THE CONVERSION OF HEAT INTO WORK.
When steam performs work a certain portion of the heat it contains is converted into work, the steam simply being a medium of conveying the heat into the cylinder in which the motion of the piston converts this proportion of heat into work. It has been proven that a given quantity of heat will pass into a given quantity of work, and conversely that a given quantity of work is convertible into a given quantity of heat, and it has also been proven that so much heat is convertible into so much work, independent of the temperature of the heat during its conversion into work, power, or energy, all three of these words being used to imply pressure, force, or weight in motion.
The accepted measurement of the conversion of heat into work is known as Joule’s equivalent; Joule having determined that the amount of power exerted in raising 772 lbs. one foot is the equivalent of the amount of heat that is required to raise the temperature of 1 lb. of water when at or near its freezing point (that is, at a temperature of 32°) one degree.
This is called the mechanical equivalent of heat, being merely the quantity of heat necessary to do a certain amount of work, but having no relation to the time in which that work was done.
The conversion of heat into work and of work into heat may be demonstrated as follows: Suppose a cylinder to be so situated that heat can neither be transferred to it or from it, and that saturated steam be admitted under the piston so as to fill one-half of the cylinder at a pressure of 50 lbs.
Suppose then that we raise the piston from an independent application of power, the steam simply expanding to fill the space given by the piston, but not exerting its force to move the piston.
Now suppose the experiment is repeated, permitting the force of the steam to lift the piston, and the temperature of the steam will be less in the second than it was in the first, proving that in the second experiment a certain portion of the heat in the steam was converted into the work of raising the piston.
If we desire to reconvert the work into heat, we may force the piston back again to its original position, and its temperature will be restored to what it was before we allowed it to raise the piston. It is here, of course, assumed that there is no friction in moving the piston in the cylinder.
The apparent or external work performed by steam in expanding and moving a piston against a given resistance is measurable by multiplying the amount of the resistance against which the piston moved by the distance it moved through, thus:
Suppose a piston weighs 100 lbs. and had resting upon it a weight of 50 lbs., and that it be raised by the expansive action of steam a distance of a foot, then, since the total resistance it moved against would be (supposing it to move frictionless in the cylinder) 150 lbs., and since the amount of motion was 1 foot, the external or apparent amount of work performed by the steam will be 150 foot lbs., or 150 lbs. moved 1 foot.
But in expanding, the steam has performed a certain amount of what is called internal work, that is to say, its particles or atoms have done work in expanding, and this work has been done at the expense of some of the heat in the steam, so that the loss of heat due to the motion of the piston is the amount of heat converted into work in moving the piston against the piston resistance, added to that converted into the internal work due to the expansion of the steam.
It is because of this internal work that the steam in expanding does not strictly follow Mariotte’s law.
The mechanical theory of heat is, that the atoms of which bodies are composed are at absolute rest when at a temperature of 461.2° below the zero of Fahrenheit, which is supposed to be absolute cold, and at any degree of temperature above this the atoms are in motion; the extent and force of their motion determines what we know as the temperature of the body.
Atoms are capable of transmitting their motion to adjoining atoms of the same or of other bodies, losing, of course, the amount of motion they transmit, and it is in this way that heat is conveyed from one to another part of the same body, or from one body to another, this being known as the heat of conduction.
But heat may be conveyed by means of what is known as radiation, and also by convection.
Thus, the air surrounding a heated body becomes heated, and by reason of its expansion it then becomes lighter and rises, a fresh supply of cooler air taking its place, becoming in turn heated, and again giving place to cooler air; the heat thus conveyed away by the fluid or air is conveyed by what is termed convection.
Heat also passes from a body in straight lines or rays, which do not heat the air through which they pass to their own temperature, but do impart that temperature to a solid body, as iron or water; the heat that passes from a body in this manner is termed radiant heat, or the heat of radiation.
In the cylinder of a steam engine, therefore, the heat contained in the steam is disposed of as follows:
A certain portion of it is converted into work through the medium of the piston.
Another portion is conveyed away by the walls of the cylinder, this portion including the heat of convection and that of radiation.
