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 = kg-m/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 meter-second
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 foot-second.
See
http://www.convertworld.com/en/dynamic-viscosity/Slug+per+foot+second.html
To determine the units of viscosity, m, in the given equation:
(a) In the Engineering English system:
The units of shear stress, t, are in pounds per square foot (lb/ft²).
The units of velocity, du/dy, are in feet per second (ft/s).
So, to maintain the equation's balance, the units of viscosity, m, must be such that the product m(du/dy) has the same units as shear stress.
Dividing the units of shear stress (lb/ft²) by the units of velocity (ft/s) gives us:
m = (lb/ft²) / (ft/s)
Simplifying the units, we can cancel out the common unit of "ft":
m = lb / (ft * s)
Therefore, the units of viscosity, m, in the Engineering English system are expressed as pounds per foot-second (lb/(ft·s)).
(b) In the SI system:
The units of shear stress, t, are in newtons per square meter (N/m²) or pascals (Pa).
The units of velocity, du/dy, are in meters per second (m/s).
Similarly, to maintain the equation's balance, the units of viscosity, m, must be such that the product m(du/dy) has the same units as shear stress.
Dividing the units of shear stress (Pa) by the units of velocity (m/s) gives us:
m = (Pa) / (m/s)
Simplifying the units, we can cancel out the common unit of "m":
m = Pa / s
Therefore, the units of viscosity, m, in the SI system are expressed as pascal-seconds (Pa·s).