A popular claim about mediaeval cathedral windows is that the panes have grown…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Non-Newtonian and viscoelastic fluids

Problem

A popular claim about mediaeval cathedral windows is that the panes have grown visibly thicker at the bottom because the glass has slowly flowed downhill under gravity over the centuries. Extrapolations of the viscosity of soda-lime window glass down to room temperature vary enormously between sources; take η∼1041 Pa s\eta \sim 10^{41}\,\mathrm{Pa\,s} as a representative value. Take the shear modulus of glass as G=30 GPaG = 30\,\mathrm{GPa}. ((a)) Estimate the Maxwell relaxation time τM=η/G\tau_M = \eta/G of glass at room temperature. ((b)) Estimate the Deborah number for an observation time of one century (1 century≈3.15×109 s1\,\mathrm{century} \approx 3.15\times 10^9\,\mathrm{s}). ((c)) State, in one sentence, what this Deborah number implies about the folklore explanation of thick-bottomed old window panes.

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