Yet another portion is converted into internal work. Referring to the latter, suppose that steam is permitted to expand and its atoms will be in motion, which motion has been derived at the expense of or from the conversion of a certain quantity of heat.
The amount of the heat so converted obviously depends upon the amount of the motion. Suppose, for example, that steam is generated in a closed vessel as in a steam boiler, and that a certain pressure having been attained, the steam is permitted to pass off as fast as it is formed from the boiler, then the amount of atomic motion will remain constant, because the pressure remains constant; but suppose instead of the steam passing off, it be confined within the boiler, then the pressure will increase and there will be a greater resistance to the motion of the atoms, hence their motion will be less, and less of their heat will therefore be converted into atomic motion, and, as a consequence, more of it will exist in the form of sensible heat; hence while the pressure of steam continues to increase, its heat is increased, not only by reason of the heat it receives from the furnace, but also by reason of that abandoned by the steam, because it is prevented by the pressure, from expending it in atomic motion.
Chapter XL.—THE INDICATOR.
The indicator is an instrument which marks or draws a figure, or diagram as it is called, which shows the pressure there is in the cylinder at every point in the piston stroke, while it also shows the resistance offered by the same body of steam to the piston on its return stroke. From the form of this figure or diagram, the engineer is enabled to discover whether those parts of the engine whose operation regulates the admission of the steam to and its exhaust from the cylinder are correctly adjusted.
From the diagram the engineer may find the average or mean effective pressure of steam on the piston throughout the stroke, for use in calculating the power of the engine.
He may also locate the point of cut off, of release, the amount of back pressure, the degree of perfection of the vacuum in a condensing engine, and the amount of compression.
From the area of the diagram the engineer may also estimate the quantity of steam that is used, and supposing it to be dry steam, he may calculate the amount of water used to make the steam, and assuming one pound of coal to evaporate so much water, he may calculate the amount of coal used to produce the steam.
The indicators commonly used upon steam cylinders contain two principal mechanical movements; first, a drum revolving the piece of paper upon which the diagram is to be marked, and second, a piston and parallel motion for moving the pencil to mark the diagram upon the revolving paper.
The drum is given a motion that, to insure a correct diagram, is exactly timed with the piston motion.
The pencil is given a vertical movement; this movement must bear a constant and uniform relation to the pressure of the steam in the engine cylinder.
An indicator may be attached to each end of the cylinder or in the middle, with a pipe passing to each end of the cylinder, as in Fig. 3358, but an indicator of the usual construction and such as here referred to, can take a diagram, or card as it is sometimes called, from but one end of the cylinder at a time. The stop valves a and b are used, so that the communication between the indicator and one end of the cylinder may be shut off while a diagram is being taken from the other end, while both ends may be shut off when the indicator is not being used.
In the figure a piece of paper (or card, as it is commonly called) is shown in place upon the drum with a diagram upon it.
The Thompson Indicator is shown in Fig. 3359, and in section in Fig. 3360.
The Tabor Indicator is shown in Fig. 3361, and in section in Fig. 3362.
Both are made with the piston and parallel motion as light as possible, in order to enable the taking of diagrams at as high a speed of engine revolution as possible.
Each consists of a cylinder and piston, the bottom surface of the latter being in communication with the bore of the engine cylinder, so as to receive whatever steam pressure there may be in the cylinder.
This indicator piston receives, on its upper surface, the pressure of a spiral spring, which acts to resist the steam pressure.
The indicator piston rod actuates an arm or line on the end of which is a pencil, which, by means of a parallel motion, is caused to move in a straight line.
The paper or card being in place upon the drum, and steam let into the indicator, the pencil lever is moved until the pencil touches the paper as lightly as possible, and as a result of the combined movements of the pencil and drum, the diagram is marked, its form being illustrated in Fig. 3363, which represents a diagram placed above a cylinder, and the engine piston in three positions; first at the beginning of the stroke; second, at the point of cut off (which is supposed to be at one-third of the stroke); and third, at the point of release where the valve first opens the port for the exhaust. For convenience, the diagram is shown as long as the cylinder, but the actual diagram usually measures about 21⁄2 inches high and 41⁄4 inches long.
