Below is a diagram of the experiment I am going to carry out.

- I will set up the apparatus as shown in the diagram above. Using the G clamp I will attach the clamp stand to the table and make sure that it is in level and stable. Then I will clamp the cylinder on the clamp stand and ensure that it doesn’t slip out.

- I will carefully fill the cylinder with liquid so that its not poured out on the floor or on me. The cylinder can be emptied by opening a tap at the bottom of the cylinder. I will position the container just below the cylinder so that it can be used to carry the liquid of the cylinders.

- I will position a ruler by the side of the cylinder and use tape to mark equal distances on the cylinder. Since in some of the liquids I have chosen the ball bearing may move relatively fast, I will need to mark slightly larger distances in order to get more accurate time readings.

For Oil the markings on the cylinder are going to be chosen 40cm apart starting from the surface of the liquid inside the cylinder.

For Washing liquid the markings on the cylinder are going to be chosen 20cm apart starting from the surface of the liquid inside the cylinder.

For Honey the markings on the cylinder are going to be chosen 20cm apart starting from the surface of the liquid inside the cylinder.

- This experiment is to be carried out by four people including me. One of us will drop the ball bearing in the liquid, the other three will each hold a stop watch and observe the ball bearing motion and measure the time difference between the times at which the ball bearing is at the marked positions. To make sure that all time measurements start at the same time the person who drops the ball bearing in the cylinder counts up to three just before releasing it.

- After all measurements are taken for the first liquid (Honey), the cylinder has to be emptied by opening the tap at the bottom and ensuring that a big enough container is placed below.

- After emptying the cylinder, I will remove it and change with another one. This is done to avoid a possible mixture of the liquids, which can affect the viscosity of the liquid under investigation (e.g. mixing Honey with Oil could change the viscosity of Oil).

- For each liquid being considered I will repeat the measurements 3 times.

To compare viscosities I will try to measure the coefficient of viscosity for each liquid. In order to do that I need to select a ball bearing such that it reaches terminal velocity after travelling a short distance. It is important that I reach terminal velocity since at that point the forces acting on the ball bearing are in equilibrium. When terminal velocity is reached the ball bearing continues its movements in constant speed. At terminal speed the ball bearing has zero acceleration, therefore the resultant force will be zero. Having the forces in equilibrium is an important fact since I can use the equation below to calculate the viscous drag.

upthrust + viscous drag = weight of ball bearing

In the formula above upthrust is the force that acts on the immersed ball bearing due to the displacement of the fluid around it and its equal to the weight of the fluid that has been displaced by the ball bearing.

upthrust = (mass of displaced liquid) x g

= (volume) x (density of liquid) x g

= (4 π r3)/3 x p g

The radius of the sphere can be measured and the density of the liquids can be looked up from a density table and then calculate the upthrust force.

I can also measure the mass of the ball bearing and then calculate its weight using the formula

weight = mg

Knowing the weight and the upthrust I can find the value of viscous drag force at terminal speed.

The viscous drag is the resistant frictional force, which acts on moving bodies inside the liquid. The viscous drag depends on the speed of the body moving inside a liquid on the geometrical shape of the body and on the type of the liquid. The formula for viscous drag of a moving sphere in the liquid is given below

F = 6 π ŋ r v

Knowing the value of viscous drag at terminal speed and the value of terminal speed I can then calculate the value of the coefficient of viscosity.

ŋ = F / (6 π r v)

Using same technique I can find the coefficient of viscosity in all three liquids under my consideration. Higher coefficient of viscosity would mean higher viscous drag or in other words higher viscosity.

## Results

To find the terminal speed I decided to mark the cylinders in equal distances and then measure the time the ball bearing took to travel through each of these equal distances. To ensure that correct times were read I decided that three of us take readings at the same time, and then took the average time out of these.

Honey

Washing Liquid

Note: The reading painted in red seems to stand out from the other readings

therefore it makes me believe its a wrong reading.

