A film of glycerine of uniform thickness fills the gap between two large flat…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Fluid statics and the continuum picture · Viscous flow and dynamical similarity

Fluids and Continuum Physics, Ch The continuum hypothesis, pressure and the stress tensor

Problem

A film of glycerine of uniform thickness

1.5\ \mathrm{mm}

fills the gap between two large flat parallel horizontal plates. The lower plate is fixed. A uniform tangential (shear) stress of

0.014\ \mathrm{Pa}

is applied to the upper plate and held constant. Glycerine is Newtonian with dynamic viscosity

\mu = 1.4\ \mathrm{Pa\,s}

; the plates are large enough that edge effects are ignored, the velocity across the gap varies linearly, and the inertia of the plate is neglected so that the steady sliding speed is reached immediately. ((a)) Predict the steady speed of the upper plate. ((b)) Predict how far the upper plate has moved after

10\ \mathrm{min}

of sustained stress. ((c)) Predict how far it has moved after

1.0\ \mathrm{h}

, and say what this tells you about whether glycerine is a solid or a fluid.

Browse the problem library