measurement ofdensity by stoke law

7/28/2019 Measurement OfDensity by Stoke Law.....................

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Measurement of Viscosity by Stokess Law

I. The purpose of the experiment

To determine the viscosity ofglycerin by using stokess Law

II. Base theory

When any object rises or falls through a fluid it will experience a viscous drag,

whether it is a parachutist or spacecraft falling through air, a stone falling through water

or a bubble rising through fizzy lemonade. The mathematics of the viscous drag on

irregular shapes is difficult; we will consider here only the case of a falling sphere. The

formula was first suggested by Stokes and is therefore known as Stokes' law.

Consider a sphere falling through a viscous fluid. As the sphere falls so its

velocity increases until it reaches a velocity known as the terminal velocity. At this

velocity the frictional drag due to viscous forces is just balanced by the gravitational force

and the velocity is constant

At this speed: Viscous drag = 6r v = Weight. The following formula can beproved (see dimensional proof)

If the density of spare is , and the density of the liquid then:

effective gravitational force = weightup-thrust =4/3r3 ()

Therefore we have for the viscosity (

Where v is the terminal velocity of the sphere.

From the formula it can be seen that the frictional drag is smaller for large spheres

than for small ones, and therefore the terminal velocity of a large sphere is greater than

that for a small sphere of the same material.

Frictional force (F) = 6rv (Stokes' law)

Viscosity = 2gr2( - )9v


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III. Apparatus of experiment

- Measuring cylinder

- Glycerin

- Stop-watch

- Small steel ball-bearings of varying diameter- Micrometer screw gauge

- Hydrometer

IV. Experimental Procedure

1. Fill the measuring cylinder with glycerin, and drop in the largest ball-bearing.

2. Fix a markX (stick label is suitable) well below the top of the liquid, so that the

bearing reaches a steady velocity by the time it reaches X. Fix a second markYnear

the bottom of the cylinder, and measure the distance lcm betweenXand Y.

3. Time the fall of ball-bearings of varying diameter between the marks Xand Y, having

measured the diameter of each in two perpendicular directions with the micrometer

screw-gauge. Note the zero error of the micrometer.

4. Measure the density of the glycerin with the hydrometer, and its temperature.

V. An arrangement of data

Zero error of micrometer gauge = . Mm

Micrometer readings

(mm)

Average diameter

(mm)Time of fall forXYcm, t(s)

..

Density of glycerin, = g cm-3= . kg m-3

Density of steel, = . gr cm-3= . kg m-3 (from physics tables)

Density of glass, = . gr cm-3= . kg m-3 (from physics tables)

Temperature of glycerin = .o C


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VI. Technique of data analysis (Calculation)

First of all by doing this experiment we find the diameter of marble by using micrometer gauge.

By this data the value radius marble can be determine using equation :

da 2

1

After that we find the velocity (in meter per second) of the marble in glycerin by following

equation:

t

yxv

Plot a graph ofa2 against v, and draw the best line passing through the origin (Fig.8.2).

Calculate the gradient, c/d.

The terminal velocity v is such that the apparent weight 3.3

4a is equal to the

viscous drag av6 . Thus the viscosity is given by:

v

ag

2

.9

2

dcg .

92

In SI units,g= 9,8 m s-2, and are in kg m-3, c is in m2, and dis in m s-1

a2

v

c

d

0

Fig.8.2


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VII. Experiment result

Experiment of glass

Nomicrometer

reading (mm)

time of fall for x-y

(75-50 cm), t(s)

1 16.46 0.8

2 16.46 0.8

3 16.45 0.7

4 16.45 0.8

5 16.46 0.8

6 16.45 0.7

7 16.47 0.7

8 16.46 0.7

9 16.47 0.7

10 16.46 0.7

NoMicrometer

reading (mm)

Time of fall for x-

y (75-50 cm), t(s)

1 16.66 0.7

2 16.65 0.7

3 16.64 0.7

4 16.66 0.7

5 16.66 0.7

6 16.65 0.7

7 16.65 0.8

8 16.65 0.7

9 16.66 0.7

10 16.64 0.7

Experiment of steal

NoMicrometer

reading (mm)

Time of fall for x-

y (80-55)cm, t(s)

1 16.36 0.3

2 16.34 0.3

3 16.35 0.3

4 16.36 0.35 16.34 0.2

6 16.35 0.2

7 16.34 0.2

8 16.34 0.2

9 16.36 0.2

10 16.35 0.3

NoMicrometer

reading (mm)

Time of fall for x-

y (80-55)cm, t(s)

