Full Report VISCOUSITY OF VISCOUS FLUIDS

THE VISCOUSITY

OF VISCOUS

FLUIDS

(PART A)

1

INTRODUCTIONThe aim of the experiment is to determine the viscosity of glycerine (a viscous fluid) by

using guinea-and-feather apparatus and to determine the viscosity of the glycerine by using

Hoeppler Method.

The theory state that a body that moving in a fluid is acted on by a frictional force in the

opposite direction of its velocity. The magnitude of this force depends on the geometry of the

body, its velocity, and the internal friction of the fluids. A measure for the internal friction is

given by the dynamic viscosity, . For a sphere of radius, r moving at velocity, v in an infinitely

extended fluid of dynamic viscosity, . G. G. Stokes derived the frictional force,

F1 = 6 . . v . r -------------------- (1)

If the sphere falls down vertically in the fluid, it will move at a constant velocity v after a

certain time, and there will be an equilibrium between all forces acting on the sphere: the

frictional force F1, which acts upward, the buoyancy force,

F1=4 π3

. r3 . ρ2 . g -------------------- (2)

which acts upward too, and the downward acting gravitational force,

F1=4 π3

. r3 . ρ1 . g -------------------- (3)

where,

1 : density of the sphere

2 : density of the fluid

g : acceleration of free fall

2

This forces fulfil the relation :

F1 + F2 = F3 -------------------- (4)

The viscosity can, therefore be determined by measuring the rate of fall, v.

¿ 29

× r2× ¿¿¿ -------------------- (5)

Where, v is to be determined from the distance, s and the time, t of fall. The viscosity then

η=29

×r 2×( ρ1− ρ2 )× g× t

s -------------------- (6)

In practice, Equation (1) has to be corrected since the assumption of an infinitely extended fluid

is unrealistic and the velocity distribution of the fluid particles with respect to the surface of the

sphere is influenced by the finite dimensions of the fluid. For the movement of the sphere along

the axis of a cylinder of radius, R and infinite length, for example, the frictional force is

3

F1=6 π × η × v×(1+2 × 4rR ) -------------------- (7)

Equation (6) thus is changed into

¿ 29

× r2×( ρ1−ρ2 ) × g ×t

s×

1

1+2× 4 ( rR ) -------------------- (8)

If the infinite length, L of the fluid cylinder is taken into account, there are further corrections of

the order r/L.

The dynamic viscosity according to Hoeppler Method using HAAKE Falling-ball viscometer is

in accordance with the following equation

¿ K ( ρ1−ρ2) × t(mPa. s) -------------------- (9)

where,

K = ball constant in mPa.s cm3 / g . s

1 = density of the ball in g cm-3

2 = density of the viscous fluid in g cm-3

t = falling time of the ball in seconds.

4

APPARATUSPART A

1 steel ball (16mm dia)

1 guinea-and-feather apparatus

6 glycerine (99%, 250ml)

Counter P

Holding magnet with clamp

Low voltage power supply (3V, 6V , 9V, 12V)

Morse key

Stand base (V-shape)

Stand rod (100cm)

Stand rod (25cm)

Multiclamp

Clamp with jaw clamp

Steel tape measure (2m)

1 pair magnets cylindrical

Connection leads

Vernier calipers

Measuring cylinder (100ml)

Electronic balance

5

Figure 1 : Experimental setup for the determination of the viscosity of glycerine

FIGURE 2 : Returning the steel ball

6

SETUP AND PROCEDURE

1. Setup the experimental apparatus as shown in figure 1.

2. The guinea-and-feather apparatus in the clamp (x) is fixed so that it is propped up on the

experiment table.

3. Turn the knurled screw (a) of the holding magnet down until stopping, so that the iron

core (b) sticks out of the coil former.

4. Connect the holding magnet to the DC output of the low-voltage power supply, and

connect morse key to the negative pole so that the connection is closed (i.e on) when the

morse key is in the rest position. Then, switch on the supply voltage (12 VDC) and the

ball was stick onto the iron core (b).

5. The knurled screw (a) was turn upward by about five turns.

6. Position the holding magnet was with the steel ball above the fluid column in a way that

the steel ball was on concenter with the cylinder axis and was completely dipped in.

