# 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.

# 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

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