APPENDIX. STRENGTH OF TIMBER. Safe Loads in Tons, Uniformly Distributed, for Whiteoak Beams. (In accordance with the Building Laws of Boston.) Formula: W = Size of Timber. 2x6 2×8 2 × 10 2 x 12 3x6 3x8 3 x 10 3 x 12 3 x 14 3 x 16 4 x 10 4 x 12 4 x 14 4 × 16 4 x 18 6 4PBD2 W safe load in pounds; P, extreme fibrestress 1000 lbs. per square inch, for white oak; B, breadth in inches; D, depth in inches; L, distance between supports in inches. Distance between Supports in feet. 10 11 12 14 15 16 17 18 19 21 23 25 26 Safe Load in Tons of 2000 Pounds. 0.67 0.50 0.40 0.36 0.33 0.2910.2710.25 0.24 0.22 5.45 7.11 For other kinds of wood than white oak multiply the figures in the table by a figure selected from those given below (which represent the safe stress per square inch on beams of different kinds of wood according to the building laws of the cities named) and divide by 1000. a1 = the first term of the series; n, number of the required term; an, the required term; d1, da, d,, first terms of successive orders of differences between a1, ag, ag, α4. successive terms. EXAMPLE.-Required the log of 40.7, logs of 40, 41, 42, 43 being given as For log. 40 n = 1; log 41 n = 2; log 40.7 n = 1.7, n − 1 = 0.7, n − 2 = − 0.3, n-3= .1.3. Maxima and Minima without the Calculus.-In the equation y = a + bx + ca2, in which a, b, and c are constants, either positive or negative, if c be positive y is a minimum when x = - b 2c; if c be negative y is a maximum when x=- b2c. In the equation y = a + bx + c/x, y is a minimum when bx = c/x. APPLICATION.-The cost of electrical transmission is made up (1) of fixed charges, such as superintendence, repairs, cost of poles, etc., which may be represented by a; (2) of interest on cost of the wire, which varies with the sectional area, and may be represented by ba; and (3) of cost of the energy wasted in transinission, which varies inversely with the area of the wire, or c/x. The total cost, y = a + bx + c/x, is a minimum when item 2 = item 3, or bxc/x. RIVETED JOINTS. Pressure Required to Drive Hot Rivets.-R. D. Wood & Co., Philadelphia, give the following table (1897): The above is based on the rivet passing through only two thicknesses of plate which together exceed the diameter of the rivet but little, if any. As the plate thickness increases the power required increases approxi mately in proportion to the square root of the increase of thickness. Thus, if the total thickness of plate is four times the diameter of the rivet, we should require twice the power given above in order to thoroughly fill the rivet-holes and do good work. Double the thickness of plate would increase the necessary power about 40%. It takes about four or five times as much power to drive rivets cold as to drive them hot. Thus, a machine that will drive 4-in. rivets hot will usually drive-in. rivets cold (steel). Baldwin Locomotive Works drive-in. softiron rivets cold with 15 tons. HEATING AND VENTILATION. Table of Capacities for Hot-blast or Plenum Heating with Fans or Blowers. (Computed by F. R. Still, American Blower Co., Detroit, Mich.) Temperature of fresh air, 0°; of air from coils, 120°; of steam, 227°. Pressure of steam, 5 lbs. Peripheral velocity of fan-tips, 4000 ft.; number of pipes deep in coil, 24; depth of coil, 60 inches; area of coils approximately twice free area. WATER-WHEELS. Water-power Plants Operating under High Pressures.The following notes are contributed by the Pelton Water Wheel Co.: The Consolidated Virginia & Col. Mining Co., Virginia, Nev., has a 3-ft. steel-disk Pelton wheel operating under 2100 ft. fall, equal to 911 lbs. per sq. in. It runs at a peripheral velocity of 10.804 ft. per minute and has a capacity of over 100 H.P. The rigidity with which water under such a high pressure as this leaves the nozzle is shown in the fact that it is impossible to cut the stream with an axe, however heavy the blow, as it will rebound just as it would from a steel rod travelling at a high rate of speed. The London Hydraulic Power Co. has a large number of Pelton wheels from 12 to 18 in. diameter running under pressure of about 1000 lbs. per. sq. in. from a system of pressure-mains. The 18-in. wheels weighing 30 lbs. have a capacity of over 20 H.P. (See Blaine's "Hydraulic Machinery.") Hydraulic Power-hoist of Milwaukee Mining Co., Idaho.-One cage travels up as the other descends; the maximum load of 5500 lbs. at a speed of 400 ft. per min. is carried by one of a pair of Pelton wheels (one for each cage). Wheels are started and stopped by opening and closing a small hydraulic valve at the engineer's stand which operates the larger valves by hydraulic pressure. An air-chamber takes up the shock that would otherwise occur on the pipe line under the pressure due to 850 ft. fall. The Mannesmann Cycle Tube Works, North Adams, Mass., are using four Pelton wheels, having a fly-wheel rim, under a pump pressure of 600 lbs. per sq. in. These wheels are direct-connected to the rolls through which the ingots are passed for drawing out seamless tubing. The Alaska Gold Mining Co., Douglass Island, Alaska, has a 22-ft. Pelton wheel on the shaft of a Riedler duplex compressor. It is used as a flywheel as well, weighing 25,000 lbs.-and develops 500 H.P. at 75 revolutions. A valve connected to the pressure-chamber starts and stops the wheel automatically, thus maintaining the pressure in the air-receiver. At Pachuca in Mexico five Pelton wheels having a capacity of 600 H.P. each under 800 ft. head are driving an electric transmission plant. These wheels weigh less than 500 lbs. each, showing over a horse-power per pound of metal. Formulæ for Calculating the Power of Jet Waterwheels, such as the Pelton (F. K. Blue).