Of the Space for Steam, and Water in Boilers. 210.-A boiler must obviously contain as much steam as will supply the engine at each stroke without any material decrease in its elastic force; and the space will therefore depend on the manner the steam is to be supplied. If it be admitted to the engine only during part of the time of the piston's descent, there must be so much steam that the use of the quantity required may not lessen the elastic force. If the steam be generated equably, and the space for it only equal to the quantity consumed at each stroke, and all the quantity be wanted during the descent of the piston, the elastic force in the boiler will vary one half, and the loss of effect be very considerable. This subject is therefore worthy of further inquiry, in order that we may see how far the maxims of practice are confirmed by just principles. Without specifying the kind of engine, it is stated, that a boiler should have space for five or six times the volume of steam required for a stroke ;* others mention eight times; Dr. Young quotes a remark that it should contain ten times the volume,† and Prony has stated that it is one of the advantages of a double acting engine, that it requires a smaller boiler than a single acting one.‡ 211.-Let it be supposed that the action of the fire is uniformly the same, and that during a time 1 it generates a volume 1 of steam, and that this volume is sufficient to supply the engine; but that the whole of it is required in some less time t; and that c is the capacity of the space for steam in the boiler, and p the elastic force at the commencement of letting on the steam. Then c + t 1 is the quantity of steam in the space cat the end of letting on the steam; and the elastic force being inversely as the space, it will be Now in a single acting engine the time t when it acts at full pressure is one half, hence, and it was the same in all the trials, but of this not more than two-thirds or twenty-seven feet could be effective as fire surface. The mean intensity of the fire must have been equal to 1200°, to produce this effect; and the fuel consumed is somewhat more than double the quantity which ought to have generated the same quantity of steam. 209.-In another trial the length of boiler was nine feet two inches, its diameter four feet, and the diameter of the tube twenty-two inches, and the force of the steam limited to the excess of fifty pounds per square inch. In this case the whole surface of the tube in contact with the water of the boiler could not exceed fifty-two feet; and two-thirds of ⚫this being taken as effective, we have thirty-five feet for the surface. Pounds of coal to Surface to a cubic Time of experi- Coals consumed per Water boiled off per boil off a cubic foot foot of water per ment. hour. hour. of water. hour. The difference in the results in these trials is chiefly owing to a difference in the density of the steam in the boiler, its state not having been ascertained; and though it might be done in an indirect manner from the number of strokes per minute and the resistance, it would not be accurate enough to furnish us with any useful conclusions. Of the Space for Steam, and Water in Boilers. 210.-A boiler must obviously contain as much steam as will supply the engine at each stroke without any material decrease in its elastic force; and the space will therefore depend on the manner the steam is to be supplied. If it be admitted to the engine only during part of the time of the piston's descent, there must be so much steam that the use of the quantity required may not lessen the elastic force. If the steam be generated equably, and the space for it only equal to the quantity consumed at each stroke, and all the quantity be wanted during the descent of the piston, the elastic force in the boiler will vary one half, and the loss of effect be very considerable. This subject is therefore worthy of further inquiry, in order that we may see how far the maxims of practice are confirmed by just principles. Without specifying the kind of engine, it is stated, that a boiler should have space for five or six times the volume of steam required for a stroke ;* others mention eight times; Dr. Young quotes a remark that it should contain ten times the volume,† and Prony has stated that it is one of the advantages of a double acting engine, that it requires a smaller boiler than a single acting one.‡ 211.-Let it be supposed that the action of the fire is uniformly the same, and that during a time 1 it generates a volume 1 of steam, and that this volume is sufficient to supply the engine; but that the whole of it is required in some less time t; and that c is the capacity of the space for steam in the boiler, and p the elastic force at the commencement of letting on the steam. Then c + t 1 is the quantity of steam in the space c at the end of letting on the steam; and the elastic force being inversely as the space, it will be Now in a single acting engine the time t when it acts at full pressure is one half, hence, * Millington's Epitome of Natural Phil. p. 251. Architecture Hydraulique, Vol. II. p. 106. P 2 c + Natural Phil. Vol. II. p. 259. is the loss of elastic force; but if we make c = eight times the quantity required, the loss is only p, or the elastic force varies only, or about one pound on the square inch. 212.