Thermodynamics
posted by Jack .
Determine the units of viscosity,m, in the following equation:
t=m(du/dy), where t is a shear stress, u a velocity, and y is a distance in (a) the Engineering English system, and (b) the SI system.

stress is force/area = kgm/s^2m^2 = kg/ms^2
I'll use v distinguish viscosity from mass
kg/ms^2 = v * (m/s / m) = v/s
v = kg/ms or kilograms per metersecond
this can be verified at wikipedia under the viscosity article.
looks like t = kg * (m/s / s) = kg m/s^2 = Newtons 
Steve is correct.
In my generation, viscosity was usually quoted in Handbooks in units of g/(cm*s), called the poise, or 1% of that, called the centipoise.
English units of viscosity were seldom used. I seem to recall some English units called Saybolt slugs. I have never heard a better argument for the metric system. 
This may help:
http://www.hydramotion.com/pdf/Website_Viscosity_Units_V2.pdf 
A sensible unit of viscosity in the English engineering system would be slugs per footsecond.
See
http://www.convertworld.com/en/dynamicviscosity/Slug+per+foot+second.html
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