SECT. VII.]
STEAM ENGINES.
•247
270 a
h — v ’
the increase which would strain the metal as far as it would hear without per
manent derangement.
519. Here we suppose the heat to be confined to a single point; but generally,
or rather in all cases, a considerable portion of surface is directly affected by the
heat: in this case a near approximation will be to double the effect of expansion,
or make,
A = 135 a
t
In the case of pipes and cylinders, the greatest difference of temperature will
never exceed 300°; and then,
the force of cohesion the cylinder loses by unequal expansion =
30° t _ 2-2 t
135 a — a
If this be added to the former, we derive,
2 - 54 a p 2’2 t
15000
+
or t =
a p
6000
The effect of irregular expansion is sensible only in small cylinders : in the case
of a cylinder of 60 inches diameter we found its thickness ‘305 inches, and it became
only '315 when corrected for expansion.
For pipes of less than 5 inches diameter,
a p
1 = 6000 (1 - 0-116 a)
For working cylinders both wear and other causes of pressure exist ; the latter
will require at least that the thickness should be double, and for wear half an inch
may be added, as about the proper quantity of allowance.
520. Rule. For the thickness of a working cylinder. Multiply four times
the elastic force of the steam in lbs. per circular inch by the diameter in inches,
and divide by 6000. The result multiplied by the quotient arising from dividing
the diameter by the diameter less 2*2, is the thickness for strength, to which half
an inch may be added for wear.
Example 1. A cylinder 24 inches in diameter is to be made of cast iron, for
steam not exceeding 3J lbs. per circular inch on the safety valve, or 11*5 + 3 - 5 = 15
elastice force, required its thickness.
We have 15 gQQQ* 24 = '24 ; and 24~~2 : 2 x *24 = *264 ;
which, added to half an inch, is *764 inches, the thickness required.
Example 2. A cast iron cylinder for a high pressure engine being 9 inches
in diameter, and for steam 50 lbs. per circular inch elastic force, required the
thickness.