-HP horse-power delivered: 8 = 62.36 lbs. per cu. ft.; E = efficiency of turbine; g = quantity of water, cubic feet per minute; h = feet effective head; d= inches diameter of jet; p = pounds per square inch effective head; c = coefficient of discharge from nozzle, which may be ordinarily taken at 0.9. .00436 Eqp=.00496 Ecd2 Vhs = .0174Ecd2 √p3. HP = 8 Egh = .00189 Egh = Ep Average Volumetric Composition, Energy, etc., of Various Gases. (Contributed by R. D. Wood & Co., Philadelphia, 1898.) 5 25 85 75 200+ of coal approx... *The real energy of bituminous producer-gas when used hot is far in excess of that indicated by the above table, on account of the hydrocarbons, which do not show, as they are condensed in the act of collecting the gas for analysis. In actual practice there is found to be about 50% more effective energy in bituminous gas than in anthracite gas when used hot enough to prevent condensation in the flues. + Cubic feet of air required to burn 1 lb. of coal with blast. STEAM-BOILERS. Steam-boiler Construction. (Extract from the Pules and Specifications of the Hartford Steam Boiler Inspection & Insurance Co., 1898.) Cylindrical boiler shells of fire box steel, and tube-heads of best flange steel. Limits of tensile strength between 55,000 and 62,000 lbs. per sq. in. Iron rivets in steel plates, 38,000 lbs. shearing strength per sq in. in single shear, and 85% more, or 70,300 lbs., in double shear. Each shell-plate must bear a test-coupon which shall be sheared off and tested. Each coupon must fulfil the above requirements as to tensile strength, but must have a contraction of area of not less than 56% and an elongation of 25% in a length of 8 in. It must also stand bending 180° when cold, when red hot, and after being heated red hot and quenched in cold water, without fracture on outside of bent portion. Crow-foot braces are required for boiler-heads without welds, and if of iron limit the strain to 7500 lbs. per sq. in., and stay-bolts must not be subjected to a greater strain than 6000 lbs. per sq. in. The thickness of double butt-straps 8/10 the thickness of plates. In lapjoints the distance between the rows of rivets is 2% the pitch. In doubleriveted lap-joints of plates up to 1⁄2 in. thick the efficiency is 70% and in triple-riveted lap-joints 75% of the solid plate. In triple-riveted double-strapped butt-seams for plates from 4 in. to 1⁄2 in. thick, the efficiency ranges from 88% to 86% of the solid plate. In high-pressure boilers the holes are required to be drilled in place; that is, all holes may be punched 14 in. less than full size, then the courses are rolled up, tube-heads and joint-covering plates bolted to courses, with all holes together perfectly fair. Then the rivet-holes are drilled to full size, and when completed the plates are taken apart and the burr removed. The rule for the bursting-pressure of cylindrical boiler-shells is the following: Multiply the ultimate tensile strength of the weakest plate in the shell by its thickness in inches and by the efficiency of the joint, and divide result by the semi-diameter of shell; the quotient is the bursting-pressure per square inch. This pressure divided by the factor 5 gives the allowable working pressure. BOILER FEEDING. Gravity Boiler-feeders.-If a closed tank be placed above the level of the water in a boiler and the tank be filled or partly filled with water, then on shutting off the supply to the tank, admitting steam from the boiler to the upper part of the tank, so as to equalize the steam pressure in the boiler and in the tank, and opening a valve in a pipe leading from the tank to the boiler the water will run into the boiler. An apparatus of this kind may be made to work with practically perfect efficiency as a boilerfeeder, as an injector does, when the feed-supply is at ordinary atmospheric temperature, since after the tank is emptied of water and the valves in the pipes connecting it with the boiler are closed the condensation of the steam remaining in the tank will create a vacuum which will lift a fresh supply of water into the tank. The only loss of energy in the cycle of operations is the radiation from the tank and pipes, which may be made very small by proper covering. When the feed-water supply is hot, such as the return water from a heating system, the gravity apparatus may be made to work by having two receivers, one at a low level, which receives the returns or other feed-supply, and the other at a point above the boilers. A partial vacuum being created in the upper tank, steam-pressure is applied above the water in the lower tank by which it is elevated into the upper. The operation of such a machine may be made automatic by suitable arrangement of valves. (See circular of the Scott Boiler Feeder, made by the Q. & C. Co., Chicago.) FEED-WATER HEATERS. Capacity of Feed-water Heaters.-The following extract from a letter by W. R. Billings, treasurer of the Taunton Locomotive Manufacturng Co., builders of the Wainwright feed-water heater, to Engineering Record, February, 1898, is of interest in showing the relation of the heating surface of a heater to the work done by it: "Closed feed-water heaters are seldom provided with sufficient surface to raise the feed temperature to more than 200°. The rate of heat trans |