Supposing the cylinder to be filled with air, and the engine piston in position 1, and the indicator piston would be at the corner a of the diagram; but if steam were admitted, the pencil would rise vertically, marking the line from a to b, which is therefore called the admission line, or by some, the induction line.
If on reaching b the pressure was enough to move the engine piston, that piston and the indicator drum would move simultaneously, and as long as live steam was admitted the line from b to c would be drawn, hence this is called the steam line, its length denoting the live steam period.
The cut off occurs when the engine piston is in position 2, and the indicator pencil at c.
From this point the pencil will fall, in proportion as the steam pressure falls from expansion until the exhaust begins, the piston then being in position 3, and the pencil at d.
The line from c to d is therefore called the expansion line or expansion curve, and the point d the point of release or point of exhaust.
We have now to explain that in reality the whole of the remainder of the line of the diagram is, in reality, the exhaust line, yet there is a difference between the part of the line from point d to the end e of the diagram, and that part from se to a, inasmuch as that during the period of exhaust from d to e, the pressure is helping to propel the piston, while after e is reached, whatever steam pressure there may remain in the cylinder acts to retard the piston.
The line from d to e is therefore the exhaust line, and that from e to a is the back pressure line or counter pressure line.
In this example it has been supposed that while the piston was moving from position 3 to the end of its stroke, and the pencil from d to e, the indicator piston would have a steam pressure on it equal to atmospheric pressure, hence the line from e to a, in this case, represents the atmospheric line, and also the back pressure line.
The atmospheric line is a line drawn when there is no steam admitted to the indicator, and represents a pressure above a perfect vacuum equal to the pressure of the atmosphere. Its use is to show the amount of back pressure, and in a condensing engine to show the degree of vacuum obtained.
It also forms a line wherefrom the line of perfect vacuum, or that of full boiler pressure, may be marked.
The steam pressure at any point in the stroke is denoted by the height of the diagram above the atmospheric line, but the steam pressure thus taken is obviously above atmospheric, and is thus the same as the pressure of a steam gauge, which is also above the atmospheric pressure, and therefore represents the pressure that produces useful effect in a non-condensing engine.
This is what may be called a theoretical diagram, because, first, it supposes the steam not to be admitted to the cylinder until the piston was at the end of its stroke, and to attain its full pressure in the cylinder before the piston lead begins to move, whereas, in order to attain a full steam pressure at the beginning of the stroke, the valve must have lead.
Second, it supposes the cut off to be effected simultaneously, whereas the valve must have time to move and close the port, and during this time the steam pressure will fall, and the curve c of the diagram will therefore be rounded more or less according to the rapidity with which the valve closed.
Third, it supposes the steam to have exhausted down to atmospheric pressure by the time the piston had reached the end of the stroke, whereas the piston will have moved some part of the back or return stroke before the steam will have had time to exhaust down to atmospheric pressure; and,
Fourth, it supposes the steam to remain at atmospheric pressure until the piston arrives at the end of its return stroke, whereas the valve will begin to close the port and cause the steam remaining in the cylinder to compress before the piston has completed its return stroke.
In practice the diagram will, under favorable conditions, accord nearer to the shape shown in the lower part of Fig. 3363, in which the closure of the port for the cut off is shown by the curve at f. At the point denoted by g the valve began to close, and at the point denoted by h the cut off was completely effected, and the expansion curve began.
The curve beginning at d is caused by the gradual opening of the exhaust port.
The height of the line of back pressure above the atmospheric line shows the amount of back pressure.
At the point m, where the back pressure line rises into a curve, the valve had closed, shutting in the cylinder a portion of the exhaust steam, which is afterwards compressed by the piston.
This curve is therefore called the compression line or compression curve. The point at which it begins cannot be clearly seen when the exhaust port is closed slowly.
The compression curve ends at p, where it merges into the admission line, but the exact point where the compression ends and the admission begins cannot always be located, this being the case when the port is opened slowly or the compression extends through a large portion of the stroke.
The admission line is, however, in most cases nearly vertical when the valve has lead, because the valve opens the port quickly while the engine piston is moving at its slowest.
