Modern Machine-Shop Practice Part 251

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.

[Ill.u.s.tration: Fig. 3370.]

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 s.p.a.cing 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 pa.s.ses 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:

Taking a similar diagram to that used for the foregoing ill.u.s.trations, as in Fig. 3371. Fix on a point A near the terminal, where the total pressure is 25 pounds. As before, this point is chosen in order that the two curves may coincide there.

Any other point might have been chosen for the point of coincidence; but a point in that vicinity is generally chosen, so that the result will show the amount of power that should be obtained from the existing terminal. This point is 3.3 inches from the clearance line, and the volume of 25 pounds 996, that is, steam of that pressure has 996 times the bulk of water.

Now if we divide the distance of A from the clearance line by 996, and multiply the quotient by each of the volumes of the other pressures indicated by similar lines, the products will be the respective lengths of the lines measured from the clearance line; the desired curve pa.s.sing through their other ends. Thus, the quotient of the first or 25 lb.

pressure line divided by 996 is .003313; this, multiplied by 726, the volume of 35 lbs. pressure, gives 2.4, the length of the 35 lb. pressure line; and so on for all the rest.

The application of either of the above curves will show that some diagrams are much more accurate than others, even though taken from engines of the same design and quality of workmans.h.i.+p.

As a general rule, those from large engines will be more correct than from small ones, and those from high more correct than from low speeds, and in either case efficiently covering the steam pipes and jacketing the cylinder, to prevent condensation, will improve the diagram.

The character of the imperfection in the expansion curve, shown by the application of a test curve, is generally too high a terminal pressure for the point of cut off, the first part of the curve being generally the most correct, and nearly all the inaccuracy appearing in the last half.

The usual explanation of this is, that the steam admitted during the live steam period condenses because of having to heat the cylinder, and that this water of condensation re-evaporates during the latter part of the stroke when this water of condensation is at a higher temperature than the expanded steam, and thus increases the pressure.

A leaky admission valve may generally, however, be looked for (or else wet steam), if the expansion curve rises much during its lower half.

TO CALCULATE THE HORSE POWER FROM A DIAGRAM.

In calculating the horse power of an engine, the only a.s.sistance given by the indicator is, that it provides a means of obtaining the average pressure of the steam throughout the piston stroke.

There are two methods of doing this, one by means of a planimeter or averaging instrument, and the other by means of lines called _ordinates_.

The ordinates or lines are drawn at a right angle to the atmospheric line, as shown in Fig. 3372, and each line is taken to represent the average height or length of one-half of the s.p.a.ce between itself and the next lines.

[Ill.u.s.tration: Fig. 3371.]

Suppose, for example, that we require to get the area of that part of the diagram that lies between the dotted lines in the figure, and it is clear that the average height of this part of the diagram is represented by the height of the full line between them.

Any number of ordinates may be used, and the greater their number the greater the accuracy obtained. It is, however, usual to draw 10.

[Ill.u.s.tration: Fig. 3372.]

The end ordinates A and D, in the figure, should be only half the distance from the ends of the diagram that they are from the next ordinate, as will be seen when it is considered that the ordinate is in the middle of the s.p.a.ce it represents.

The ordinates being drawn their lengths, are added together, and the sum so obtained is divided by the number of ordinates, which gives the average height of the ordinates.

Suppose, then, that the average height of the ordinate is two inches, and that the scale of the spring of the indicator that took the diagram was 30 lbs., then the average pressure, shown by the diagram, will be 60 lbs. per square inch. Or in other words, each inch in the height of the ordinate represents 30 lbs. pressure per square inch.

The mean effective pressure having been found, the indicated horse power (or I. H. P. as it is given in brief) is found by multiplying together the area of the piston (minus half the area of the piston rod when great accuracy is required) and the travel of the piston in feet per minute, and dividing the product by 33,000, an example having been already explained.

It is to be observed, however, that when great accuracy is required a diagram should be taken from each end of the cylinder, as the mean effective pressure at one end of the cylinder may vary considerably from that at the other.

This will be the case when a single valve is used with equal lap, because, in this case, the point of cut off will vary on one stroke as compared with the other, which occurs by reason of the angularity of the connecting rod.