7. Mark the guinea-and-feather apparatus some centimetres above its bottom and the

distance of fall, s between the lower edge and the mark (c) is measured.

8. The counter P was set to zero by pressing the key “0”

9. Trigger off the morse key, and the falling ball is observed.

10. Release the morse key as soon as the ball has reached the mark (c).

11. The reading of the time of fall, t from the counter P was read and record on the data

sheet.

NOTE :a) If the ball does not falls with a delay :

- Check the connections.

- Turn the iron core a bit upward.

- Choose a lower voltage for holding magnet.

b) If the ball falls without the morse key’s being triggered :

-Turn the iron core a bit downward.

7

12. Repeating The Measurement : Get grip of the steel ball from outside on the bottom of the

vessel with the pair of magnets sticking together (red mark outward), and the ball moved

slowly upward along the wall of the vessel until it reaches the holding magnet. Using a

bent of wire, for example, push the ball exactly below the iron core (see Figure 2).

- Turn the knurled screw upward again, set the counter P to zero, and repeat the

measurement of the time of fall.

13. The procedure no. 12 was repeated to obtain five measurements of the time of fall.

14. The average diameter of the steel ball and its mass was determined.

15. The diameter of the guinea-and-feather apparatus was determined.

8

DATA

PART A

Diameter of steel ball, d = 16.00 0.02mm

Diameter of guinea-and-feather apparatus, D = 48.08 0.02mm

Mass of steel ball, = 16.3 0.1g

Density of steel ball, 1 = 7599.07kg.m-3

Density of the glycerine, 2 = 1260kg.m-3

The distance of fall, s = 59.5 0.1cm

Times of

fall,

t 0.001s

1.497 1.709 1.618 1.589 1.592

Average :

1.601

9

ANALYSIS1. From the measuring results, calculate the average value for times of fall of the ball in

glycerine.

2. Calculate the viscosity of the fluids according to the equation 8.

3. Calculate the percentage difference between calculated value and the value quoted in the

literature.

4. Calculate the viscosity of the glycerine according to equation 9

5. Calculate the percentage difference between value calculated in Analysis (4) and the

value obtained from the literature.

6. Compare the result obtained in part A with the result obtained in part B

.

Note that, when compare or state the result with the value taken from the literature, the

temperature of the fluid must be quoted. Why ?

10

ANALYSIS ANSWERS

1. From the measuring results, calculate the average value for times to fall of the ball in the

glycerine.

average value=reading1+reading2+reading3+reading4+reading5

the number of readings

PART A

¿ 1.497+1.709+1.618+1.589+1.5925

= 1.601s

PART B

¿ 3.684+3.684+3.661+3.645+3.4105

= 3.617s

2. Calculate the viscosity of the fluid according to the equation 8.

¿ 29

× r2×( ρ1−ρ2 ) × g ×t

s×

1

1+2× 4 ( rR )

¿29

× 82×(7599.07−1260.00 ) × (9.81 )×(1.601)

59.5×

1

1+2× 4 ( 824.04 )

= 6498.17 mPa.s

11

12

3. Calculate the percentage difference between calculated value and the value quoted in the

literature.

percentage difference= experiment value−theory valuetheory value

×100 %

Experiment value = 6498.17 mPa.s

Value in literature= 9420 mPa.s

¿ 6498.17−94209420

×100 %

= -31.02%

= 31.02%

4. Calculate the viscosity of the glycerine according to Equation 9

¿ K ( ρ1−ρ2) × t(mPa. s)

= 33.82 (8.036 – 1.260) × 3.617

= 828.89 mPa.s

13

5. Calculate the percentage difference between value calculated in Analysis (4) and the value

obtained from literature.

percentage difference= experiment value−theory valuetheory value

×100 %

Experiment value : 828.89 mPa.s

Value in literature : 9420 mPa.s

¿ 828.89−94209420

×100 %

= -91.21%

= 91.21%

6. Compare the result obtained in Part A with the result obtained in Part B.

The value of viscosity in experiment part A is 6498.17 mPa.s and it is higher than

the value of viscosity in experiment part B that is 828.89 mPa.s.

