Nequila Lovelace
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24/30
MEDC 0501
Experiment 2
MEASUREMENTS IN VISCOSITY
Abstract
For this experiment, participants were to examine the forces in two fluids considering
the mechanics of motion. This involved two procedures. In procedure 1, a measure of the
volume of water from a dripping capillary tube was recorded with varying water level
heights. It was observed, that by increasing the height of the water level in the constant head
apparatus, the volume of water that was collected after 15 minutes increased. For procedure
2, small metal spheres were released into a tube of glycerin. The time taken for the sphere to
descend between two areas along the tube (labelled X and Y) were recorded. From the results
obtained one can deduce that the smaller sphere took a longer time to travel between the two
labelled point.
Performance = 5 marks
Missing main results. (0.5 mark)
Introduction
Viscosity is the quantity that describes a fluid’s resistance to flow, gradual
deformation, or tensile stress. The reciprocal of the viscosity is called the fluidity, a measure
of the ease of flow. Molasses, for example, has a greater viscosity than water.
Density refers to how tightly a material is packed together; defined a mass per unit volume
𝑚𝑎𝑠𝑠
. It is represented by the symbol, ρ.
𝑣𝑜𝑙𝑢𝑚𝑒
Stoke’s Law states that the force that retards a sphere moving through a viscous fluid is
directly proportional to the velocity and the radius of the sphere, and the fluid’s viscosity.
Fluid pressure is the force acting per unit area on an object in the fluid or on the surface of a
closed container.
(4 marks)
Theory
𝐲₂ − 𝐲₁

Gradient =

The radius of the capillary can be calculated using the mass of the water thread m
(kg), the length of the thread L (m), and the density of water, ρ = 1000 kgm−3
𝒙𝟐 −𝒙₁
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𝒎
r = √𝝅𝑳𝝆 m

A proper analysis of this ‘streamlined’ or ‘laminar’ flow shows that the expression
relating the volume of liquid transmitted per second, Vt (m³sˉ¹) the coefficient of
viscosity, η (Nsmˉ²), the radius, r (m), of the tube, and the pressure gradient, Pl
(Nmˉ³), (where l is the length of the tube and P is the pressure difference) is given by:
𝑽
𝒕
=
𝝅(𝑿−𝑯)𝝆𝒈𝒓⁴
𝟖𝜼𝒍
m³sˉ¹
This equation is known as Poiseuille’s formula.
ẟ𝒓
𝟏 ẟ𝒎
ẟ𝑳
 𝒓 = 𝟐 (𝒎 + 𝑳)
Where;
m = absolute error in the weighing scale
m = mass of the water
L = absolute error in the meter ruler
L = length of the water thread
𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒓𝒂𝒗𝒆𝒍𝒍𝒆𝒅 𝒃𝒚 𝒔𝒑𝒉𝒆𝒓𝒆

Terminal velocity, Vt = 𝒕𝒊𝒎𝒆 𝒕𝒂𝒌𝒆𝒏 𝒕𝒐 𝒕𝒓𝒂𝒗𝒆𝒍 𝒕𝒉𝒆 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆

radius² = (

Calculating the viscosity of glycerin, η using gradient
𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓 𝒐𝒇 𝒔𝒑𝒉𝒆𝒓𝒆
𝟐
𝟐
)²
𝒄
η = 𝟗 g 9 (ρ – ơ) × (𝒅)
(1 mark)
Precautions
Procedure 1
1. All readings were taken at eye level to avoid parallax.
2. Excess water dripping from the capillary tube after the 15 minutes had expired was
prevented from hitting the table by placing a replacement beaker to collect it. ?
3. It was ensured that the volume of water was checked right on the 900 second mark.
Procedure 2
1. All readings were taken at eye level to avoid parallax.
2. The micrometer screw gauge was utilized properly ? when recording the diameter of
each sphere. Not Clear.
3. The reaction time of the participant controlling the stop watch was as best as possible.
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(0.5 mark)
Method
As stated in lab manual.
Tables of Results
Procedure 1
TABLE SHOWING THE HEIGHT VALUES, VOLUME OF WATER COLLECTED
& VOLUME PER SECOND FOR EACH 15 MINUTE INTERVAL.
Height X (m)
Height H (m)
X-M (m)
0.474
0.210
0.480
0.210
0.477
0.210
0.479
0.210
Error in metre rule ± 0.0005 m
0.264
0.270
0.267
0.296
Volume of water
(m3)
Time (s)
1.06 × 10ˉ⁵
1.07 × 10ˉ⁵
1.08 × 10ˉ⁵
1.09 × 10ˉ⁵
900
900
900
900
Volume per second
(volume of water ÷
time) (m³/s)
1.1 × 10ˉ⁸
1.1 × 10ˉ⁸
1.2 × 10ˉ⁸
1.2 × 10ˉ⁸
Error in measuring cylinder ± 1 × 10ˉ⁶ m³
Error in weighing scale ± 1 × 10ˉ⁵ kg
Mass of beaker = 0.1972 kg
Mass of beaker + water = 0.19728 kg
Length of capillary tube = length of thread, L = 0.1345 m
Diameter of capillary tube = 0.0004 m
Procedure 2
TABLE SHOWING THE DIAMETER, TIME TAKE FOR FALL AND THE
TERMINAL VELOCITY OF EACH SPHERE
Micrometer
reading (mm)
10.27
10.26
9.45
7.10
7.08
6.30
10.25
10.25
9.44
7.11
7.10
6.30
November 22nd,2022
Average
diameter
(mm)
Average
diameter
(m)
Time for
fall
between
X&Y (s)
Terminal
Velocity
(msˉ¹)
a² (radius²)
(m²)
10.26
10.26
9.45
7.11
7.09
6.30
0.01026
0.01026
0.00945
0.00711
0.00709
0.0063
0.79
0.75
0.67
1.00
0.96
1.07
0.6861
0.7227
0.8090
0.5065
0.5420
0.5646
2.63 × 10ˉ⁵
2.63 × 10ˉ⁵
2.23 × 10ˉ⁵
1.26 × 10ˉ⁵
1.26 × 10ˉ⁵
9.92 × 10ˉ⁶
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Error in stopwatch ± 0.01 s
Error in micrometer screw gauge ±0.01 mm or ± 1 × 10ˉ⁵ m The error is half of this.
Error in rule ± 0.0005 m
Distance between X & Y = 54.2 cm or 0.542 m
(0.5 mark)
Calculations
Procedure 1

Plot a graph of V/t vs (X − H) and obtain its gradient.

Use the gradient to find viscosity, η
Gradient = y₂ - y₁
x₂ - x₁
= 1.1875 × 10ˉ⁸ – 1.1250 × 10ˉ⁸
0.292 – 0.272
= 6.25 × 10ˉ¹⁰
0.02
= 3.1 × 10ˉ⁸ m²/s 1 mark
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
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Calculate the radius of the capillary tube using r = √m/π × L ρ
𝒎
r = √𝝅𝑳𝝆 m
8 ×10ˉ⁵
= √𝜋 ×0.1345 ×1000 m
= √1.89 × 10ˉ⁷ m
= 4.35 × 10ˉ⁴ m 1 mark

Finding the viscosity of water
𝑽
𝒕
𝑉
𝑡
=
=
𝝅(𝑿−𝑯)𝝆𝒈𝒓⁴
𝟖𝜼𝒍
𝜋𝜌𝑔𝑟⁴
8𝜂𝑙
m³sˉ¹
× (X-H) m³sˉ¹
y = mx + c
where;
y=
𝑉
m=
𝑡
𝜋𝜌𝑔𝑟 4
8𝜂𝑙
x = (X-H)
c=0
The fragment m =
𝜋𝜌𝑔𝑟 4
8𝜂𝑙
will be used to find the viscosity; making η the subject of the
formula.
Therefore,
η=
=
𝜋𝜌𝑔𝑟 4
8𝑚𝑙
𝜋×1000×9.81×(4.35×10ˉ4 )⁴
8 ×(3 ×10ˉ8 )×0.1345
η = 5.57 × 10ˉ¹⁹ Nsmˉ¹
Nsmˉ¹
1 mark
Procedure 2

