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 621⁄2 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.
Fig. 3375.
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.