The percentage difference of experiment part A is 31.02% that is lower than the

experiment part B that have a percentage difference 91.21%.

When compare or state the result with the value taken from the literature, the temperature of the

fluid must be quoted. Why ?

-It is to make sure the temperature uniformity.

14

DISCUSSION PART A

The experiment went as expected with no unusual events. For this Viscosity of Viscous

Fluids experiments, the theory state that the magnitude of frictional force of a body moving in a

fluids depends on the geometry of the body, its velocity and internal friction of the fluid. A

measure for the internal friction is given by the dynamic viscosity, . Therefore, viscosity can be

determined from the distance, time of fall, gravity, density of the sphere and the viscous fluids,

besides the radius of the guinea-and-feather apparatus and the sphere since the sphere move

along the axis of a fluid cylinder of radius.

The diameter of the steel ball, d, diameter of the guinea-and-feather apparatus, D, density

of the steel ball, 1, density of the glycerine, 2, and the distance of fall, s was measured and

recorded in the Data Sheet. Also included in the data sheet is the time of fall, s and its average

value. All information that has been filled in the data sheet leads to the value of the viscosity.

The value of viscosity can be determined by using the Equation 8.

The value of the viscosity from the experiment is lower than the theoretical value that

quoted in literature. In order to obtain how accurate this experiment was carried out, the

percentage difference must be calculated. The calculation revealed this experiment has a high

percentage difference. Several errors could explain the difference. Error in reaction time, as the

stopwatch is a very sensitive instrument, the fact that the reaction time in starting and stopping

the stopwatch varies from person to person. The other error that may occur is parallax error, due

to the incorrect positioning of the eye during read the scale in metre rule. Other than that, zero

error may also occur in vernier calipers that have been used to measure the diameter of the steel

ball and the diameter of the guinea-and-feather apparatus.

15

There are many ways to overcome this problem that I can use in order to obtain more

accurate result thus reduce the difference. To overcome the reaction time error’s, two or three

times reading should be taken and the average time computed. The way to overcome the parallax

error is make sure the eye look perpendicularly on the metre rule scale while the reading is being

taken. To settle the zero error that may occur in vernier calipers, all the reading taken using this

vernier calipers have to be compensated accordingly.

16

CONCLUSIONPART A

Overall, the experiment succeeded in showing the viscosity of glycerine (a viscous fluid)

can be determined by using guinea-and-feather apparatus. Difference existed in calculation that

showed at the analysis part. The percentage difference is 31.02%. These differences, however,

can be accounted for by experimental error.

17

THE VISCOUSITY

OF VISCOUS

FLUIDS

(PART B)

18

INTRODUCTION

The aim of the experiment is to determine the viscosity of glycerine (a viscous fluids) by

using guinea-and-feather apparatus and to determine the viscosity of the glycerine by using

Hoeppler Method.

The theory state that a body that moving in a fluid is acted on by a frictional force in the

opposite direction of its velocity. The magnitude of this force depends on the geometry of the

body, its velocity, and the internal friction of the fluids. A measure for the internal friction is

given by the dynamic viscosity, . For a sphere of radius, r moving at velocity, v in an infinitely

extended fluid of dynamic viscosity, . G. G. Stokes derived the frictional force,

F1 = 6 . . v . r -------------------- (1)

If the sphere falls down vertically in the fluid, it will move at a constant velocity v after a

certain time, and there will be an equilibrium between all forces acting on the sphere: the

frictional force F1, which acts upward, the buoyancy force,

F1=4 π3

. r3 . ρ2 . g -------------------- (2)

which acts upward too, and the downward acting gravitational force,

F1=4 π3

. r3 . ρ1 . g -------------------- (3)

where,

1 : density of the sphere

2 : density of the fluid

g : acceleration of free fall

19

This forces fulfil the relation :

F1 + F2 = F3 -------------------- (4)

The viscosity can, therefore be determined by measuring the rate of fall, v.

