Rule. The area of a segment may be obtained, very approximately, by dividing the cube of the width (or height) by twice the length of the chord, and adding to the quotient the product of the width into two-thirds of the chord.
Example. If we suppose the height h of the segment in [Fig. D] to be equal to 18 inches, and the length l to be equal to 48 inches, we have
18³ ÷ (48 × 2) + (48 × 2⁄3 × 18) = 60.7 + 576.0 = 636.7 square inches.
Fig. C.Fig. D.
In order to calculate the contents of the steam and water spaces of a boiler, the same rule, as above, may be employed. The volume of the steam space may be readily obtained by the above rule, taking the distance from the water level to the top of the shell for the height, and the diameter of the shell, measured at the water line, for the length of the segment lines.
The area of the segment thus found, expressed in square inches, divided by 144, and multiplied by the length of the boiler in feet, is equal to the steam space, in cubic feet, this result is slightly reduced by the space occupied by the braces.
In order to find the volume of the water space, it is first necessary to find the total area of the boiler head, and this minus the area of the segment above the water line, is equal to the area of the segment below the water line. From this must also be subtracted the combined cross sectional area of the tubes.
Thus, the rule for finding the volume of the steam space in cubic feet.
1. Find the area of the segment of the boiler head, above the water line, in square inches.