EXPLANATION OF TABLE. Initial pressure is the full pressure of steam per square inch, acting on the piston previous to the closing of steam-valve. Full pressure of steam one-fourth of stroke, implies that when the piston has progressed through one-quarter of the length of its course, the steam-valve closes, leaving the remaining portion of the stroke to be performed by the impetus which the piston has acquired, and by the expansion of steam. Mean pressure of steam expresses the average pressure of steam throughout the stroke, and may be found by considering the full pressure as 1, or the unit of the ratio of expansion, and adding to it the hyperbolic logarithm of the ratio. This multiplied by the pressure, and divided by the ratio of expansion, gives the mean pressure throughout the stroke. Note. The deduction of one-fifth from the mean pressure is an allowance for the power absorbed in effecting the movement of the whole machine, and for which deduction is made from the mean pressure to establish an elementary number, so as to avoid the deduction of one-fifth in each calculation. Load in lbs., signifies the pressure, power, or force of steam on the piston, less the allowance for friction, to overcome an equal resistance opposed to it; or, in other words, the weight of water lifted, plus friction, is considered to be equal to the power exerted on the piston. Economical working is intended to express the number of strokes per minute at which an engine may be driven so as to obtain the maximum effect or duty resulting from slow combustion, and effective condensation. Safe working is considered to be the limit of speed at which an engine may be driven, without suffering undue wear and tear. The effective horse-power per stroke is given in order to ascertain the power due to an engine, from working a greater or less number of strokes per minute. To find the hourly consumption of coals per horse-power.— Reduce the quantity of coals consumed to pounds, and divide that number by the number of hours, the quotient will be the weight consumed per hour; then divide by the horse-power of the engine, the result will be the number of pounds of coals consumed per horse-power. Ex.-An 80-inch engine, working at 135 horse-power, consumed 1,550 bushels of coals in 480 hours. Required the quantity of coals consumed per horse-power per hour. 1,550 × 94 145,700, 135 = 1,079.2 COMBINED-CYLINDER ENGINES- -To find the proportional capacity of the larger cylinder, when the smaller one is considered as unity:Divide the force of the steam in inches of mercury by half that force, plus 30, and the quotient is the capacity of the larger cylinder.* Ex.-Required the capacity of the larger cylinder of Hornblower's engine, when the smaller one is 10 inches diameter (100 circular inches) and 10 inches stroke (1000 cylindrical inches capacity), the force of the steam being 120 inches mercury. 2)120 The proportion is = 1.33 to 1, or equal to 1,333 cy lindrical inches for the capacity of the larger one. To find the horse-power of non-condensing or condensing combined cylinder-engines :— Multiply the hyperbolic logarithm, plus 1, of the relative capacity of the large cylinder to the small one, by the square of the small cylinder's diameter, and the velocity of its piston in feet per minute. Then multiply this product by the absolute force of the steam in pounds per circular inch, and divide by 33,000 for the horse-power of the combined cylinder. Ex-Required the power of the Hornblower's combined cylinder engine before-mentioned, the small cylinder being 10 inches diameter, the velocity of its piston 100 feet per minute, the absolute force of the steam upon it 120 inches of mercury = (120 × 385) 46.2 lbs. per circular inch, and the relative capacity of the large cylinder to the small one 1.33 to 1. The hyperbolic log. + 1 of 1·33 = 1.2851789 × by square of 10...... * 100 Tredgold on the Steam-engine. pp. 195 and 218. To find the point at which steam should be cut off to obtain the greatest amount of effective work: Divide 24,250 by the pressure per square inch on the piston, and add 65 to the quotient; then divide 24,250 by the useless resistance, and to this quotient add 65 for a divisor; the quotient arising from dividing the former by the latter, multiplied by the length of the stroke, will give the point of the stroke at which the steam must be cut off to yield the maximum amount of useful work. Ex.-Required the point of the stroke at which steam must be cut off to afford the largest amount of useful work, the length of stroke being 12 feet, the pressure upon the piston 35 lbs. per square inch, and the vacuum resistance, together with the friction of the engine = 4 lbs. 757.85 0.102 × 12 = 1.224 feet at which steam must be 6127.5 cut off. TABLE, SHOWING THE APPROXIMATE AMOUNT OF SAVING IN FUEL RESULTING FROM WORKING STEAM EXPANSIVELY.