¿ 29

× r2× ¿¿¿ -------------------- (5)

Where, v is to be determined from the distance, s and the time, t of fall. The viscosity then

η=29

×r 2×( ρ1− ρ2 )× g× t

s -------------------- (6)

In practice, Equation (1) has to be corrected since the assumption of an infinitely extended fluid

is unrealistic and the velocity distribution of the fluid particles with respect to the surface of the

sphere is influenced by the finite dimensions of the fluid. For the movement of the sphere along

the axis of a cylinder of radius, R and infinite length, for example, the frictional force is

20

F1=6 π × η × v×(1+2 × 4rR ) -------------------- (7)

Equation (6) thus is changed into

¿ 29

× r2×( ρ1−ρ2 ) × g ×t

s×

1

1+2× 4 ( rR ) -------------------- (8)

If the infinite length, L of the fluid cylinder is taken into account, there are further corrections of

the order r/L.

The dynamic viscosity according to Hoeppler Method using HAAKE Falling-ball viscometer is

in accordance with the following equation

¿ K ( ρ1−ρ2) × t(mPa. s) -------------------- (9)

where,

K = ball constant in mPa.s cm3 / g . s

1 = density of the ball in g cm-3

2 = density of the viscous fluid in g cm-3

t = falling time of the ball in seconds.

21

APPARATUSPART B

HAAKE Falling-ball viscometer

Counter P

22

SETUP AND PROCEDURE

1. Description of the HAAKE falling Ball Viscometer :

The main component of the Falling Ball Viscometer is a cylindrical measuring tube (1)

and spherical ball (2). The measuring tube is positioned slightly inclined about 10 to the

vertical position and is surrounded by outer glass tube which can be filled with

temperature controlled liquid (3).

The assemblies is pivoted and can be turned up-side down as shown in Figure 3.

In this experiment, the measuring tube has been filled with glycerine (sample to be

tested). The liquid should reach level just beyond the capillary of the stopper. This

capillary is a passage for air bubble to escape to the reservoir and prevent undesireable

change of pressure in the measuring tape.

23

2. The tube turn upside down at least once for the ball run through up and down in order to

improve the homogeneity of the sample and its temperature uniformity.

3. The ball returned to the initial position at the top mark of the measuring tube. The time of

fall between the top mark (A) to the bottom mark (B) of the measuring tube is measured.

4. Step 3 repeated, at least five times and the times of fall recorded. The average value of

measuring results was determined.

24

DATA

PART B

Diameter of the steel ball, d = 1.100 0.001cm

Density of steel ball, 1 = 8.036g.cm-3

The steel ball constant, K = 33.82 mPa.s.cm-3.g-1.s-1

Density of the glycerine, 2 = 1.260g.cm-3

Times of

fall

t = 0.001s

3.684 3.684 3.661 3.645 3.410

Average :

3.617

25

ANALYSIS

1. From the measuring results, calculate the average value for times of fall of the ball in

glycerine.

2. Calculate the viscosity of the fluids according to the equation 8.

3. Calculate the percentage difference between calculated value and the value quoted in the

literature.

4. Calculate the viscosity of the glycerine according to equation 9

5. Calculate the percentage difference between value calculated in Analysis (4) and the

value obtained from the literature.

6. Compare the result obtained in part A with the result obtained in part B

.

Note that, when compare or state the result with the value taken from the literature, the

temperature of the fluid must be quoted. Why ?

26

ANALYSIS ANSWER1. From the measuring results, calculate the average value for times to fall of the ball in the

glycerine.

average value=reading1+reading2+reading3+reading4+reading5

the number of readings

PART A

¿ 1.497+1.709+1.618+1.589+1.5925

= 1.601s

PART B

¿ 3.684+3.684+3.661+3.645+3.4105

= 3.617s

1 Calculate the viscosity of the fluid according to the equation 8.

¿ 29

× r2×( ρ1−ρ2 ) × g ×t

s×

1

1+2× 4 ( rR )

¿29

× 82×(7599.07−1260.00 ) × (9.81 )×(1.601)

59.5×

1

1+2× 4 ( 824.04 )

= 6498.17 mPa.s

27

2 Calculate the percentage difference between calculated value and the value quoted in the

literature.

