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 \eta 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

  1. From Viscosity. NEXUS/Physics - Physics for Life Science Students. Wikibook: https://www.compadre.org/nexusph/course/Viscosity. (Accessed 2 February 2023).


Icon for the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License

Physics 131: What Is Physics? by E.F. Redish and 2-Minute Classroom is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

Share This Book