1 19.04 0.2

2 19.04 0.2

3 19.05 0.2

4 19.04 0.25 19.04 0.2

6 19.05 0.3

7 19.03 0.2

8 19.03 0.2

9 19.03 0.2

10 19.04 0.2

Density of glycerin, = 1.20 gr cm-3

=1.20x103

kg m-3

Density of steel, = 7.60 g cm-3

= 7.60x103

kg m-3

(from physics tables)

Density of glass, = 2.40 g cm-3

= 2.40x103

kg m-3

(from physics tables)

Temperature of glycerin = 27.5oC


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VIII. Data Analysis

Experiment no. 1(for glass)

Nomicrometer reading

(mm)time of fall for x-y

(75-50 cm), t(s)terminal

velocity (m/s)a

2(Radius)

2(m

2)

1 16.46 0.8 0.019 67.73

2 16.46 0.8 0.019 67.73

3 16.45 0.7 0.021 67.65

4 16.45 0.8 0.019 67.65

5 16.46 0.8 0.019 67.73

6 16.45 0.7 0.021 67.65

7 16.47 0.7 0.021 67.82

8 16.46 0.7 0.021 67.73

9 16.47 0.7 0.021 67.82

10 16.46 0.7 0.021 67.73

Total 164.59 7.4 0.203571 677.24683

Average 16.459 0.74 0.020357 67.724683

To find viscosity of glass we use equation:

v

ag

2

.9

2

sekonpaxxx 633 1085.8020.072.671020.11040.28.9.

92

Experiment no.2 (for glass)


(mm)time of fall for x-y

(75-50 cm), t(s)terminal

velocity (m/s)a

2(Radius)

2(m

2)

1 16.66 0.7 0.021 69.39

2 16.65 0.7 0.021 69.313 16.64 0.7 0.021 69.22

4 16.66 0.7 0.021 69.39

5 16.66 0.7 0.021 69.39

6 16.65 0.7 0.021 69.31

7 16.65 0.8 0.019 69.31

8 16.65 0.7 0.021 69.31


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9 16.66 0.7 0.021 69.39

10 16.64 0.7 0.021 69.22

Total 166.52 7.1 0.211607 693.2229

Average 16.652 0.71 0.021161 69.32229

To find viscosity of glass we use equation:

v

ag

2

.9

2

sekonpaxxx 633 1063.8021.0

32.691020.11040.28.9.

9

2

Experiment no.1 (for Iron)


(mm)


(75-50 cm), t(s)

terminal

velocity (m/s)a

2(Radius)

2(m

2)

1 16.36 0.3 0.083 66.91

2 16.34 0.3 0.083 66.75

3 16.35 0.3 0.083 66.83

4 16.36 0.3 0.083 66.91

5 16.34 0.2 0.125 66.75

6 16.35 0.2 0.125 66.83

7 16.34 0.2 0.125 66.75

8 16.34 0.2 0.125 66.75

9 16.36 0.2 0.125 66.91

10 16.35 0.3 0.083 66.83

Total 163.49 2.5 1.041667 668.22468

Average 16.349 0.25 0.104167 66.822468

To find viscosity of iron we use equation:

vag

2

.92

sekonpaxxx 633 1096.8104.0

82.661020.11060.78.9.

9

2


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Experiment no.2 (for Iron)


(mm)


(75-50 cm), t(s)

terminal

velocity (m/s)a

2(Radius)

2(m

2)

1 19.04 0.2 0.13 90.632 19.04 0.2 0.13 90.63

3 19.05 0.2 0.13 90.73

4 19.04 0.2 0.13 90.63

5 19.04 0.2 0.13 90.63

6 19.05 0.3 0.08 90.73

7 19.03 0.2 0.13 90.54

8 19.03 0.2 0.13 90.54

9 19.03 0.2 0.13 90.54

10 19.04 0.2 0.13 90.63Total 190.39 2.1 1.208333 906.2089

Average 19.039 0.21 0.120833 90.62089

To find viscosity of iron we use equation:

v

ag

2

.9

2

sekonpaxxx 733 1004.1121.0

62.901020.11060.78.9.

9

2

Setelah Nulis persamaan di atas sisakan satu lembar doble polio ya!!!!

