Notice particularly that the area of the piston is expressed in square inches, because the pressure is given in pounds per square inch; but that the stroke is reduced to feet because we measure work in foot-pounds and, consequently, must express in feet the distance which the piston moves. If an engine has more than one cylinder, the horse-power of each can be calculated and the results added; or, if the cylinders are arranged to do equal amounts of work, we can find the horsepower of one cylinder and multiply this by the number of cylinders. The mean effective pressure can be obtained for any engine by the use of a device called an "indicator," which draws a diagram showing just what the pressure is in the cylinder at each point in the stroke. From this diagram, we can calculate the average or mean effective pressure for the stroke. This pressure must not be confused with the boiler pressure or the pressure in the steam pipe. For instance, when the steam comes from the boiler to the engine at 100 lb. pressure, the mean pressure in the cylinder will not be 100 lb., as it would be very wasteful to use steam from the boiler for the full stroke. Instead, the M. E. P. (Mean Effective Pressure) will be from 20% to 85% of the boiler pressure depending on the type of the engine and the load it is carrying. Horse-power calculated as explained here is called Indicated Horse-power because an indicator is used to determine it. The indicated horse-power represents the power delivered to the piston by the steam. 110. Gas Engines.-The most common type of gas or gasoline engine works on what is called the four stroke cycle. Such an engine is called a four-cycle engine. Fig. 71 shows in four views the operation of such an engine. Four strokes, or two revolutions, are required for each explosion that occurs in the cylinder. Consequently, in calculating the horse-power of a single cylinder gas engine, the number of working strokes (or N in the horse-power formula) is one-half of the R. P. M. There is another type of gasoline engine called the two-cycle engine. A single cylinder two-cycle engine has one working stroke for each revolution of the crank shaft and N is therefore the same as the number of R. P. M. The mean effective pressure of a gas engine is from 40 to 100 lb. per square inch, depending chiefly on the fuel used. For gasoline or natural gas or illuminating gas it is usually between 80 and 90 lb. per square inch. What horse-power could be delivered by a single cylinder 5 in. by 8 in. four-cycle gasoline engine running 450 R. P. M.? Note.-Use a value of P-80 lb. per square inch. 111. Air Compressors.—An air compressor is like a double acting steam engine in appearance; but, instead of delivering up power, it requires power from some other source to run it. This power is stored in the air and later is recovered when the air is used. An air compressor takes air into the cylinder, raises its pressure by compressing it, and then forces it into the air line or the storage tank. In calculating the horse-power of a compressor, the same formula can be used as for a steam engine. The value of P to use is not the pressure to which the air is raised, but is the average or mean pressure during the stroke. It is usually somewhat less than half the final air pressure; for example, when an air compressor is delivering air at 80 lb. pressure, the mean pressure on the piston is about 33 lb. Most air compressors are double acting, though there are many small single acting ones. Example: A double acting 12 in. by 14 in. air compressor is running 150 R. P. M. It is supplying air at 100 lb. and the mean pressure in the cylinder is 37 lb. per square inch. Calculate the horse-power necessary to run it. In this case 12 appears in the denominator in order to reduce the 14 inches to feet. 112. Brake Horse-power.-The Brake Horse-power of an engine is the power actually available for outside use. It, therefore, is equal to the indicated horse-power minus the power lost in friction in the engine. Brake horse-power can be readily determined by putting a brake on the rim of the fly-wheel and thus absorbing and measuring the power actually delivered. Fig. 72 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 R FIG. 72. 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 3.1416X2XRXN ft. per minute and the brake horse-power will be 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 and it is 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 5X8 gas engine in article 110, we also determined the brake horse-power 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 horse-power. 3.1416X2X3X450-8482 186,604÷33,000=5.65, Answer. Explanation: Our data is equivalent to that 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 would rise 8482 ft. per minute and the work done per minute would be 22 lb. X8482 ft. 186604 footpounds per minute. Hence, the brake-horse power of the engine is 5.65. = 113. Frictional Horse-power.-If this engine gave 7.13 indicated H. P. (I. H. P.), but the power available at the flywheel was only 5.65, it stands to reason that the difference, or 1.48 H. P., was lost between the cylinder and fly-wheel. The explanation is that this power is expended in simply overcoming the friction of the engine; and this horse-power is, therefore, called the Frictional Horse-power. At zero brake horsepower, the entire I. H. P. is used in overcoming friction. 114. Mechanical Efficiency.-The ratio of the Brake Horsepower to the Indicated Horse-power gives the mechanical efficiency, meaning the efficiency of the mechanism in transmitting the power through it from piston to fly-wheel. This is usually expressed in per cent. In the case of the engine of which we figured the I. H. P. and B. H. P., the mechanical efficiency was 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 per cent. mechanical efficiency. The mechanical efficiency of a steam engine should be above 90% at full load. PROBLEMS 191. The cage in a mine weighs 2200 lb. and the load hoisted is 3 tons, The hoisting speed is 20 ft. per second. Calculate horse-power necessary. allowing 25% additional for friction and rope losses. 192. A 10 in. by 12 in. air compressor runs 150 R. P. M. The M. E. P. is 30 lb. Calculate the horse-power required to run it. 193. A pump lifts 2000 gallons of water per minute into a tank 150 ft. above it. Find the horse-power of the pump. |