### Practical Investigation Into Viscosity

Aim: To investigate the rate of descent of an object falling through a liquid due to gravity and the factors which affect the viscosity of the liquid.

Theory: Viscosity is the resistance a material has to change in form. This property can be thought of as an internal friction. Something which is very important when investigating viscosity is laminar flow. If a fluid or gas is flowing over a surface, the molecules next to the surface (the ones clinging to the walls) have zero speed. As we get farther away from the surface the speed increases. This difference in speed is a friction in the fluid or gas. It is the friction of molecules being pushed past each other. You can imagine that the amount of clinging-ness between the molecules will be proportional to the friction. This amount of clinging-ness is called viscosity. Thus, viscosity determines the amount of friction, which in turn determines the amount of energy absorbed by the flow.

Viscosity can be determined in the following way: Work is force times distance and it takes energy to do work whilst power is the energy times time. Imagine a school laboratory filled knee deep with oil. On top of the oil is a large plate of metal that we want to slide across the surface to the other side of the room. If you think about the cube of oil under the metal plate resisting the motion we can determine a unit for viscosity:

- Friction is a force (in Newtons) acting along the direction of travel times the distance (in meters) so it is a Nm.
- This frictional force obviously scales with the surface area (in m2) of the top of the cube, which brings us to Nm/m2.
- We move the plate a distance (in meters) so now we have Nm/m3 of work.
- Multiplying by time (in Seconds) to get to power, we end up with Nms/m3 which simplifies to Ns/m2. This is viscosity; a unit of power per unit of area.

The SI unit for viscosity is called a Poiseuille and abbreviated to Pl. However this is not widely used and an older version is. This is cgs, which is a shorter version of the above formula expressed in dyne-seconds per cm2 which, is called a Poise. However this is becoming less widely used and now a centa-Poise or one hundreth of a Poise is used because water has a viscosity of 1.002cP which is very close to 1.

Jean Louis Poiseuille (1799 - 1869)

While the viscosity of solids and liquids falls with temperature, the viscosity of a gas increases. While counter intuitive, the rise in gas viscosity as a function temperature can be understood. As a gas gets higher in temperature it has more collisions, and thus, more friction with its neighboring molecules.

Another surprise is that pressure has very little effect on viscosity. Viscosity’s virtual independence from pressure means that water flowing in a pipe has an insignificant change in friction whether at 60 psi or 20,000 psi!

This independence even applies to gases. Until the pressure is less than 3% of normal air pressure the change is negligible on falling bodies.

The Poiseuille and the Poise are units of dynamic viscosity sometimes called absolute viscosity.

1 Poiseuille (Pl) = 10 poise (P) = 1000 cP

P = 0.1Pl

1 centi-Poise (cP) = .01 poise

## Viscosity and Density

The Poise is not related to density. To come up with a unit incorporating density we look at the Poiseuille divided by density. Remember that a Poiseuille is a Newton-second per square meter or ns/m2. Remembering that a Newton is a Kilogram - meter per second squared or kg m/s2

we can re write the Poise unit as kg m s/m2s2 which simplifies to kg/ms. Corresponding units for density would be the Kilogram per cubic meter or kg/m3 so dividing a Poise Unit by density gives us

kg m3/kg m s which simplifies to m2/s. The common kinematic viscosity unit is the Stokes, abbreviated St. Instead of being in SI units, the stoke is in cgm units of cm2/s and one ten-thousandths the size.