41 Viscous Force
E.F. Redish and 2-Minute Classroom
Viscous Forces[1]
E.F. Redish
When an object moves in a fluid — a liquid or gas — it drags bits of the fluid with it along its surface. This results in a layer of fluid sliding over a neighboring layer of fluid. The interactions of the molecules in the fluid result in a kind of internal friction that acts to slow the relative motion of neighboring layers of fluid. This internal friction is summarized in the viscosity of the fluid.
What is Viscosity η?
2-Minute Classroom
The Units and Some Values of Viscosity
E.F. Redish
Viscosity has dimensions of Mass/(Length*Time). It will, therefore, have units (in the SI system) of kg/m⋅s. Sometimes it’s convenient to express this unit in different forms.
For example, since we will typically be building a force with it, we might want to rearrange this so it looks like Newtons: 1 N = 1 kg⋅m/s2. So we can make the units of viscosity include a Newton by multiplying by m2⋅s and dividing by the same factor. Looking at the dimensions of 
and pulling out a force (Mass*Length/(Time2), the result is
[η] = Mass/(Length*Time) = (Mass*Length/Time2) (Time/Length2).
So the units of viscosity will be
[η] = Newtons * seconds / meters2.
The unit “Newton/meter2” is a unit of pressure called a Pascal. So the units you will see for viscosity are typically “Pascal-seconds (Pa⋅s)”.
The measured viscosities for air and water at standard temperature and pressures are:
| Material | η [Pa⋅s] |
| Air | 1.81 x 10-5 |
| Fresh water | 1.00 x 10-3 |
| Sea water | 1.07 x 10-3 |
- From Viscosity. NEXUS/Physics - Physics for Life Science Students. Wikibook: https://www.compadre.org/nexusph/course/Viscosity. (Accessed 2 February 2023). ↵
