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# viscosity of golden syrup

Extracts from this document...

Introduction

An Investigation to Measure the Viscosity of Golden Syrup.

Aim: - the aim of my investigation is to measure the viscosity of golden syrup and see if this value depends upon the temperature of the syrup.

Apparatus not included in diagram: - micrometer, 5 ball bearings as provided by the school, stop clock, magnet, marker pen, metre rule, weighing scales, thermometer, water bath. (The measuring cylinder is 50 cm3)

Certain aspects have to be taken into account to ensure that the experiment is carried out safely. These are: -

• If heating the syrup, be careful not to burn yourself on hot equipment.
• Goggles should be worn to prevent syrup from entering the eye.

Variables that need to be considered are:- the size of the ball bearing to be dropped, the temperature of the syrup, the amount of syrup used, the length that the distance travelled is measured over, the depth beneath the top that the speed and distance are measured from, the type of syrup used and the density of the syrup.

I have decided to change the size of the ball bearing to see how this effects viscosity and a further study will be done changing the temperature of the syrup. The differing size ball bearings will be dropped at a constant temperature. To make this a fair test I will have to keep all other variables the same. To do this I will:-

• Keep the amount of syrup used, the type of syrup (golden) used and the measuring cylinder that it is in the same.
•  Mark the measuring cylinder so that I can measure time and distance from the same set values to the same end point.
• Leave a set distance at the top of the syrup to allow the ball bearing to accelerate to a constant speed.

To measure the viscosity of golden syrup I will need to measure the radius of the ball bearing as this can be used in the formula 4/3 Πr3   multiplying it by gravity and then the density of steel to calculate the weight of the ball bearing and calculate the downward force on the object. This came about as m=ρV and W=mg. Substituting in W= ρVg. The volume of a sphere = 4/3Πr3. Substituting in again, W=4/3Πr3ρsteelg.

r= radius of sphere (m)

ρsteel=density of steel (7.8 g/cm3)

g=gravity (9.81m/s2)

However, there is more than this acting on the ball bearing. Viscous drag is a force opposing the weight of the object and this is calculated by using Stokes’ law. F=6ΠrηV.

F=viscous drag (N)

r=radius of sphere (m)

η=coefficient of viscosity (Ns/m2)

V=velocity (m/s)

Also, in an upwards direction is upthrust. This is calculated by the amount of the material displaced. As this is spherical (the ball bearing) this can be calculated by the formula W=mg. As m=ρV and V=4/3Πr3 upthrust can be written as 4/3Πr3ρsyrupg.

Putting all of these formulas in the same equation, depending on which direction they are acting you get to the equation: -

4/3Πr3ρsteelg = 6ΠrηV + 4/3Πr3ρsyrupg

This is quite a lengthy equation and can be cancelled down to: -

4/3r2ρsteelg = 6ηV + 4/3r2ρsyrupg

This can be used to plot a graph.

To analyse my results I will plot a scatter graphs for each temperature plotting velocity against the radius squared.

This can be shown by the equation calculated earlier: -

4/3r2ρsteelg = 6ηV + 4/3r2ρsyrupg

Rearranging you get 6ηV= 4/3r2ρsteelg - 4/3r2ρsyrupg

Then put in the form y=mx + c

V = 4g/18η steel - ρsyrup) r2

Y =        m            x  +c

y=V

m= 4g/18η steel - ρsyrup)

x= r2

The gradient of the line of best fit can then be used to calculate the viscosity of syrup.

So, I will have to take measurements of the radius of the ball bearings, the density of syrup using ρ=m/V and the velocity of the ball bearing. The density of the syrup can be found by putting a set volume of syrup (50cm3) in a pre-massed measuring cylinder and then re-massing the cylinder with syrup after. The change in mass will give the mass of the syrup. The density will vary at different temperatures so will have to be measured at each temperature. These can be used to calculate the density. The density of steel is 7850 kgm-3. The velocity can be found by speed = distance/time. So I will need to measure the time it takes the ball bearing to travel 10 cm down the measuring cylinder.