A diagram as drawn by the indicator does not account for all the steam that is used in the cylinder, however, as will be seen from Fig. 3363, because, as the paper drum of the indicator receives its motion from the engine cross head, its length represents the length of the piston stroke, whereas, there is a part of the cylinder bore between the piston (when it is at the end of the stroke) and the cylinder cover that is filled with steam as is also the steam passage.
This steam performs no useful work during the live steam period, but obviously expands during the expansion period, and therefore affects the expansion curve, and must be taken account of in calculating the consumption of steam, of water, or of coal from the diagram, or in marking in the true expansion curve.
In calculating the horse power, however, it may be neglected, as it does not enter into that subject.
But in any calculation involving the amount of steam used, the clearance must be marked in by a line at a right angle to the admission line and distant from the nearest point of the admission line to an amount that bears the same proportion to the whole length of the diagram as the clearance does to the whole contents of the cylinder.
The clearance line is shown at l, l′, in Fig. 3363, its distance from the admission line representing the amount of clearance which includes the contents of the steam port and passage, as well as that of the cylinder bore that is between the cylinder cover and the piston, when the latter is at the end of the stroke.
A method of measuring the amount of clearance has already been given with reference to stationary steam engines.
A diagram for a condensing engine is shown in Fig. 3364, which corresponds to Fig. 3363, except that the line of perfect vacuum or no pressure is marked in.
It represents a perfect vacuum, and must be marked on all diagrams from which the consumption of steam is to be calculated, because the quantity of steam used obviously includes that which is used in counter balancing the pressure of the atmosphere.
Learners often get confused on this point, hence it may be more fully explained as follows:
Suppose the engine piston to be blocked, in the middle of the cylinder, and has on one side of it a pressure of 20 lbs. of steam by steam gauge, and on the other the pressure of the atmosphere, and we might pump out the steam, thus leaving the cylinder empty on that side of the piston.
The atmosphere would then exert a pressure of about 141⁄2 lbs. per square inch on one side of the piston, and if we slowly admitted steam again, it would have to get up a pressure of 141⁄2 lbs. per square inch before the atmospheric pressure would be counterbalanced and the piston be in equilibrium.
But the steam gauge would at this time stand at zero, and not show that there was any steam in the cylinder, because the zero of the steam gauge is atmospheric pressure.
When, therefore, the steam gauge showed a pressure of 20 lbs. of steam in the cylinder, there would actually be a pressure of 341⁄2 lbs. of steam per square inch.
The clearance line and the vacuum line must both, therefore, be marked on the diagram when the quantity of steam used is to be computed from the diagram, and also when the proper or theoretical expansion curve is to be marked on the diagram.
This is clear, because in finding the expansion curve for a given volume of steam the whole of its volume must be taken into account, and this whole volume is represented by the area inclosed within the clearance line, the steam line, the expansion curve, the exhaust line, and the line of perfect vacuum, or line of no pressure.
The atmospheric line should be drawn after the diagram has been taken, and while the indicator is hot, as the expansion of the indicator affects the position of this line. It is drawn with the steam shut entirely off from the indicator, whose piston therefore has atmospheric pressure on both sides of it.
Whether the engine is condensing or non-condensing, the same amount of steam (all other things being equal) is used, the only difference being that in a condensing engine a greater portion of the steam is available for driving the piston.
If the condenser produced a perfect vacuum, the whole of the steam would be utilized in propelling the piston.
The “line of no pressure,” or of perfect vacuum, is marked as far below the atmospheric line as will represent the pressure of the atmosphere, which is, at the sea level, about 14.7 lbs. per square inch when the barometer stands at 29.99 inches.
THE BAROMETER.
A barometer is an instrument for denoting the pressure or weight of the atmosphere, which it does by means of a column of mercury inclosed in a tube, in which there is a vacuum, which may be produced as follows:
A tube having a parallel bore and closed at one end is filled with mercury and while the finger is placed over the open end of the tube, it is turned upside down and inverted in a cup of mercury that is open to receive the pressure of the atmosphere.
The finger is then removed from the end of the tube and the mercury will fall, leaving a vacuum at its upper end.
The pressure of the atmosphere on the surface of the mercury in the cup forces the mercury up the tube, because the surface of the mercury in the tube has no atmospheric pressure on it, the action being the same as that already described with reference to the principles of action of a pump.