Show a sample calculation for the terminal velocity and radius, (a²).
𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒓𝒂𝒗𝒆𝒍𝒍𝒆𝒅 𝒃𝒚 𝒔𝒑𝒉𝒆𝒓𝒆
Terminal velocity, Vt = 𝒕𝒊𝒎𝒆 𝒕𝒂𝒌𝒆𝒏 𝒕𝒐 𝒕𝒓𝒂𝒗𝒆𝒍 𝒕𝒉𝒆 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆
=
0.542 𝑚
0.79𝑠
= 0.686 m/s
radius² = (
𝒅𝒊𝒂𝒎𝒆𝒕𝒆𝒓 𝒐𝒇 𝒔𝒑𝒉𝒆𝒓𝒆
November 22nd,2022
𝟐
)²
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=(
𝟎.𝟎𝟏𝟎𝟐𝟔
𝟐
)²
= (0.00513)²
= 2.63 × 10ˉ⁵ m² 1 mark

Plot a graph of a² vs vt
1 mark

Calculate the gradient of the above graph.
𝒄
Gradient (𝒅) = y₂ - y₁
x₂ - x₁
=
=
𝒄
𝟐.𝟑𝟕𝟓 × 10ˉ⁵ − 𝟏.𝟑𝟕𝟓 × 10ˉ⁵
𝟎.𝟔𝟖𝟓−𝟎.𝟓𝟔𝟎
𝟏 ×𝟏𝟎ˉ⁵
𝟎.𝟏𝟐𝟓
(𝒅) = 8 × 10ˉ⁵ m/s (ms)

(0.5 mark)
Calculating the viscosity of glycerin, η using gradient
𝟐
𝒄
η = 𝟗 g 9 (ρ – ơ) × (𝒅)
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2
= × 9.81 × (7750 – 1260) × 8 × 10ˉ⁵ m/s
9
= 1.132 Nsmˉ¹ 1 mark
Error Analysis
Procedure 1
Errors in the slope
Maximum slope
mmax =
𝐲₂ − 𝐲₁
=
𝒙𝟐 −𝒙₁
1.1875 × 10ˉ8 −1.1250× 10ˉ⁸
0.292−0.272
6.25 × 10ˉ¹⁰
= 0.02
= 3.1 × 10ˉ⁸ m²/s
Minimum slope
𝐲₂ − 𝐲₁
mmin = 𝒙𝟐 −𝒙₁
=
1.1825 × 10ˉ8 −1.1150×10ˉ⁸
0.2696−0.2912
6.75 × 10ˉ¹⁰
= −0.0216
= -3.1 × 10ˉ⁸ m²/s
Error in slope = mmax - mmin
2 √4
3.1 × 10ˉ8 −(−3.1 × 10ˉ8 )
=
6.2 × 10ˉ8
2 √4
=
4
= 1.5 × 10ˉ⁸ m²/s
Percentage error in r⁴ = 𝟒
Where,
ẟ𝒓
𝒓
𝟏 ẟ𝒎
= 𝟐 (𝒎 +
ẟ𝑳
November 22nd,2022
𝑳
ẟ𝒓
𝒓
× 𝟏𝟎𝟎%
)
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Nequila Lovelace
ẟ𝑟
𝑟
1 ẟ𝑚
= (
2
𝑚
ẟ𝑟
ẟ𝐿
+
𝐿
)
1 1 × 10ˉ⁵
4.35 × 10ˉ⁴
ẟ𝑟
816032215
= 2 (8 × 10ˉ⁵ +
5 × 10ˉ⁴
)
0.13545
1
4.35 × 10ˉ⁴
ẟ𝑟
4.35 × 10ˉ⁴
= 2 × 0.1287
= 0.06435
Then r⁴ = 4
ẟ𝑟
𝑟
× 100%
= (4 × 0.06435) × 100%
= 25.74% error in r⁴