Table Result Calculation

No Viscosity () Pa sekon 2

1 8.85x10 0.36 0.1296

2 8.63x10 0.25 0.0625

3 8.96x10 0.58 0.3364

4 1.04x10 1.19 1.4161

total 36.84 1.9446

N

9.21


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)1(

2

NN

)14(4

2

4

2

3

2

2

2

1

)3(4

101.945x 6

60.16205

2

4.026x10

%100Re xerrorlative

%00437.0)%1037.4(%1004.37x10%1001021.9

10026.4Re 35

6

2

xxxx

xerrorlative

After we calculate, we will find

%00437.01021.9 6 x

IX. Interpretation

According our measurement of viscosity glycerin by hygrometer, the value that we get is 8.8

Pa sekon in temperature 27.50

C. So for accuracy of the experiment can we find by following

equation:

%100exp

%

valuetheory

valuetheoryvaluerimetalerror

%1001080.8

1080.81021.9%

6

66

x

xx

error

%6.4%100046.0% error


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The magnitude value of viscosity of glycerin that we that from experiment by mean of

Stokes Law is 9.21x106

Pa sekon. While, viscosity that we get by measure using hygrometer is

8.8x106

Pa sekon. Its means the value of viscosity of glycerin approach on the measure by using

hygrometer. Error in this experiment is 4.6%. because the error less than 10%, so this experiment

can be accepted.

The experimentally determined value of viscosity glycerin is approach to the measure

using hygrometer. Within the experimental uncertainty. Thus this experiment that we done by

calculating analysis was a successful and accurate determination viscosity with relative error in

this experiment just 0.00437%.

X. Comment

From the experiment that we have done, the result of the experiment is not exactly equal with

the theory, its caused by some error that we have when this experiment did. The error is

classified to three, there are:

1. Gross Error (error that caused by human):

among them is missreading when read the scale of the micrometer gauge, and fault when we

calculate the data in analysis the data because the data is in decimal.

2. Systematic errors (error that caused by instrument and environment):

a) Instrumental error: the error that occurs because of tools is broken or didnt work

properly, in this experiment the tool (micrometer gauge) can be calibration on zero scale.

b) Enviromental error: the error that occur because of the disturbance of enviroment such as

the temperature not constant.

3. Random error : due to unknown causes and occur even when all systematic error have been

accounted for

XI. Conclusion

In this experiment, the value of viscosity of glycerin that we get by mean of Stokes Law

is determined to be 9.21x106

Pa sekon if compare with viscosity that we get by measure using

hygrometer is 8.8x106

Pa sekon. the value of viscosity of glycerin approach on the measure by

using hygrometer. Error in this experiment is 4.6%


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Questions and Solution:

1.What can you conclude about measuring the viscosity by Stokess Law?

Solution:

In this experiment, the value of viscosity of glycerin that we get by mean of Stokes Law is

determined to be 9.21x106

Pa sekon if compare with viscosity that we get by measure using

hygrometer is 8.8x106

Pa sekon. the value of viscosity of glycerin approach on the measure by

using hygrometer. Error in this experiment is 4.6%

2.Explain the errors of this experiment!

Solution:

From the experiment that we have done, the error is classified to three, there are:

1. Gross Error (error that caused by human): among them is missreading, there are missing

when we read the scale of the balance, and fault when we calculate the data in analysis the

data because the data is in decimal. improperapplication, and the wrong on calibrating

tools (balance).

2. Systematic errors (error that caused by instrument and environment):

c) Instrumental error: the error that occurs because of tools is broken or didnt work

properly

d) Enviromental error: the error that occur because of the disturbance of enviroment.

3. Random error : due to unknown causes and occur even when all systematic error have beenaccounted for

3.Calculate the percentage errors (the order of accuracy) of this experiment!

Solution:

According our measurement of viscosity glycerin by hygrometer, the value that we get is 8.8

Pa sekon in temperature 27.50

C. So for accuracy of the experiment can we find by following

equation:

%100exp%

valuetheory

valuetheoryvaluerimetalerror

%1001080.8

1080.81021.9%

6

66

x

xx

error

%6.4%100046.0% error


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Reference

Djonoputro, B.D. 1977. Teori Ketidakpastian. Bandung: Universitas ITB.

Halliday, D., Resnick, R., and Walker, J. (1993),Fundamentals of Physics, 4th edn (extended),John Wiley & Sons, New York.

Unname. Strokes Law. (online)www.fas.harvard.edu/~scphys/nsta/lab4.docbe access on April 9th2011.
http://www.fas.harvard.edu/~scphys/nsta/lab4.dochttp://www.fas.harvard.edu/~scphys/nsta/lab4.dochttp://www.fas.harvard.edu/~scphys/nsta/lab4.dochttp://www.fas.harvard.edu/~scphys/nsta/lab4.doc


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Measurement of Viscosity by Stokess Law(Physics Laboratory II)

Lab Report

WRITTEN BY,

KOMANG GEDE YUDI ARSANA (NIM. 1013021018)

PHYSICS DEPARTMENT OF EDUCATION

FACULTY OF MATHEMATIC AND SCIENCE

GANESHA UNIVERSITY OF EDUCATION

March 2011

measurement ofdensity by stoke law

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