FOR DETERMINING AREAS AND CALCULATING THE CONTENTS OF STEAM AND WATER
SPACES IN THE STEAM BOILER.
In order to ascertain the number of braces, which are necessary to
strengthen that part of the boiler head, which is not stayed by the
tubes, it is first necessary to know its area; the part to be stayed is
_a segment of a circle_.
_The length of the segment_ is measured above the top row of the tubes,
and its _height or width_ is equal to the distance from the top of the
tubes to the top of the boiler shell.
Since, however, part of this segment is braced by the boiler shell,
and also by the top row of the tubes, it has been generally agreed
that the length of the segment should be measured two inches above the
tubes, and the height or width, should be measured from a line, drawn
two inches above the tubes, to a point within three inches from the top
of the boiler shell, as shown in the illustration by the dotted line.
Thus, referring to Fig. D, the length of the segment is equal to l, and
the height is equal to h.
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.
[Illustration: 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._
2. _Divide this by 144, and multiply the quotient by the length of the
boiler in feet._
To find the volume of the waterspace in cubic feet.