1 mark
Order of Accuracy
Error in viscosity, η.
𝛿𝑟
1 𝛿𝑚 𝛿𝐿
= (
+
)
𝑟
2 𝑚
𝐿
𝛿𝜂
𝛿𝑟
𝛿𝑚 𝛿𝑙
= (4 × ) +
+
𝜂
𝑟
𝑚
𝑙
𝛿𝜂
𝛿𝑚 𝛿𝐿
𝛿𝑠𝑙𝑜𝑝𝑒 𝛿𝑙
= (2 × (
+
)) +
+
𝜂
𝑚
𝐿
𝑠𝑙𝑜𝑝𝑒
𝑙
𝛿𝜂
1 × 10−5 5 × 10−4
1.5 × 10ˉ⁸ 5 × 10−4
= (2 × (
+
)) +
+
𝜂
8 × 10−5
0.1345
0.1345
3.1 x 10ˉ⁸
Error in viscosity = 0.74
1 mark
Conclusion: the viscosity of water at 25ºC was 5.57 × 10ˉ¹⁹ Nsmˉ¹.
Procedure 2

Errors in the slope
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Maximum slope
mmax =
𝐲₂ − 𝐲₁
=
𝒙𝟐 −𝒙₁
3.250 × 10ˉ8 −0.9675× 10ˉ⁹
0.735−0.550
3.1 × 10ˉ⁸
= 0.185
= 1.67 × 10ˉ⁷ ms
Minimum slope
𝐲₂ − 𝐲₁
mmin = 𝒙𝟐 −𝒙₁
=
2.425 × 10ˉ8 −1.10 ×10ˉ⁸
0.86−0.47
1.3 × 10ˉ⁸
= 0.39
= 3.3 × 10ˉ⁸ ms
Error in slope = mmax - mmin
2 √4
=
1.67 × 10ˉ⁷ −3.3 × 10ˉ⁸
2 √4
1.34 × 10ˉ7
=
4
= 3.3 × 10ˉ⁸ m²/s

