A tank of glycerine at rest has density

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

Bending, Ringing, Breaking and Flowing, Ch Strain and stress in a deformed solid

Problem

A tank of glycerine at rest has density ρ=1260 kg m−3\rho = 1260\,\mathrm{kg\,m^{-3}}. Consider a point at depth d=4 md = 4\,\mathrm{m} below the free surface, taking atmospheric pressure as zero (gauge). ((a)) Using the hydrostatic pressure law p=ρgdp = \rho g d, held from the first fluids course as the solution of the equilibrium equation for a fluid at rest, find the pressure at this depth (g=9.8 m s−2g = 9.8\,\mathrm{m\,s^{-2}}). ((b)) At this point the stress state is σij=−p δij\sigma_{ij} = -p\,\delta_{ij}. Construct Mohr's circle for any pair of perpendicular directions in a vertical plane through the point (state its centre and radius), and use it to give the normal stress and shear stress on a surface tilted at an arbitrary angle θ\theta to the horizontal. State what this implies about slip surfaces (planes carrying nonzero shear) at this point, however deep the tank is made.

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