Table Of the Expansive Force of Steam 514

An important improvement of Mr. Watt's was carried into practice in 1778. It consists in shutting off the steam from the cylinder, some time before the piston has completed its stroke, so that the remainder may be performed by the expansion of the steam already contained in the cylinder. This serves as a method of regulating the acting force of the engine, because, as the steam can be shut off at any part of the ascending or descending stroke, so much steam may be admitted as barely to carry the piston through its required motion, and by the adjustment of the valve gear, the quantity of steam admitted may at all times be varied in an instant. If this were the only advantage, it is a great one; but it will be seen that a great saving of fuel will likewise be effected by this method.

We shall endeavour to explain this more clearly by the aid of a diagram. The pressure of steam, as ascertained by numerous and carefully conducted experiments, is so nearly in direct proportion to its density, that for practical purposes it may be assumed to be in that ratio; and its density is of course inversely as the space occupied by it. Having premised thus much, let a 1 c A represent a cylinder into which the steam flows during the whole period of the stroke; at the end of which, or when the piston arrives at 1 c, the steam is discharged from the cylinder; then the effect being as the pressure of the steam multiplied by the space through which it acts, which pressure is in this case the same throughout the stroke, if the line a h represents the pressure, and a 1 the space through which it acts, the area of the rectangle alch will represent the effect

Now let abfh represent another cylinder of the same diameter as the former, but four times as long, and let it be supposed that only the same quantity of steam is admitted as before, the steam being cut off when the piston has reached to the position c 1, which is only 1/4 of the stroke in the cylinder a b; the piston will in this case continue to descend, but the pressure upon it will gradually decrease; and when the piston has made half its stroke, as the original volume of steam a 1 will then be expanded into double its bulk, or occupy the space a 2; its density, and consequently its pressure, will only be half as great as at the moment at which it was cut off, or when the piston was in the position c 1; therefore if the line c 1 represent the full pressure of the steam, the line d 2 will represent its pressure at the position 2. At the end of the stroke, or when the piston arrives at fb, the steam will be expanded into four times its original volume; consequently its pressure will then be only one fourth of its original pressure, and will be represented by the line b e.

In this case the total effect of the steam will be represented by the area he e b 1 a which exceeds the effect of the steam in the first supposed case, by the area c d e b 1, which therefore represents the increase of power due to the expansive action of the steam.

The curve c d e represents the ratio in which the pressure of the steam decreases as the piston descends in the cylinder, and if we deduct the area included by the points c defc, from the area of the rectangle c 1 b f, we shall obtain the area of the figure ceil, which represents the effect of the expansive action. Now, as the curve c d e differs but little from a parabola, the mean pressure may be readily computed by the following rule. It is only an approximation, but it is sufficiently near the truth for all practical purposes, so long as the steam does not expand to more than four times its original volume, and within those limits gives a result rather below the true one.

Rule

To the pressure of the steam, above the pressure of the atmosphere, add 15 lbs per square inch for the atmospheric pressure, and call the sum the total pressure of the steam; square the fraction of the stroke during which the steam acts expansively, and deduct 7/10 of the product from unity, and the remainder, multiplied by the total pressure, will be the mean pressure, after deducting 15 lbs for the pressure of the atmosphere in the case of non-condensing engines.

Rule 515

Example in a non-condensing engine; suppose the pressure of the steam, at the commencement of the stroke, to be 451bs per square inch above the atmosphere, and that the steam is cut off at 1/4 of the stroke: required, the mean pressure of the steam.

First. Full pressure . . . . . . . . . . . . . . . .. . . . .. . . . . . . . . . . . . . . . . ..

45 lbs

Atmospher . . . . . . . . . . . . . .. . . . .. . . . . . . . . . . . . . . . . .. . . .. . .

15 . .

Total pressure . . . . . . . . . . . . . .. . . . .. . . . . . . . . . . . . . . . .

60 lbs

Then. Steam cut off at 1/4 ......................................................

. 25 . .

Expands throughout 3/4 ...............................................

.75

Which is to be squared ................................................

.75

375

525

.5625

Deduct 7/10 ...................................................................

.7

.39375

From unity ....................................................................

1.

. 60625

Multiply by total pressure ............................................

60 lbs.

36.37500

Deduct for atmospheric pressure ..................................

15

Mean pressure ...............................................................

21.375 lbs

The mechanical effect being as the pressure of the steam, and the space through which such pressure is exerted, the effect of the steam whilst acting at full pressure in the above example, will be as 451bs through a space 1 = 45, but the total effect will be as 21.375lbs through a space 4, which is equal to 85.5, or nearly double the former, and shows the great advantage to be derived from using steam expansively. There are, however, in practice certain limitations to the extent to which steam may be allowed to expand, for independently of the inconvenience of the great size of the cylinder when the expansion is-carried to an extreme, the pressure of the steam upon the piston should never be less than the resistance from the friction, etc. added to the pressure of the atmosphere in non-condensing engines, or the pressure of the non-condensed steam in condensing engines; but in the preceding example, the pressure at the end of the stroke is merely equal to that of the atmosphere. Mr. Tredgold gives the following rule for ascertaining the point at which the steam should be cut off, so as to produce the greatest effect: -

Divide the amount of the friction, etc. added to the pressure of the atmosphere, in non-condensing engines, or of the non-condensed steam of condensing engines, by the pressure of the steam in the boiler, and the quotient will give the proportion of the stroke at which the steam should be cut off.