CHAPTER XII HORSE-POWER SECTION 1. WORK. SECTION 2. HORSE-POWER TRANSMITTED BY A BELT. SECTION 3. HORSE-POWER OF A STEAM ENGINE. SECTION 4. HORSE-POWER OF A GAS ENGINE. SECTION 5. ELECTRIC HORSE-POWER. SECTION 6. HORSE-POWER OF A PUMP. § 1. WORK 271. Definition and Illustration. Work is the effort of a force in overcoming resistance. In a locomotive drawing a train, the motive power is the steam which presses against the pistons with a force sufficient to overcome the combined resistance of friction of bearings, inertia and weight. When a weight is raised, or falls under gravity; when velocity is imparted to a piece of material, or a velocity increased, or a constant velocity maintained under a varying resistance, work is done. 272. Law and Formula of Work. The law of work should be committed to memory: Work equals force times the distance through which it acts. In order to formulate this law for use in computation, the following symbols may be employed: W = work in foot-pounds; F= force in pounds; S distance in feet. Then W=FXS. This formula tells us that the work done by any force can be determined only when we know two things: (1) The number of pounds of force; (2) The distance in feet through which the force acts. The formula also tells us that when these two things are known, the work done may be computed by multiplying force in pounds by distance in feet. Observe that the product is not called pounds-feet or feet-pounds, but foot-pounds. It should now be clear that the work done by any force is determined by multiplying the force in pounds by the distance in feet, and that the product is the work in footpounds, or is the number of foot-pounds of work. Therefore, Work (in foot-pounds) = Force (in lbs.) × Distance (in ft.); 273. Problems in Work. Under the usual headings solve the following problems, arranging your work so that (1) Formula, substitution, and solution are near the left margin; (2) Data are near the right margin. In all computations on work and horse-power, may be taken as 3.14. 1. A weight of 525 pounds is lifted vertically through a distance of 51 feet. Compute the work done. 2. A baseball, dropped from one of the windows at the top of the Washington monument, was caught by a professional catcher at the foot of the monument. Assuming the window to be 545 feet from the ground, the catcher's hands 4 feet from the ground, and the ball to weigh 5 ozs., compute the work done by the ball. 3. The piston of the Corliss engine in the applied mechanics laboratory at Pratt Institute moves through a distance of 30 inches at each stroke. Compute the work done by the piston in one stroke when the steam presses against the piston with an average force of 348 pounds. 4. The average pressure of the steam against the piston of an engine was 60 pounds per square inch. If the area of the piston was 78.5 square inches, what was the work done by the engine in 1 hour when making 50, 25-inch strokes per minute? 5. Compute the work done by the piston of Problem 3 in 8 strokes. 6. Compute the work done by the piston of Problem 3 in 3 minutes, when the engine is making 100 strokes per minute. A single-acting engine is one in which the steam is admitted to only one side of the piston. A double-acting * engine is one in which the steam is admitted alternately to each side of the piston. The end of the cylinder through which the piston rod works is called the crank end; the other is called the head end. In computing the steam pressure on the piston of a double-acting engine, deduction must be made for the area of the piston rod. 7. The piston of the Corliss engine in the mechanical laboratory is 12 inches in diameter, and the piston rod is 21⁄2 inches. Compute the area of the piston against which the steam presses both for the head end and the crank end. 8. Relation of Revolutions to Stroke. At each revolution of an engine, the piston travels through a distance equal to how many times the length of the stroke? Therefore the number of strokes per minute equals how many times the number of revolutions? R.P.M. or r.p.m. is the abbreviation for number of revolutions per minute. * Unless otherwise specified, the engines in the problems which follow are double-acting. 9. Compute the work of the engine in Problem 7 when running 55 strokes per minute with a mean effective pressure of 50 pounds to the square inch. 10. If the number of strokes in Problem 9 were only half as many per minute, what part as much work would be done by the piston per minute? What part as much in 2 minutes? What part as much in 5 minutes? Prove your answers by computation. 11. If the number of strokes were the same as in Problem 9, and the pressure were only half as much, what part as much work would be done per minute? Prove your answer by computation. 12. Formulate and compute the approximate diameter of the piston in Problem 4. Size of an Engine. The size of an engine is indicated. by the product of two numbers, commonly called the bore and the stroke: (1) The diameter of the piston in inches. (2) The length of the stroke in inches. Thus an engine 10×24 is an engine having a piston 10 inches in diameter and a stroke of 24 inches. 13. Interpret the following engine sizes: 10×30, 12×30, 24x48, 32x72. 14. The Ball engine in the applied mechanics laboratory of Pratt Institute is 8×8. Formulate and compute the piston area and the work done when the engine is making 40 revolutions per minute with an average pressure of 50, no allowance being made for size of rod. 15. A Hamilton Corliss engine 26 ×42, with a piston rod 43", is making 75 r.p.m., with the gage at 125 lbs. Formulate and compute the work done in 8 minutes, if 50% of the gage pressure is effective. 16. A belt is driven by a 9-inch pulley making 150 r.p.m. Formulate and compute the work done by the belt when the effective pull is 184 lbs. 17. If the belt in Problem 16 is 8 inches wide formulate and compute the effective pull per inch of width and the work per inch of width. 18. A 15-inch pulley running 114 r.p.m., drives a 12-inch belt under an effective pull of 38 lbs. per inch of width. Formulate and compute the work of the belt per hour. § 2. HORSE-POWER TRANSMITTED BY A BELT 274. Illustrations of a Rate. If a train runs 150 miles in 3 hours, its rate is 50 miles an hour. A motor-boat which covers 45 miles in 2 hours has made the distance at 221 miles per hour. The rate of a belt which moves at a velocity of 50 feet in a second, is 3000 feet per minute. The rim of a 9-inch pulley making 140 r.p.m. has a velocity or rate of 330 feet per minute. A force of 20 pounds, acting through a distance of 300 feet in 5 minutes, does 6000 footpounds of work at a rate of 1200 foot-pounds per minute. A hoisting engine which lifts 550 pounds to a height of 60 feet in 1 minute, works at a rate of 33,000 foot-pounds per minute. All of the preceding illustrations show what a rate is, and should make clear the following definition. 275. Definition of Horse-Power. Horse-power is the unit of rate at which work is done. This unit is 550 footpounds per second or 33,000 foot-pounds per minute. We therefore have the following law and formula: Horse-power = If H.P.-horse-power, Work in foot-pounds 33000X time in minutes W = work in foot-pounds, T-time in minutes, F=force in pounds, S=distance in feet through which the force acts, then (1) W H.P.= 33000XT |