When cut off valves or two admission valves are used, it may occur from improper adjustment of the valves. It occurs in all engines, because on one side of the piston the piston rod excludes the steam from the piston face, unless, indeed, the piston rod pa.s.ses through both covers, in which case the rod area must be subtracted from the piston area.

If the expansion curve in a diagram from a non-condensing engine should pa.s.s below the atmospheric line, then the mean effective pressure of that part of the card that is below the atmospheric line must be subtracted from the mean effective pressure of that part that is above the atmospheric line, because the part below represents back pressure or pressure resisting the piston motion.

The planimeter affords a much quicker and more accurate method of obtaining the average steam pressure from a diagram.

[Ill.u.s.tration: Fig. 3373.]

Coffin's averaging instrument or planimeter is shown in Fig. 3373. The diagram is traced by the point O, and the register wheel gives the area of the diagram.

A quick method of approximating the mean effective pressure (or M. E. P.

as it is called) of a diagram is to draw a line _a_ _b_, in Fig. 3374, touching the expansion curve at _a_, and so inclined that the s.p.a.ce _e_ is, as near as the eye can judge, equal to the s.p.a.ce _d_. Then the line _f_ drawn in the middle of the diagram, and measured on the scale of the spring that was used to take the diagram, represents the mean effective pressure, or M. E. P. of the diagram.

CALCULATING THE AMOUNT OF STEAM OR WATER USED.

The amount of water evaporated in the boiler is not accounted for by an indicator diagram or card, and the full reasons for this are not known.

It is obvious, however, that the loss, from the steam being unduly wet or containing water held in suspension, is not shown by the diagram, and this amount of loss will vary with the conditions.

Thus the loss from this cause will be less in proportion as the point of cut off occurs earlier in the stroke, because, as the water is at the same temperature as the steam, it will, as the temperature of the steam reduces from the expansion, evaporate more during the expansion period, doing so to a greater extent in proportion as the cut off is early, on account of there being a wider variation between the temperature of the steam at the point of cut off and at the end of the stroke. On the other hand, however, in proportion as the cut off is earlier, the proportionate loss from condensation during the live steam period is greater, because a greater length of the cylinder bore is cooled during the expansion period, and it has more time to cool in.

Whatever steam is saved by the compression, from the exhaust, must be credited to the engine in calculating the water consumption from the indicator card or diagram, since it fills, or partly fills, the clearance s.p.a.ce.

In engines which vary the point of cut off, by varying the travel of the induction or admission valve, the amount of compression is variable with the point of cut off, and increases in proportion as the live steam period diminishes; hence to find the actual water or steam consumption per horse power per hour, diagrams would require to be taken continuously from both ends of the cylinder during the hour; a.s.suming, however, that the point of cut off remains the same, that the amount of compression is constant, that the steam is saturated, and neither wet nor superheated, steam and the water consumption may be computed from the diagram as follows:

WATER CONSUMPTION CALCULATIONS.--An engine driven by water instead of steam, at a pressure of 1 lb. per square inch, would require 859.375 lbs. per horse power per hour; the water being of such temperature and density that 1 cubic foot would weigh 62-1/2 lbs. If the mean pressure were more than 1 lb., the consumption would be proportionately less; and, if steam were used, the consumption would be as much less as the volume of steam used was greater than an equal weight of water. Hence, if we divide the number 859.375 by the mean effective pressure and by the volume of the terminal pressure, the result will be the theoretical rate of water consumption in pounds per I. H. P. per hour.

[Ill.u.s.tration: Fig. 3374.]

For the terminal pressure we may take the pressure at any convenient point in the expansion curve near the terminal, as at A, Fig. 3375, in which case the result found must be diminished in the proportion that the portion of stroke remaining to be made, A _a_, bears to the whole length of the stroke _a_ _b_; and it may also be diminished by the proportion of stroke remaining to be made after the pressure at A has been reached in the compression curve at B. In other words, A B is the portion of the stroke A B, during which steam at the pressure at A is being consumed. Hence the result obtained by the above rule is multiplied by A B, and the product divided by _a_ _b_.

To ill.u.s.trate, suppose the mean effective pressure of the diagram to be 37.6 lbs., and the pressure at A, 25 lbs., of which the volume is 996.