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What internal pressure (in the absence of an external presure) can be sustained (a) by a glass tube, (b) by a glass spherical flask, if in both cases the wall thickness is equal to Deltar=1.0mm and the radius of the tube and the flask equals r=25mm? |
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Answer» Solution :(a) Consider a transverse section of the tube and concentrate on an element which subtends and angle `Deltavarphi` at the centre. The forces acting on a portion of length `Deltal` on the element are (1) tensile forces side ways of magnitude `sigmaDeltarDeltal`. The resultant of these is `2sigmaDeltarDeltalsin(Deltavarphi)/(2)~~sigmaDeltarDeltalDeltavarphi` radially towards the centre. (2) The force due to fluid PRESSURE `=prDeltavarphiDeltal` Since these balance, we get `p_(max)~~sigma_m(Deltar)/(r)` where `sigma_m` is the maximum tensile force. Putting the values we get `p_(max)=19*7` atoms. (b) Consider an element of area `dS=pi(rDeltatheta//2)^2` about z-axis chosen arbitrarily. There are tangential tensile forces all around the ring of the cap. Their resultant is `sigma[2pi(r(DELTATHETA)/(2))Deltar]SI n(Deltatheta)/(2)` Hence in the limit `p_mpi((rDeltatheta)/(2))^2=sigma_mpi((rDeltatheta)/(2))DeltarDeltatheta` or `p_m=(2sigma_mDeltar)/(r)=39*5` atoms.  
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