The weight of the atmosphere is equal to the weight of that part of the column of mercury that is above the surface of the mercury in the cup, hence lines may be drawn at different heights representing the weight of the atmosphere, or of any other gas, when the column of mercury stands at the heights denoted by the respective lines.
But as mercury expands by heat, a definite degree of temperature must be taken in marking a column, to represent the weight, this temperature being 32° Fahrenheit.
Similarly, as the weight of the atmosphere varies, according to the height at which it is taken from the surface of the earth, a definite height must be taken.
The sea level is that usually taken, the mean or average atmosphere (at that level) being 14.7 lbs. per square inch.
For higher altitudes, the mean atmospheric pressure in lbs. per square inch may be found by multiplying the altitude or height above sea level by .00053, and subtracting the product from 14.7.
Each pound on the square inch is represented by a height of 2.036 inches of mercury, hence the height of a column of mercury at a temperature of 32° that will balance the mean weight of the atmosphere is 29.92 inches, and to avoid fractions, it is usual (for purposes not requiring to be very exact) to say that the atmospheric pressure at sea level is represented by 30 inches of mercury.
The atmospheric pressure is also, to avoid using fractions, taken roughly at 15 lbs. per square inch at sea level.
Each 2 inches of mercury will, under these conditions, represent 1 lb. of pressure.
Vacuum gauges are based upon the same principles and subject to the same variations as to altitude as mercury gauges or the barometer.
To find the absolute pressure, or pressure above zero, or a perfect vacuum, we may add the pressure of the boiler steam gauge to that shown by the mercury gauge or barometer.
In Fig. 3364 the line of no pressure is marked at 15 lbs. per square inch below the atmospheric line of the diagram, the atmospheric pressure being for convenience taken as 15 lbs. above a perfect vacuum.
The line of no pressure serves as a guide in showing the effectiveness of the condenser, as well as for computing the volume of steam used, but is not necessary in computing the horse power of a non-condensing engine, because the gauge pressure has its zero marked to correspond with the atmospheric pressure.
In computing the consumption of steam or water from the diagram, therefore, both the clearance line and the line of no pressure must be marked on the diagram, and lines of the diagram extended so as to include them, thus accounting for all the steam that leaves the steam chest from the piston stroke.
Indicator springs are varied in strength to suit the pressure of steam they are to be used for.
The scale of the spring is the number of lbs. pressure per square inch represented by a vertical motion of the pencil; thus, a 40 lb. spring is one in which a pressure of steam of 40 lbs. per square inch would cause the piston to rise an inch above the atmospheric line of the diagram.
The strength or tension of the spring is so adjusted as to cause the diagram to be about 21⁄2 inches high, let the steam pressure be what it may. The following are the scales of springs of the Thompson and Tabor indicator.
THOMPSON INDICATOR. |
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| Scale of spring. |
Used for pressure above atmosphere if not more than |
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| 15 | lbs. | 21 | lbs. | per | square | inch. |
| 20 | „ | 38 | „ | „ | „ | „ |
| 30 | „ | 94 | „ | „ | „ | „ |
| 40 | „ | 90 | „ | „ | „ | „ |
| 60 | „ | 143 | „ | „ | „ | „ |
TABOR INDICATOR. |
||||||
| 10 | lbs. | 14 | „ | „ | „ | „ |
| 12 | „ | 20 | „ | „ | „ | „ |
| 16 | „ | 30 | „ | „ | „ | „ |
| 20 | „ | 40 | „ | „ | „ | „ |
| 24 | „ | 48 | „ | „ | „ | „ |
| 30 | „ | 60 | „ | „ | „ | „ |
| 32 | „ | 64 | „ | „ | „ | „ |
| 40 | „ | 80 | „ | „ | „ | „ |
| 48 | „ | 96 | „ | „ | „ | „ |
| 50 | „ | 100 | „ | „ | „ | „ |
| 60 | „ | 120 | „ | „ | „ | „ |
| 64 | „ | 128 | „ | „ | „ | „ |
| 80 | „ | 160 | „ | „ | „ | „ |
A spring that is strong enough for a given pressure may be used for any less pressure.
