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# Viscosity of Fluids

Extracts from this document...

Introduction

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

Middle

0 - 10 cm

11.81

10.58

9.37

10.5

10 - 15cm

23.26

16.35

14.22

17.94

15 - 20cm

26.63

24.05

21.07

23.92

30

0 - 10cm

7.81

6.31

5.47

6.53

10 - 15cm

12.23

10.48

9.56

10.76

15 - 20cm

17.16

15.09

12.83

15.02

35

0 - 10cm

4.68

4.37

5.52

4.85

10 - 20cm

9.14

8.68

9.49

9.1

40

0 - 10cm

2.05

2.16

2.26

2.16

10 - 20cm

5.77

5.95

5.5

5.74

45

0 - 10cm

2.18

2.09

1.81

2.03

10 - 20cm

4.73

4.61

4.82

4.72

As I am going to determine the viscosity of the honey at specific temperatures, I will need to consider the following equations

Upthrust is :                        4 π r3 ρ(fluid)  g

3

Viscous drag is :                  6 π r η v

Weight of ball is :                4 π r3 ρ(solid)   g

3

Where:

ρ is density

The magnitudes of the above forces are related as shown below:

4 π r3 ρ(fluid)  g   +     6 π r η v    =     4 π r3 ρ(solid)  g

3                                                     3

As I will be calculating the viscosity I will need to rearrange the equation to:

6 π r η v    =

Conclusion

The temperature of the fluid was taken at the beginning but could have decreased after each set of results were taken, therefore if I were to conduct this experiment again I would take the temperature before each set of results so that a greater degree of accuracy could be obtained.After the first experiment the ball bearing was still covered in honey, if I were to repeat this experiment I would wash the ball bearing each time it was used so that its current surface properties would not affect the results by its change in friction altering the acceleration.The measuring cylinder was quite narrow and this may have affected the ball bearings decent due to the friction from the sides of the tube.  I would use a wider tube to counteract this affect.

## Conclusion

The experiment conducted above was accurate overall, leading to a clear set of results that proved my prediction.  If I were to repeat this experiment I would consider the above points and put each of the ideas into practice to ensure a completely accurate experiment.

I would also like to compare these results with other fluids so that a clearer picture can be gained as to the effect of temperature on viscosities of other liquids compared to properties such as density and concentrations.

## References

Physics 2000

Project A Level

This student written piece of work is one of many that can be found in our GCSE Forces and Motion section.

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