# How to calculate viscosity

Written by timothy banas
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Liquid viscosity is a measure of the internal friction of a liquid. Liquids with high viscosities flow slowly, whereas low viscosity liquids flow quickly. Lava has a relatively high viscosity; water has a relatively low one. You can measure the viscosity of a liquid by measuring the velocity of a sphere as it falls through the liquid. The velocity of the sphere, combined with the relative densities of the sphere and the liquid, can be used to calculate the viscosity of the liquid.

Skill level:
Moderately Easy

### Things you need

• Balance
• Meter stick
• Small metal ball bearing
• Marker
• Stopwatch

## Calculating the Density of the Ball Bearing

1. 1

Measure the mass of your ball bearing, using your balance. For instance, suppose the mass of the ball bearing is 0.1 kilograms (kg).

2. 2

Calculate the volume of the ball bearing by measuring its radius and plugging the value into the equation for the volume of a sphere. Suppose the ball bearing has a radius of 0.01 meter (m). The volume would be:

Volume = 4/3 x pi x (0.01m) ^3 = 0.00000419m^3

3. 3

Calculate the density of the ball bearing by dividing its mass by its volume. The density of the ball bearing in the example would be:

Density = 0.1kg / 0.00000419m^3 = 23,866kg/m^3

## Calculating the Density of the Liquid

1. 1

Measure the mass of your graduated cylinder when it is empty. Then measure the mass of your graduated cylinder with 100 millilters (ml) of liquid in it. Suppose the empty cylinder had a mass of 0.2kg, and with fluid its mass was 0.45kg.

2. 2

Determine the mass of the fluid by subtracting the mass of the empty cylinder from the mass of the cylinder with the fluid. In the example:

Mass of liquid = 0.45kg - 0.2kg = 0.25kg

3. 3

Determine the density of the fluid by dividing its mass by its volume. Example:

Density of fluid = 0.25kg / 100 mL = 0.0025kg/mL = 0.0025kg/cm^3 = 2,500kg/m^3*

1ml is equal to 1cm^3 *There are 1,000,000 cubic centimetres in 1 cubic meter

## Measuring the Viscosity of the Liquid

1. 1

Fill your tall graduated cylinder with the liquid so that the liquid is about 2cm from the top of the cylinder. Use your marker to make a mark 2cm below the surface of the liquid. Make another mark 2cm from the bottom of the cylinder.

2. 2

Measure the distance between the two marks on the graduated cylinder. Suppose that the distance is 0.3m.

3. 3

Let the ball bearing go on the surface of the liquid and use your stopwatch to time how long it takes for the ball to fall from the first mark to the second mark. Suppose it took the ball 6 seconds (s) to fall the distance.

4. 4

Calculate the velocity of the falling ball by dividing the distance it fell by the time it took. In the example:

Velocity = 0.3m / 6 s = 0.05m/s

5. 5

Write the equation for calculating the viscosity of the liquid from the data you have collected:

Viscosity = (2 x (ball density - liquid density) x g x a^2) / (9 x v), where

g = acceleration due to gravity = 9.8m/s^2 a = radius of ball bearing v = velocity of ball bearing through liquid

Plug your measurements into the equation to calculate the viscosity of the liquid. For the example, the calculation would look like this:

Viscosity = (2 x (23,866 - 2,500) x 9.8 x 0.01^2) / (9 x 0.05) = 93.1 Pascal seconds

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