# Viscosity of Fluids

Jo Falconer                April 2002

Viscosity of Fluids

## Background Theory

Viscosity is the resistance of a fluid to flow.  This resistance can be to a solid trying to pass through a liquid or against the liquid itself whilst trying to move past stationary objects.  Viscosity can also act on fluids of differing viscosities between one another.

All fluids, exhibit viscosity to some degree. Viscosity may be thought of as fluid friction, just as the friction between two solids resists the motion of one over the other, it is also possible to cause an acceleration of one fluid relative to the other.  Viscosity resists the motion of a solid through a fluid but also makes it possible for a propeller or other device to accelerate the solid through the fluid.

George Gabriel Stokes developed a way to measure the viscosity of fluids by studying the force exerted on a spherical object moving through a fluid.  This force is known as the viscous drag.  This force, in relationship to the terminal velocity of the sphere, gives the coefficient of viscosity (viscosity) of the fluid using stokes law:

## F = 6 π r η v

Where:

F is the overall force

r is the radius of the sphere

η is the viscosity of the fluid

v is the terminal velocity of the sphere

The viscosity is calculated by rearranging the above equation to:

η =              F

6 π r v

Along with the viscous drag, another force is acting in the fluid.  This is known as the UPTHRUST.  It affects an object in liquid due to the object displacing some of the liquid.  The weight of the object should cause it to sink but if the upthrust of the liquid is equal to or higher than the force of the weight, the object will sit either partially immersed or float completely in the fluid.

An object, when dropped into a liquid, will first accelerate due to the downward force of its weight, then as the viscous drag force increases due to the increase in the objects speed the downward force will decrease and the acceleration will stop.  This is the objects terminal velocity and it will continue at this velocity unless another force acts upon the object i.e. the upward force of the bottom of the container.

## What effects viscosity?

Temperature:

As temperature increases the viscosity of a fluid decreases (gets runnier or easier for an object to pass through the liquid).

Density:

The denser the fluid the more viscous it will be.

Concentration:

If water were to be added, the fluid would become closer to the viscosity of water.

Friction:

This is caused by the surface properties of the object passing through the fluid.

Gravity:

Although gravity on Earth is 9.8ms-2 if the experiment were to be carried out else where i.e. on the moon, the same viscosity would not be calculated.

## Investigation

I am going to investigate the effect of temperature on the viscosity of honey.  To do this I will use a falling ...