* PARALLEL MOTION.-The following rules and practical observations, relative to the parallel motion are extracted from Messrs. Hann and Gener's work on the steam-engine: Lever Engines." Having given the length of the levers and that of the link which connects them, to find at what point of the link the piston-rod is to be attached, so as to move in a vertical line nearly." "If the lever be of equal length, the piston-rod must be attached to the middle of the link." "If the lever be unequal, draw a line from the centre of motion of the one lever to that of another; this will cut the link in some point; take the distance of this point from the top of the link and * Tredgold. set it off from the bottom of the link; the point thus obtained is that to which the piston-rod must be attached." "Multiply the length of the beam from the centre of motion by the length of the link for a dividend.” "Add the length of the beam to that of the radius-rod for a divisor." “The quotient will be the distance from the bottom of the link to which the piston-rod must be attached." o' "Ex.-Given the length of the beam or lever A B = 6 feet, the length of the radius rod E' 5 feet; find how far from = must be put on. 6 x 5 the = 30 6 +9 15 30 = 2 the quotient 15 9 feet, the length of the link BE bottom of the link the piston-rod the distance E P from the bottom of the link at which the piston rod is to be attached." "If the upper lever be given, and the point in the link where the piston rod is attached, to find the length of the lower lever, which is generally called the radius rod.” "As the distance of the point from the bottom is to that from the top of the link, so is the length of the upper lever to the length of the radius rod." "Ex.-Given the length of the lever A B = of the link BE 6 feet, the length from the bottom of 2 feet: find the As the whole length of the link is 5 feet, and E P is equal to 2 feet, the remaining part of the link must be equal to 3 feet. Then by the rule 2:36: radius rod. "FULL PARALLEL MOTION. Divide the square of the distance of the back link from the centre of motion by the length of the parallel bar, and the quotient will be the length of the radius rod." "Ex.-Given the radius of the beam 12 feet, and the length of the parallel bar 5 feet; to find the length of the radius rod." "As the length of the parallel bar is 5 feet, the distance of the back link from the centre of motion will be 12. 57 feet." 72-49 Hence by the rule 9 feet, the length of the radius rod. 5 5 "The radius rod being made to work from a stated centre, find the length of the parallel bar, and that of the radius rod." "Add the distance between the vertical line and the axis of the radius rod to twice the radius of the beam." "Divide the square of the radius of the beam by the above sum, and the quotient will be the length of the parallel bar." "If the radius rod be shorter than the parallel bar, divide the square of the radius of the beam by the difference instead of the sum." "The distance between the vertical line and the axis of the radius rod, added to or subtracted from the parallel bar, according as the radius rod is longer or shorter than the parallel bar, gives the length of the radius rod." Or, add the radius of the beam to the distance between the vertical line and axis of the radius rod; divide the square of this sum by twice the radius of the beam, added to the above-named distance for the length of the radius rod." "When the length of the stroke is taken into consideration, subtract the square of half the length of the stroke from the square of the radius of the beam, and extract the square root of the remainder. To this root add the above radius of the beam, and multiply this sum by half the radius of the beam for a dividend.” "Then add the above root, the radius of the beam, and the distance between the vertical line and the end of the radius rod together for a divisor." "And if the above dividend be divided by this divisor, the quotient will give the length of the parallel bar; and this, added to the distance between the vertical line and the end of the radius rod, will give the length of the radius rod." Ex.-"Given the length of the beam 12 feet, the length of the stroke 6 feet, and the distance between the vertical line and the end of the radius rod = 4 feet; to find the length of the radius rod." "By the rule 12o = 144 and 32 9, and 144 square root of which is 11.62 nearly." "Then 11.62 + 12 = 23.62, and 23.62 × 6= is the dividend mentioned in the rule." "Next 11.62 + 12 + 4: 9 = 135, the 141.72, which 27.62, the divisor; therefore 141.72 divided by 27.62 gives 5·13, the length of the parallel bar; consequently 5-13+4= 9.13 feet, length of radius rod.' |