A layer of light oil of dynamic viscosity Pa s is sheared so that the velocity field…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

Fluids and Continuum Physics, Ch The Navier-Stokes equations and exact viscous solutions

Problem

A layer of light oil of dynamic viscosity μ=0.12\mu = 0.12 Pa s is sheared so that the velocity field is the simple shear u=(Sy,  0,  0),S=250 s−1,\mathbf{u} = (Sy,\;0,\;0), \qquad S = 250\ \mathrm{s^{-1}}, with xx along the flow and yy across it. The oil is treated as an incompressible Newtonian fluid. ((a)) Find the rate-of-strain component exye_{xy}. ((b)) Find the viscous shear stress τxy\tau_{xy}. ((c)) Find the viscous normal stress τyy\tau_{yy}.

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