I will use five ball bearings ranging from 900 x10-5 in diameter to 150 x10-5 in diameter and at 20°C and then at 30°C and 40°C. I will repeat the experiment 3 times which means my results will be more reliable.

Method

1. Arrange apparatus as shown in diagram
2. Measure the distance between the two pen lines.
3. Measure the density of the syrup using the.
4. Drop the largest 9.00 x10-5 ball bearing into the syrup.
5. When it passes the upper line start the stop clock.
6. When it passes the lower line stop the stop clock.
7. Write down the time taken for the ball bearing to drop.
8. Extract the ball bearing from the syrup using a magnet.
9. Repeat steps 4-8 for the other four ball bearings.
10. Repeat steps 4-9 twice to ensure reliable results.
11. Repeat steps 1-10 for 30°C and 40°C.

Using the measuring cylinder to measure the volume of syrup can be measured to the nearest ±2ml. To do this accurately you must be at eye level with the top of the syrup and it must be within the scale of the measuring cylinder. The mass of the syrup is measured using weighing scales that measure to ±0.005 g.  The radius of the ball bearing can be measured to the nearest ±0.00001m using a micrometer. They will all be measured twice to ensure accuracy in the measurement and the micrometer must be placed across the diameter of the sphere. The distance travelled by the ball bearing, 0.100 metres will be measured by a metre rule between two lines on the measuring cylinder. A meter rule can be sensitive to the nearest ±0.0005m. This value will be measured twice if the same and thrice if not so to ensure accuracy in the reading. The ball bearing must be allowed time to accelerate to its terminal velocity in the syrup so the distance will start 0.030 metres below the top of the syrup. The time will be measured using a stop clock which is sensitive to the nearest 0.005 seconds. However, when using a stop clock human error comes into the equation when both starting and stopping the clock. This value will be close to ±0.5 seconds if both ends of the measuring cylinder are considered. To ensure that these readings are accurate you must be at eye level with the lines on the cylinder for the time, and the distance on the meter rule. The temperature of the syrup, especially at 40ºC, will vary as when it is taken out of the water bath it immediately looses heat. The water bath is also at just above 40ºC; somewhere around 45ºC. This gives a sensitivity reading of the temperature of the syrup to ±5ºC. All of the above must be measured accurately.

The viscosity of golden syrup should be calculated as the same value for all ball bearings used at the same temperature. This is due to the weight, upthrust and viscous drag all being affected by the radius of the ball bearing, so a change in the radius will affect all three equally, thus meaning no change in viscosity. Also, at the same temperature, the atoms in the syrup will be moving at the same speed and colliding with the ball bearing. As the size of the ball bearing decreases less collisions will occur meaning more viscous drag. However, this is proportional to the weight of the object and as the weight decreases, so will the number of collisions. These values are proportional to each other so the size of the ball bearing will differ the weight and the number of collisions. These two values are proportional to each other and acting in opposite directions so will cancel each other out.

As, the syrup heats up, the number of collisions will increase which will increase viscous drag, but this is outweighed by the weakening in bond strength as the temperature increases. The syrup will become runnier and the ball bearing should pass smoother through the syrup as the density will have decreased.

Modifications

After reviewing the experiment there was numerous modifications that I had to make from my original plan. These are: -

• The syrup had to be put back into the heated water in between dropping each separate ball bearing to ensure that the temperature was what it should be for each run.
• The distance allowed for the ball bearing to accelerate had to be shortened to accommodate for the shorter than anticipated length of the test tube from 0.03 meters to 0.025 meters.
• The distance timed to calculate the velocity of the ball bearing had to be shortened to accommodate for the shorter than anticipated length of the test tube from 0.10 meters to 0.07 meters.
• A 30 centimetre ruler was used to measure where to mark the distance timed on the cylinder rather than a meter ruler as it was easier to measure with the smaller ruler. This was due to the ruler being harder to hold due to its long length.
• The distance travelled had to be remarked after it had been in the water bath as the water washed the pen off.