The height of the diagram will, however, be less, and accuracy is best secured by having the diagram up to the limit of about 21⁄2 inches, using a spring that is light enough to secure this result.
Diagrams of high speed engines, however, will have their lines
more regular in proportion as a stronger spring is used.
This occurs because the spring, being under more tension, is less liable to vibration.
An indicator requires careful cleaning and oiling with the best of oil, as the slightest undue friction seriously impairs the working of the instrument.
Instructions upon the care of the instrument, and how to take it apart, etc., are usually given by the makers of the indicator.
There are various methods of giving to the paper drum of the indicator a motion coincident with that of the engine piston, but few of them give correct results.
Reducing levers, such as shown in Fig. 3365, are constructed as follows:
Fig. 3365 represents a reducing lever with the indicators attached. a c is a strip of pine board three or four inches wide and about one and one-half times as long as the stroke of the engine. It is hung by a screw or small bolt to a wooden frame attached overhead. A link c one-third as long as the stroke is attached at one end to the lever, and at the other end to a stud screwed into the cross head, or to an iron clamped to the cross head by one of the nuts that adjust the gibs, or to any part of the cross head that may be conveniently used. The lever should stand in a vertical position when the piston is at the middle of the stroke. The connecting link c, when at that point, should be as far below a horizontal position as it is above it at either end of the stroke. The cords which drive the paper drums may be attached to a screw inserted in the lever near the point of suspension; but a better plan is to provide a segment, a, b, the centre of which coincides with the point of suspension, and allow the cord to pass around the circular edge. The distance from edge to centre should bear the same proportion to the length of the reducing lever as the desired length of diagram bears to the length of the stroke. On an engine having a stroke of 48 inches, the lever should be 72 inches, and the link c 16 inches in length, in which case, to obtain a diagram 4 inches long, the radius of the segment would be 6 inches. It is immaterial what the actual length of the diagram is, except as it suits the operator’s fancy, but 4 inches is a length that is usually satisfactory. It may be reduced to advantage to 3 inches at very high speeds. The cords should leave the segment in a line parallel with the axis of the engine cylinder.
The pulleys over which they pass should incline from a vertical plane and point to the indicators wherever they may be located. If the indicators and the reducing lever can be placed so as to be in line with each other, the pulleys may be dispensed with and the cords carried directly from the segment to the instruments, a longer arc being provided for this purpose. The arm which holds the carrier pulleys on each indicator should be adjusted so as to point in the direction in which the cord is received.
In all arrangements of this kind the reduced motion is not mathematically exact, because the leverage is not constant at all points of the stroke.
Pantagraph motions have been devised for overcoming these defects. Two forms have been successfully used, which, if well made, well cared for, and properly handled, reproduce the motion on the reduced scale with perfect accuracy. They are shown in working position in Figs. 3366 and 3367.
Fig. 3366 represents the manner of attaching the pantagraph motion, or lazy tongs, as it is sometimes called, when the indicators are applied to the side of the cylinder. It works in a horizontal plane, the pivot end being supported by a post b erected in front of the guides, and the working end receiving motion from an iron attached to the cross head.
By adjusting the post to the proper height and at a proper distance in front of the cross head, the cords may be carried from the cord pin c to the indicators, without the intervention of carrier pulleys.
If the indicators are attached to the side of the cylinder, the simplest form of pantagraph shown in Fig. 3367 may be used. The working end a receives motion from the cross head, and the front piece b is attached to the floor. The cord pin d is fixed in line between the pivot and the working end, and the pulleys e, attached to the block c, guide the cords to the indicators.
The indicator rigging that gives the best results at high speeds is a plain reducing lever like that first described, provided at the lower end with a slot that receives a stud, screwed into the cross head. The length of the lever should be one and one-half times the engine stroke, as given on the preceding page.
Whatever plan is followed, it is desirable to avoid the use of long stretches of cord. If the motion must be carried a long distance, strips of wood may often be arranged in their place and operated with direct connections. Braided linen cord, a little in excess of one-sixteenth of an inch in diameter, is a suitable material for indicator work.
To take a diagram, a blank card is stretched smoothly upon the paper drum, the ends being held by the spring clips. The driving cord is attached and so adjusted that the motion of the drum is central.
