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The significance of the parameter
, appearing in the previous expression for the stress tensor, can be seen from the form taken by the relation (1.25) in the
special case of simple shearing motion. With
as the only nonzero
velocity derivative, all of the components of
are zero apart from the
shear stresses

(1.27) 
Thus,
is the constant of proportionality between the rate of shear and the tangential
force per unit area when parallel plane layers of fluid slide over one another. This constant of proportionality is generally
referred to as viscosity. It is a matter of experience that the force acting between layers
of fluid undergoing relative sliding motion always tends to oppose
the motion, which implies that
.
The viscosities of dry air and pure water at
and atmospheric pressure are about
and
, respectively. In neither case does the viscosity exhibit
much variation with pressure. However, the viscosity of air increases by about
percent, and
that of water decreases by about 3 percent, per degree Centigrade
rise in temperature (Batchelor 2000).
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Richard Fitzpatrick
20160331