Oil

Since the speed of the ball bearing in oil was comparatively fast I decided that we mark the cylinder into 40 cm distances. I did this to enable more accurate time readings.

The mass of the ball bearing is 16.09 gram. Its weight is calculated below.

weight = 16.09 * 10-3 * 9.8 = 157.68 * 10-3

The radius of the ball bearing is 0.5cm.

Honey

Terminal speed = Distance/Time

To calculate the terminal speed I will use the average of the times that are very close at the end of the table. For Honey I noticed two values of times close together (see table of results for honey above).

Average Time = (56+55)/2 = 55.5

Terminal speed = 0.2/55.5 = 0.0036 ms-1

The density of Honey is p = 1420 kgm-3

upthrust=4/3 π r3 p g = 4/3 π 0.0053 x 1420 x 9.8=0.022 N

At terminal speed:

upthrust + viscous drag = weight

viscous drag = weight – upthrust

viscous drag = F = 157.68 * 10-3 - 0.022 = 0.13568 N

ŋ = F / (6 π r v)

= 0.13568 /(6 π x 0.005 x 0.0036)

= 399.9 Nsm-2

Washing Liquid

Terminal speed = Distance/Time

To calculate the terminal speed I will use the average of the times that are very close at the end of the table. For Washing Liquid I noticed three values of times close together (see table of results for Washing Liquid above).

Average Time = (1.54+1.56+1.56)/3 = 1.553

Terminal speed = 0.2/1.553 = 0.13 ms-1

The Density of Washing liquid =1120 kgm-3

upthrust=4/3 π r3 p g =4/3 π 0.0053 x1120x9.8 =0.017 N

At terminal speed:

upthrust + viscous drag = weight

viscous drag = weight – upthrust

viscous drag = F = 157.68 * 10-3 - 0.017 = 0.14068 N

ŋ = F / (6 π r v)

= 0.14068/(6 π x 0.005 x 0.13)

= 11.5 Nsm-2

Oil

Terminal speed = Distance/Time

To calculate the terminal speed I will use the average of the times that are very close at the end of the table. For Oil I noticed two values of times close together (see table of results for Oil above).

Average Time = (0.40+0.41)/2 = 0.405

Terminal speed = 0.2/0.405 = 0.49 ms-1

The density of Oil is p = 894 kgm-3

upthrust=4/3 π r3 p g =4/3 π 0.0053 x 894 x 9.8=0.014 N

At terminal speed:

upthrust + viscous drag = weight

viscous drag = weight – upthrust

viscous drag = F = 157.68 * 10-3 - 0.014 = 0.14368 N

ŋ = F / (6 π r v)

= 0.14368 /(6 π x 0.005 x 0.49)

= 3.11

## Conclusion

The table below shows coefficients of viscosity of the three liquids used in the experiment:

As shown in the table above honey has the highest viscosity, it is in fact approximately 100 times more viscous than oil and about 40 times more viscous than washing liquid.

The table below shows the upthrust force acting on the ball bearing when immersed in each of the liquids

The upthrust force is higher in honey, this is predictable since the density of honey is greater.

The table below shows the terminal speed values for the three liquids.

Terminal speed in honey is slower this is because the upthrust and viscous drag in honey are greater than the other two liquids.

## Evaluation

There were a few wayward results. This could have been because human error on the time reading. Also I noticed that the honey was not pure, some little solid pieces seemed to float in it. These could have slowed the ball bearing and therefore a higher value of viscosity.

Also I am not very sure whether the ball bearing really reached terminal velocity, as the cylinders probably were not long enough for the ball bearing to reach terminal velocity. If I used longer cylinders I would have been able to mark more distances on the cylinders and make more time readings, until I was sure enough that the ball was really moving with constant speed.

In the absence of longer cylinders one way to improve the experiment would have been to give the ball bearing a high enough initial speed which would let the ball bearing to reach terminal speed quicker.

Comparing Viscosities Page of