Order of Accuracy
Error in viscosity, η =
ẟ𝜼
𝜼
=[
𝒄
𝒅
𝒄
𝒅
ẟ( )
=[
]
𝒆𝒓𝒓𝒐𝒓 𝒊𝒏 𝒔𝒍𝒐𝒑𝒆
𝒔𝒍𝒐𝒑𝒆
𝟑.𝟑 × 𝟏𝟎ˉ⁸
= 𝟖 × 𝟏𝟎ˉ⁵
= 4.125 × 10ˉ⁴
]
1 mark
Conclusion: The viscosity of glycerin at 25ᵒC was 1.132 Nsmˉ¹.
Discussion
The linear relation between Vt and (X – H) indicates that as one increases, the other
does the same. This can be seen on the straight-line graph plotted- direct proportionality
observed.
If one was to compare the viscosity of blood to that of glycerin and water, it would be
found that blood is more viscous than water but less viscous that glycerin. Unlike water,
blood is non-Newtonian because its viscosity increases at low flow velocities (e.g., during
circulatory shock). For liquids such as water, viscosity can be perceived as a measure of the
liquid’s resistance to flow or how thick it is. Therefore, it can be understood that the viscosity
of blood will be higher than the viscosity of water. Low flow states permit increased
molecular interactions to occur between red cells and between plasma proteins and red cells.
This can cause red cells to stick together and form chains of several cells (rouleau formation)
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within the microcirculation, which increases the blood viscosity. Increased viscosity increases
the resistance to blood flow and thereby increases the work of the heart and impairs organ
perfusion. Some patients with anaemia have low haematocrits, and therefore reduced blood
viscosities. Too high a blood viscosity may cause thin blood vessels to rupture as the physical
properties do not cater for such viscous blood flow. Blood flow is laminar except where the
great vessels branch off and turbulence occurs. Blood flow is turbulent in the heart and the
arch of the aorta during a great part of systolic ejection.
1 mark
Viscosity is seen in every day life. Due to its high viscosity, extracting and processing
honey can occasionally be challenging. For instance, if the honey is excessively thick and
sticky, it will be challenging to remove it from the honeycomb, filter it, and package it. The
amount of water, kind, and sugar content in honey all affect its viscosity. Honey loses
viscosity as water content is increased. Honey's viscosity is influenced by temperature, and
heat is frequently used to reduce honey's viscosity and facilitate processing. 1 mark
Personally, procedure two was not only the easier part of the experiment to perform
but it is also to understand. Calculations were easier and results were more accurate. ? Not
Clear.
Advantages and Disadvantages
Procedure 1
Advantage – Results were more detailed and therefore more accurate and reliable. ?
Disadvantage – Is a procedure that takes very long and as a result, participants were unable
to take repeat reading to determine an average for more accurate results.
Procedure 2
Advantage – Took a short time and the concept was easier to grasp.
Disadvantage – The extraction process to remove spheres from the tube, resulted in glycerin
getting on the table, other apparatus and on participants. ?
Source of Errors
Procedure 1

The water height was not increased far enough each time, this resulted in the volume
of water collected each time to be very close. It did not allow for a wider range of
numbers for a better investigation of accuracy. Improvement?
November 22nd,2022
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Procedure 2


Surface of spheres were worn down, resulting in an inconsistent diameter reading.
Improvement?
The speed at which at which the spheres descended the tube was fast so the human
reaction time for starting and stopping the stopwatch may result to inaccurate results.
This can be improved by allowing for repeat reading and then have the average
calculated.
(0.5 mark)
References
Akshit (2021) 12 viscosity examples in daily life, StudiousGuy. StudiousGuy. Available at:
https://studiousguy.com/viscosity-examples/ (Accessed: November 30, 2022).
Yildirim Çinar, A. Mete Şenyol, Kamber Duman, Blood viscosity and blood pressure: role of
temperature and hyperglycemia, American Journal of Hypertension, Volume 14, Issue 5, May
2001, Pages 433–438, https://doi.org/10.1016/S0895-7061(00)01260-7
Viscosity of Blood (no date) Image for Cardiovascular Physiology Concepts, Richard E
Klabunde PhD. Available at:
https://www.cvphysiology.com/Hemodynamics/H011#:~:text=Increased%20viscosity
%20increases%20the%20resistance,influences%20blood%20viscosity%20is%20tempe
rature. (Accessed: November 30, 2022).
Admin (2022) Viscosity of water - what is viscosity and what is the viscosity of water?,
BYJUS. BYJU'S. Available at: https://byjus.com/chemistry/viscosity-ofwater/#:~:text=The%20viscosity%20of%20water%20at,deformation%20at%20a%20gi
ven%20rate. (Accessed: November 30, 2022).
Admin (2022) Viscosity - definition, meaning, types, formula, unit, example, BYJUS. BYJU'S.
Available at: https://byjus.com/physics/viscosity/ (Accessed: November 30, 2022).
Viscosity (no date) Encyclopædia Britannica. Encyclopædia Britannica, inc. Available at:
https://www.britannica.com/science/viscosity (Accessed: November 30, 2022).
Vedantu (2022) Stokes' theorem and Terminal Velocity for jee, VEDANTU. Vedantu.
Available at: https://www.vedantu.com/iit-jee/stokes-theorem-and-terminal-velocity
(Accessed: November 30, 2022).
No in-text citation (0.5 mark)
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