percentage difference= experiment value−theory valuetheory value

×100 %

Experiment value = 6498.17 mPa.s

Value in literature= 9420 mPa.s

¿ 6498.17−94209420

×100 %

= -31.02%

= 31.02%

3 Calculate the viscosity of the glycerine according to Equation 9

¿ K ( ρ1−ρ2) × t(mPa. s)

= 33.82 (8.036 – 1.260) × 3.617

= 828.89 mPa.s

28

4 Calculate the percentage difference between value calculated in Analysis (4) and the value

obtained from literature.

percentage difference= experiment value−theory valuetheory value

×100 %

Experiment value : 828.89 mPa.s

Value in literature : 9420 mPa.s

¿ 828.89−94209420

×100 %

= -91.21%

= 91.21%

5 Compare the result obtained in Part A with the result obtained in Part B.

The value of viscosity in experiment part A is 6498.17 mPa.s and it is higher than

the value of viscosity in experiment part B that is 828.89 mPa.s.

The percentage difference of experiment part A is 31.02% that is lower than the

experiment part B that have a percentage difference 91.21%.

When compare or state the result with the value taken from the literature, the temperature of the

fluid must be quoted. Why ?

-It is to make sure the temperature uniformity.

29

DISCUSSIONPART B

Based on Hoeppler Method, to determine the dynamic viscosity using HAAKE Falling-

ball viscometer is in accordance with the Equation 9 that has been state at the introduction.

According to the Equation 9, the viscosity of fluids can be determined from the viscometer ball

constant, K, density of the ball and viscous fluid with the value of falling time of the ball that has

been recorded. The value for the viscometer constant, K has been given.

All the information and data that has been taken is recorded in the data sheet. All

information that has been filled in the data sheet leads to the value of the viscosity. As I have

state that to determine the viscosity using HAAKE Falling-ball viscometer is in accordance to

Equation 8. The value of the viscosity from the experiment is too lower than the theoretical value

that quoted in literature. In order to obtain how accurate this experiment was carried out, the

percentage difference must be calculated. The calculation revealed this experiment has a very

high percentage difference.

There are several errors that could explain the difference. Systematic error such as zero

error may occur in vernier calipers that have been used to measure the diameter of the steel ball.

Error in the operation of viscometer equipment, as the HAAKE Falling-ball viscometer needs to

turn by 180, upside down. The temperature in the HAAKE Falling-ball viscometer that not in

uniformity state also can cause error during carried out this experiment.

There are many solutions to cope with the error. Before used the vernier calipers, the

jaws must be closed with nothing between them to check the presence of zero error. If there is

zero error, the vernier calipers need to compensate accordingly. In order to compensate for the

error, all readings taken with this vernier calipers should be adjusted by deducting or adding the

value of zero error with the actual reading. Error in operating the viscometer equipment can be

reduced by taking several readings of the same quantity and same angle of turns thus

subsequently obtaining the average value. To make sure the uniformity of the temperature of the

viscometer, the tube needs to be turn upside down at least once for the spherical ball run through

up and down.

30

CONCLUSIONPART B

Overall, the experiment succeeded in showing the viscosity of the glycerine can be

determined by using Hoeppler Method. Difference existed in calculation that showed at the

analysis part. The percentage difference is 91.21%. These differences, however, can be

accounted for by experimental error.

31

REFERENCES1. Makmal Fizik (2011). “Buku Eksperimen Amali Fizik I.” University of Tun Hussein Onn

Malaysia: Penerbit UTHM.

2. Daniel Joseph, Toshio Funada, Jing Wang (2007). “Potential flows of viscous and

viscoelastic fluids” Cambridge: Cambridge University Press.

3.  Amer Nordin Darus (1989). “Aliran bendalir likat” Kuala Lumpur: Dewan Bahasa dan

Pustaka.

4. http://www.dow.com/glycerine/resources/table18.htm access date 23 August 2011

5. http://msdssearch.dow.com/PublishedLiteratureDOWCOM/

dh_0032/0901b803800322bd.pdf?filepath=glycerine/pdfs/noreg/115-

00678.pdf&fromPage=GetDoc access date 24 August 2011

32