For convenience two diagrams, one from each end of the cylinder, may be made on the same card, as shown in Fig. 3368.
TESTING THE EXPANSION CURVE.
The usual manner of testing the expansion curve of a diagram is to compare it with a curve representing Mariotte’s law for the expansion of a perfect gas.
A theoretic expansion curve that will accord with Mariotte’s law may be constructed on the diagram by the following method:
The diagram, as drawn by the indicator, will have the atmospheric line upon it, and from this as a basis we may mark in the line of no pressure or line of perfect vacuum.
To do this we draw, beneath the atmospheric line, a line as far beneath it as will represent the atmospheric line, on the same scale as the spring used, in the indicator, to draw the diagram.
Suppose, for example, that a 30 lb. spring was used, and assuming the atmospheric pressure to be 15 lbs. per inch, then the line of no pressure would be drawn half an inch below the atmospheric line, because 15 lbs. pull on the spring would cause it to distend half an inch.
The clearance line must then be drawn in, according to directions that have already been given.
The next thing to do is to divide the length of the diagram into any convenient number of equal parts, by vertical lines parallel to, and beginning at, the clearance line, as shown in Fig. 3369. These lines are numbered as shown, ten of them being used because that is a convenient number, but any other number would do.
We next decide at which part of the diagram its expansion curve and the test curve shall touch, and in this example we have chosen that it shall be at line 10.
We have now to find what pressure the length of line 10 represents on the scale of the indicator spring, which in this case we will suppose to be 25 lbs., the line measuring 25⁄30 of an inch, and a 30 lb. spring having been used to draw the diagram. Next multiply the pressure (25 lbs.) by the number of the line (10), and divide the product (250) by the number of each of the other lines in succession, and the quotient will be the pressures to be represented by the lines.
For example, for line 9 we have that 250 divided by 9 gives 27.7, hence line 9 must be long or high enough to represent a pressure of 27.7 lbs. above a perfect vacuum, or in this case 27.7⁄30 of an inch.
For line 8 we have that 250 divided by 8 gives 31.25 lbs., hence line 8 must be high enough to represent a pressure of 31.25 lbs. above a perfect vacuum.
The atmospheric line is, in this case, of no other service than to form a guide wherefrom to mark in the line of no pressure, or of perfect vacuum.
Now take the case of line 5, and 250 divided by 5 gives 50, hence the height of line 5 must represent a pressure above vacuum of 50 lbs.
Having carried this out for all the lines from line 10 to line 1, we draw in the true expansion curve, which will touch the tops of all the lines.
Another method of drawing this curve is shown in Fig. 3370. Having drawn the clearance line b c, and vacuum line d c, as before and chosen where the curves shall touch (as at a), then draw from a a perpendicular a a.
Draw line a b, parallel to the vacuum line, and at any convenient height above or near the top of the diagram.
From a draw a c, and from a draw a b parallel to d c, then from its intersection with a c, erect the perpendicular b c, locating on a b, the theoretical point (c) of cut-off.
From a number of points on a b (which may be located without regard to equally spacing them), such as e, f, g and h, draw lines to c, and also drop perpendicular lines, as e e, f f, g g, h h.
From the intersection of e c with b c, draw a horizontal line to e. From the intersection of f c with b c, draw a horizontal line, and so on; and where these horizontals cut the verticals (as at e, f, g, h) are points in the curve, which begins at c, and passes through e, f, g, h, to a.
But this curve does not correctly represent the expansion of steam. It would do so if the steam remained or was maintained at a uniform temperature; hence it is called the isothermal curve, or curve of same temperature. But in fact steam and all other elastic fluids fall in temperature during their expansion, and rise during compression, and this change of temperature slightly affects the pressure.
A curve in which the combined effects of volume and resulting temperatures is represented is called the adiabatic curve, or curve of no transmission; since, if no heat is transmitted to or from the fluid during change of volume, its sensible temperature will change according to a fixed ratio, which will be the same for the same fluid in all cases.
A sufficiently close approximation to the adiabatic curve to enable the non-professional engineer to form an idea of the difference between the two may be produced by the following process: