The units of viscosity.

There is a group of liquids and gases for which the viscosity is independent of velocity gradient and, for practical purposes, dependent only on temperature. The group includes most of the common mobile liquids and most of the common gases, which from the point of view of engineers, is very convenient. Liquids and gases in this group are called Newtonian fluids. By implication there are non-Newtonian substances typified by milk, paint, toothpaste and egg white.

 

Viscosity has units and these can be deduced from Newton's original definition in any given system of units. Unfortunately for engineers, systems of units have cycles of acceptability like fashion and as a result useful data is stored in at least three consistent systems and in many inconsistent systems as well.

 

If we start with the current fashion for S.I. we can put each term in kilograms, metres and seconds :-

 

 can be rearranged to give  which, when written in basic units, gives m the units of

                                                   .

which rearranges to give m the units of  in the S.I system. It can also be expressed in . Neither unit has a name.

 

In the c.g.s. system the units are gram/cm.sec and 1 gram/cm.sec is called a poise and frequently viscosities are quoted in centipoise to give easily remembered numbers like 1 centipoise as the viscosity of water. The two Imperial systems give units of pound/foot.sec and slug/foot.sec neither of which have names.