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 space.

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; assuming, 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 62⁄2 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.

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 illustrate, 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.

Then 859.375/(37.6 × 996) = 22.94 pounds water per I. H. P. per hour, the rate that would be due to using an entire cylinder full of steam at 25 pounds pressure every stroke. But as the period of consumption is represented by b a (b a being the stroke), the following correction is required:

(22.94 × 3.03)/3.45′′ = 20.15; 3.03 inches being the portion b a, and 3.45 inches being the whole length b, a. This correction allows for the effects of clearance as well as compression, since, if more clearance had existed, the pressure at a would not have been reached till later in the stroke, and the consumption line b a would have been longer.

But such a rate can never be realized in practice. Under the best attainable conditions, such as about the load indicated on the diagram, or more on a large engine with steam tight valves and piston, and well protected cylinder and pipes, the unindicated loss will seldom be less than 10 per cent., and it will be increased by departure from any of the above conditions to almost any extent. It will increase at an accelerating ratio as the load is diminished, so that such calculations applied to light load diagrams would be deceptive and misleading; in fact, they have but little practical value, except when made for comparison with tests of actual consumption for the purpose of determining the amount of loss under certain given conditions.