-If the steam be cut off before the stroke be completed, the variation will obviously be greater; for example, in a single engine cut the steam off at half the descent, and the variation of elastic force in the boiler will be one-eleventh, nearly, when the capacity for steam in the boiler is eight times the quantity required for a stroke. 213. In the double acting engine, the steam acting at full pressure, the time t is nearly the same as the time denoted by 1, and about three times the quantity required for the stroke may be sufficient; but if the steam be cut off at any fractional portion of the stroke, put t equal to that fraction, and it will be found to what the capacity must be increased to render the variation of force inconsiderable. Thus if it be cut off at half the stroke, then the same as in single engines, and we should not make c less than 8. But it must be remarked that it is in all these cases c times the volume of steam used as it is in the boiler, and not c times the capacity of the cylinder, because during the time the steam acts by expansion there is none entering the cylinder. 214.-For each cubic foot of water converted into steam in an hour by a low pressure boiler, we may assume that one cubic foot of steam is used at a stroke without material error; and if, as agrees with other parts of the arrangement of an engine, the variation be limited to one-thirtieth of the force of the steam, we shall have -t one-thirtieth, or 30 ( 1 − t ) = c. That is, calling the interval 1 from the time the steam valves are opened to the cylinder to a succeeding time of opening them to it; let the fraction of that interval during which the steam valves are open be subtracted, and thirty times the difference will be the space for steam in cubic feet in a low pressure engine. Thus, let it be a double acting engine where the steam is cut off at two-thirds of the stroke; theu, the whole stroke is the distance of the times of opening the steam valves, and two-thirds is the fraction; therefore 1 is, and 30 x is ten cubic feet. 215.—In a high pressure boiler the same rule applies; only instead of being the space in feet, thirty times the difference must be divided by the density of the steam compared with the atmospheric steam as unity. This may be done with sufficient nearness in practice, by dividing by the number of atmospheres equal to the force of the steam in the boiler. If in a double acting high pressure engine, which admits the steam only during half the stroke, the force of the steam in the boiler be four atmospheres, then for each cubic foot of water the boiler is to boil off per hour there should be 216.—Even in a double engine, which is intended to act at full pressure throughout the stroke, there is the time of opening and closing the valves to be deducted, and in some of the usual modes one-fourth of the stroke at least is expended, so that we can scarcely in any case say that less than eight, divided by the atmospheres representing the force of the steam in the boiler, should be allowed as the space in feet for steam for each cubic foot of water boiled off per hour. 217.-Space for Water in a Boiler. That there should be water to cover the sides of the boiler a little higher than the flues, is clear; but there is another condition which is less obvious but of considerable importance in effect, and it is particularly interesting in steam boats, where we wish to have neither more of space nor weight than is absolutely necessary. 1 The quantity of water an engine consumes is not admitted with perfect regularity; it is most equably done when forced in by a pump worked by the engine, and the portion admitted regulated by a float ball. See Plate I. Fig. 2. The quantity necessary to produce the steam must however be admitted, and its temperature we will suppose to be 100°; now the water in the boiler we will suppose to be 225°, and the proportion of the quantity in the boiler to that admitted ought to be such that the temperature should not be lowered so as to reduce the force of the steam onethirtieth part; otherwise a manifest disadvantage must take place in the action of the steam. But the depression of the temperature of the water two degrees will diminish its elastic force one-thirtieth, hence, supposing the quantity introduced at each time to be 1, and the quantity in the boiler to be a, we must have whence we find x = 62 nearly; that is, there must be sixty-two times as much water in the boiler as is introduced at one feed, otherwise the force of the steam will be lowered more |