In this case 12 appears in the denominator in order to reduce the 14 inches to feet. It, 106. Brake Horsepower. The brake horsepower of an engine is the power actually available for outside use. therefore, is equal to the indicated horsepower minus the power lost in friction in the engine. Brake horsepower can be readily determined by putting a brake on the rim of the flywheel and thus absorbing and measuring the power actually delivered. R Iw FIG. 80.-Prony brake for determination of brake horsepower. Figure 80 shows such a brake arranged for use. This form is known as the "Prony Brake." It consists of a steel or leather band carrying a number of wooden blocks. By tightening the bolt at A, the friction between the blocks and the rim of the wheel can be varied at will. The corresponding pull which this friction gives at a distance R ft. from the shaft is weighed by a platform scale or spring balance. From the scale reading must be deducted the weight due to the unbalanced weight of the brake arms, which can be determined by reading the scales when the brake is loose and the engine is not running. If an engine is capable of maintaining a certain net pressure W on the scale, and meanwhile maintains a speed of N revolutions per minute, we can readily see that this is equivalent to an effective belt pull of W pounds on a pulley of radius R running at N revolutions; or it can be considered as being equivalent to raising a weight equal to W by means of a rope wound around a pulley of radius R turning at N revolutions per minute. This weight would be lifted at the rate of 3.1416 X 2 X RX N ft. per minute The work done in foot-pounds per minute will be W X ft. per min. or W × 3.1416 × 2 × R × N = foot-pounds per minute. The brake horsepower is this amount divided by 33,000. The brake and wheel rim will naturally get hot during a test, as all of the work done by the engine is transformed back into heat at the rubbing surfaces of the pulley rim and the brake. It is necessary to keep a stream of water playing on the rim to remove this heat. It is also best to have special brake wheels for testing. These have thin rims and inwardly extending flanges on the rims so that a film of water can be maintained on the inner surface of the rim. Example: Suppose that at the time of testing the 5- × 8-in. gas engine in Art. 104, we also determined the brake horsepower by means of a Prony brake having a radius of 3 ft., and that a net pressure of 22 lb. was exerted on the scales (the speed of the engine was 450 r.p.m.). Let us calculate the brake horsepower. = 8482 3.1416 X 2 X 3 X 450 186,604 ÷ 33,000 = 5.65, Answer. per minute is 22 lb. X 8482 ft. the brake horsepower of the engine = Explanation: Our data are equivalent to those of hoisting a weight of 22 lb. by a rope winding upon a pulley of 3-ft. radius turning at 450 r.p.m. The 22-lb. weight is raised 8482 ft. per minute, and the work done 186,604 ft.-lb. per minute. Hence, is 5.65. 107. Frictional Horsepower. If this engine gave 7.13 indicated horsepower (i.hp.), but the power available at the flywheel was only 5.65, it stands to reason that the difference, or 1.48 hp., was lost between the cylinder and the flywheel. The explanation is that this power is expended simply in overcoming the friction of the engine; and this horsepower is, therefore, called the frictional horsepower. At zero brake horsepower, the entire indicated horsepower is used in overcoming friction. 108. Mechanical Efficiency.-The ratio of the brake horsepower to the indicated horsepower gives the mechanical efficiency, meaning the efficiency of the mechanism in transmitting the power through it from piston to flywheel. This is usually expressed in per cent. In the case of the engine of which we figured the indicated horsepower and brake horsepower, the mechanical efficiency is: The mechanical efficiency of a gas engine is lower than that of a steam engine on account of the idle strokes which use up work in friction while no power is being generated, but at full load a well-built gas engine should show over 80% mechanical efficiency. The mechanical efficiency of a steam engine should be above 90% at full load. In every case, however, the efficiency is less than 100%. PROBLEMS 178. The cage in a mine weighs 2200 lb., and the load hoisted is 3 tons. The hoisting speed is 20 ft. per second. Calculate the horsepower necessary, allowing 25% additional for friction and rope losses. 179. A 10- by 12-in. air compressor runs at a speed of 150 r.p.m. The m.e.p. is 30 lb. per square inch. Calculate the horsepower required to run it, neglecting friction losses. 180. If the mechanical efficiency of the air compressor in the preceding problem is 60%, what actual horsepower is required to run it? 181. Find the indicated horsepower of a 10- by 12-in. steam engine which runs at a speed of 250 r.p.m. if the m.e.p. is 60 lb. per sq. in. 182. What will be the indicated horsepower of a single-cylinder, fourcycle gas engine using the following data: 183. A body can do as much work in descending as is required to raise it. Knowing this fact, calculate the horsepower that could be developed by a waterpower which discharges 800 cu. ft. of water per second from a height of 13.6 ft., assuming that 25% of the theoretical power is lost in the wheel and in friction. 184. What would be the brake horsepower of a steam engine which exerted a net pressure of 100 lb. on the scales, at a radius of 4 ft., when running at 250 r.p.m.? 185. A hydraulic turbine is direct-connected to a direct-current generator. During a normal season the waterpower available to the turbine is theoretically equivalent to 500 hp. If the full load efficiency of the turbine is 80% and that of the generator 92%, what horsepower is developed by the generator at full load? 186. A centrifugal pump running at 1500 r.p.m. requires 90 hp. to drive it and is to be belt-driven from a 48-in. pulley on a high-speed automatic engine running at 275 r.p.m. What should be the diameter and width of face of the pulley on the pump if the pulley is to be 1 in. wider than the belt? |