. Then, by rule 4 in Gravitation, ✔height 64.33 = velocity. EXAMPLE. What is the velocity of a stream issuing from a head of 10 feet? If the velocity be 50.72 feet per second, what is the head? This would be true were it not for the effect of friction, which in pipes and canals increases as the square of the velocity. The mean velocity of a number of experiments gives 5.4 feet for a height of one foot. The theoretical velocity is (√64}) 8. OF SLUICES. To find the Quantity of Water which will flow out of an Opening. RULE.-Multiply the square root of the depth of the water by 5.4; the product is the velocity in feet per second. This, multiplied by the area of the orifice in feet, will give the number of cubic feet per second. EXAMPLE. If the centre of a sluice is 10 feet below the surface of a pond, and its area 2 feet, what quantity of water will run out in one second? √10×5.4×234.1496 feet, Ans. NOTE.-If the area of the opening is large compared with the head of the water take of this velocity for the actual velocity. OF VERTICAL APERTURES OR SLITS. The quantity of water that will flow out of one that reaches as high as the surface is 3 of that which would flow out of the same aperture if it were horizontal at the depth of the base. Or, velocity at bottom × depth x 2 3 of cubic feet per second. X breadth of slit number OF STREAMS OR JETS. To find the Distance a Jet will be projected from a Vessel through an opening in the Side: RULE. BC will always be equal to twice the square root of AO X O B. If o is 4 times as deep below A, as a is, o will discharge twice the quantity of water that will flow from a in the same time, because 2 is the square root of A o, and 1 is the square root of A a. A a B NOTE. The water will spout the farthest when o is equidistant from A and B ; and if the vessel is raised above a plane, B must be taken upon the plane. The quantities of water passing through equal holes in the same time are as the square roots of their depths. EXAMPLE. —A vessel 20 feet deep is raised 5 feet above a plane; how far will a jet reach that is 5 feet from the bottom? √15×10×2=24.48 feet, Ans. When a prismatic vessel empties itself by a small orifice, in the time of emptying itself, twice the quantity would be discharged if it were kept full by a new supply. To find the Vertical Height of a Stream projected from a Pipe. RULE. Ascertain the velocity of the stream by computing the quantity of water running or forced through the opening; then, by rule 5 in Gravitation, page 140, find the required height. EXAMPLE. If a fire-engine discharges 16.8 cubic feet of water through a inch pipe in one minute, how high will the water be projected, the pipe being directed vertically?" 16.8×1728 area of inches in a foot seconds in a minute 91.6, or velocity of stream in feet per second; then, by rule, page 140, 91.6811.45, and 11.452131.10 feet, Ans. NOTE. This rule gives a theoretical result; the result in practice is somewhat less. VELOCITY OF STREAMS. In a stream, the velocity is greatest at the surface and in the middle of the current. To find the Velocity of a River or Brook. RULE. Take the number of inches that a floating body passes over in one second in the middle of the current, and extract its square root; double this root, subtract it from the velocity at top, and add 1; the result will be the velocity of the stream at the bottom; and the mean velocity of the stream is equal the velocity a the surface velocity at the surface +.5. EXAMPLE.-If the velocity at the surface and in the middle of a stream be 36 inches per second, what is the mean velocity? /36×2-36+1=25, the velocity at bottom. To find the Velocity of Water running through Pipes. RULE. Divide height of head in inches by length of pipe in inches, and the square root of the quotient, multiplied by 23.3, will give the velocity in inches at the orifice. EXAMPLE. What is the velocity when the head is 9 feet, the pipe 24 inches long and 24 inches bore? 108 2423.349.49 inches per second, Ans. Quantities of Water discharged from Orifices of various forms, the Altitude being constant, at 34.642 Inches. Nature and dimensions of the tubes and orifices. 1. A circular orifice in a thin plate, the diameter being 1.7 inches 2. A cylindrical tube 1.7 inches in diameter, and 5.117 3. A short conical adjutage, 1.7 inches in diameter Cubic inches discharged in a minute. 10783 14261 10526 10409 5. The same, the length of the cylinder being 13.65 inches long 9830 6. The same, the length of the cylinder being 27.30 inch Results prove that the discharge of water through a straight cylindrical pipe of an unlimited length may be increased only by altering the form of the terminations of the pipe, by making the inner end of the pipe of the same form as the vena contracta, and the extremity a truncated cone, having its length about 9 times the diameter of the cylinder or pipe attached, and the aperture at the outlet to the diameter of the cylinder as 18 is to 10. By giving this form, the discharge is over what it would be by the cylinder alone as 24 is to 10. WAVES. The undulations of waves are performed in the same time as the oscillations of a pendulum, the length of which is equal to the breadth of a wave, or to the distance between two neighbouring cavities or minences. |