Measurement OfDensity by Stoke Law.....................
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Transcript of 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)
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 16.66 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)
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 16.36 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)
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 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