Middle

98.075

92.685

Max mass of measuring cylinder (x10-3kg)

21.345

19.585

20.905

Min mass of measuring cylinder(x10-3kg)

21.335

19.575

20.895

Max mass of syrup

(x10-3kg)

77.01

78.51

71.80

Min mass of syrup(x10-3kg)

76.99

78.49

71.78

Max Density (ρ) (kgm-3)

1546.4

1576.5

1441.8

Min Density (ρ) (kgm-3)

1533.7

1563.5

1429.9

Sensitivity (kgm-3)

± 6.4

±7.5

± 6.0

At room temperature

 Ball bearing Distance (m) ±0.0005m Time 1 (s)±0.5s Time 2 (s) ±0.5s Time 3 (s) ±0.5s Average time (s) Velocity (x10-4m/s) 1 0.045 17.0 16.4 N/A 16.7±0.3 27.0±0.8 2 0.045 24.0 23.9 N/A 23.9±0.1 18.8±0.3 3 0.045 65.8 57.8 N/A 61.8±4.0 7.3±0.6 4 0.045 161.2 138.1 N/A 149.7±11.6 3.0±0.3 5 0.045 295.2 248.9 N/A 272.0± 23.2 1.7±0.2
 Ball Bearing Max Distance (m) Min Distance (m) Max Average time (s) Min Average time (s) Max Velocity (x10-4m/s) Min Velocity (x10-4m/s) Sensitivity(x10-4m/s) 1 0.0455 0.0445 17.0 16.4 27.7 26.2 ±0.8 2 0.0455 0.0445 24.0 23.8 19.1 18.5 ±0.3 3 0.0455 0.0445 65.8 57.8 7.9 6.8 ±0.6 4 0.0455 0.0445 161.3 138.1 3.3 2.8 ±0.3 5 0.0455 0.0445 295.2 248.8 1.8 1.5 ±0.2

At 30°C

 Ball bearing Distance (m) ±0.0005m Time 1 (s) ±0.5s Time 2 (s) ±0.5s Time 3 (s) ±0.5s Average time (s) Velocity (x10-4m/s) 1 0.080 27.1 22.7 25.1 25.0±2.3 32±3.5 2 0.080 37.0 27.7 40.2 34.9±7.2 22.9±6.7 3 0.080 107.2 66.9 83.3 85.8±21.4 9.3±3.2 4 0.080 196.8 129.4 167.6 164.6±35.2 4.9±1.3 5 0.080 256.2 184.1 254.0 231.4±47.3 3.5±0.9
 Ball Bearing

Conclusion

1. Increase the viscosity of the syrup. This is due to the air bubbles being a circular shape, the strongest shape, and the ball bearing is not able to pass through the bubble. This means that the ball bearing is not flowing directly through the syrup and slows the velocity of the ball down. This turbulent flow could occur at any time and is incredibly hard to see so can not be accounted for.
2. The air bubbles could speed the velocity of the ball bearing up, as air is less dense than syrup, thus giving the impression that the viscosity of the syrup is less.

If I were to complete the investigation again and there were numerous resources that I could use there are a number of modifications that I would make: -

• Complete the experiment in a heat controlled room, pre setting the temperature to the desired one of the syrup. This would mean that the experiment could be completed quicker as you would not have to keep putting the syrup back in the water bath between the readings. This would lower the error readings on the temperature as it would not fluctuate as much.
• The distance the ball bearing travelled would be measured by a light gate which would accurately record the time taken. This would lower the error reading on the time and possibly lead to a change in velocity of the ball bearing.
• The distance the ball bearing travelled would be measured by laser measurement to ensure a precise reading.

Finally, I set out to find the viscosity of syrup, and as far as I know I have calculated this, as there is no value known to man. I, also, wanted to see if this value varied with the temperature that the syrup was at. I found that it did and as the temperature increased the viscosity decreased.

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4 star(s)

This is a 4-5 star piece of work. It has an excellent plan and lots of detail. The results are excellent and the calculations are very detailed considering all possible sources of error and calculating error as well. Overall lots of detail and scientific understanding displayed here but I feel parts of it could be clearer. It would be good to see worked calculations in some examples to show clearly steps of the process because there is a lot going on in this experiment. Overall very good work.

Marked by teacher Patricia McHugh 13/05/2013

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