"The area of a [circular] diametrical section, S, of a thin spherical shell is very nearly given by formula:S = 2 \pi rtwhen t represents the thickness, and r = the inner radius of the shell, and t is supposed to be very small compared with r. The whole force, F, to be resisted by the tenacity of section S is equal to the excess of the internal fluid pressure per unit of area over the external pressure, into the area of the plane passing through this section, orF = \pi r^2 pAssuming that every portion of section S is equally strained by F, and designating by k the coefficient of the ultimate tenacity of the material of which the shell is composed, the bursting pressure will be found from the equation: \pi r^2 p = 2 \pi rtk; hencep = \frac{2tk}{r} { I.}and the proper ratio of the thickness to the radius of a thin hollow sphere is given by the formula:\frac{t}{r} = \frac{p}{2k}..."
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