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Prove that in similar conditions a cylindrical container will withstand a pressure half as great. |
Answer» Solution :Imagine a small area along a generatrix to be cut out of the cylindrical surface (Fig.). Four elastic FORCES are seen to act on the area. Two of them are parallel to the generatrix, their normal components are zero and so they offer no resistance to the gas pressure and should not be taken into account. The remaining two are PERPENDICULAR to the GENERATRICES, the sum of their normal components is the normal force `T_n = 2 sigma ld sin alpha`. The force of pressure is `F = pS = 2pal - 2plR sin alpha` .  It follows from the balance of the forces that `p = sigma d//R`which was to be proved. |
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