PROPORTIONS OP BOILERS.

267

very easily proportioned to the steam they have to bear by theformuke which will be given below. Certain restrictions areplaced upon the proportions of boilers by the nature of theriveted joints. That these may be steam and water tight underpressure, and at the same time not unnecessarily weakened byrivets, it has been found best to use plates of about -fa or inchthick, and plates of other dimensions are very seldom employedin,,the construction of boilers. Thick plates are inefficientlyriveted, thin ones inefficiently caulked, and this restricts theavailable thickness for the plates within nearly the limits whichhave been stated. It is necessary, therefore, in proportioningboilers, having given the working pressure, to choose the dia-meter which is suitable for such a thickness of plates, lesseningthe diameter for high-pressure boilers and increasing it for low-pressure ones. Length does not affect the strength in vesselssubject to internal pressure, and hence the diameter is the vari-able quantity over which we have most control in proportion-ing the external shell. But the flues, as will be shown, decreasein strength with their length, and this dimension is in that casemore easily modified than the diameter.

The general equation expressing the resistance of thin hollowvessels to internal strain is, for spherical vessels,

(nearly) ... (2)

and for cylindrical vessels, bursting longitudinally,

This equation gives the bursting pressure in lbs. per squareinch, when the thickness of the plates c in inches, the tenacityof the joints t in lbs. per square inch, and the diameter d ininches, are given.

Thus, for a boiler 7 feet or 84 inches diameter, inch or•375 inch thick, and with joints having a tenacity of 34,000 lbs.per square inch, the bursting pressure

2 x 34000 x -37584

303£ lbs.

= r

The value of t for various materials is given in the followingtable:—