Viscosity is the measure of a material’s resistance to motion under an applied force. There are several formulas and equations for viscosity calculation. If youwant a simple science experiment, measure the speed of a metal ball dropped in a container of liquid. The velocity of the ball, combined with the relative densities of the ball and the liquid, can be used to calculate the viscosity of liquids.

## TRY THIS OUT

### Calculating the Density of the Ball

- Measure the mass of your ball, using your balance. For instance, suppose the mass of the ball is 0.1 kilograms (kg).
- Find the radius of the ball by first measuring the diameter (distance of a straight line through the ball at the widest part). Divide the diameter by 2; this gives the radius of your ball.
- Calculate the volume of the ball by plugging the radius 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 (0.01 m) ^3 = 0.00000419 m^3
- Calculate the density of the ball by dividing its mass by its volume. The density of the ball in the example would be: Density = 0.1 kg ÷ 0.00000419 m^3 = 23,866 kg/m^3

### Calculating the Density of the Liquid

- 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 0.2 kg, and with fluid its mass was 0.45 kg.
- 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 = 0.45 kg – 0.2 kg = 0.25 kg
- Determine the density of the fluid by dividing its mass by its volume. Example: Density of fluid = 0.25 kg ÷ 100 mL = 0.0025 kg/mL = 0.0025 kg/cm^3 = 2,500 kg/m^3*
- 1 mL is equal to 1 cm^3 *1 million cubic centimeters equal 1 cubic meter

### Measuring the Viscosity of Liquid

- Fill your tall graduated cylinder with the liquid to be tested so it is about 2 cm from the top of the cylinder. Use your marker to make a mark 2 cm below the surface of the liquid. Mark another line 2 cm from the bottom of the cylinder.
- Measure the distance between the two marks on the graduated cylinder. Suppose that the distance is 0.3 m.
- Let the ball 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 to fall the distance.
- Calculate the velocity of the falling ball by dividing the distance it fell by the time it took. In the example: Velocity = 0.3 m ÷ 6 s = 0.05 m/s

Calculate the viscosity of 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 = 9.8 m/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

### Viscosity Calculation Formula:

viscosity = shear stress / shear rate

*The result is typically expressed in centipoise (cP), which is the equivalent of 1 mPa s (millipascal second).*

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