CHEMICAL ENGINEERING LABORATORY 1
(BKC1752)
Title of Experiment
: Pressure Change Analysis
Date of Experiment
: 03/04/2023
Instructor’s Name
: Dr. Siti Hatijah Binti Mortan
Group No.
: 01
Section
: 02G
List of Students:
Name
ID
1. KIVENRAJ A/L BALAN
KA22049
2. PRIVEEN RAJ THEVAR A/L SELVAN
KA22081
3. HARITH SUFYAN BIN SYAMSUL AZRI
KA22074
4. NARMATHA A/P RAJALINGGAM
KA22105
5. EMMANUEL PAUL A/L RICHARD PAUL
KA22087
6. SHARUL SAZWAN BIN MOHD. AHMADI
KA22066
Marks:
1.
Abstract
6.
Results
2.
Methodology flowchart
7.
Discussion
3.
Data Tabulation
8.
Conclusions
4.
Graph
9.
References
5.
Calculations
10. Grammar and Spelling
TOTAL
Tear here
Subject Code: BKC1752
Please keep for student reference.
Date Submitted :
Title of Experiment:
Submitted by;
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Received by;
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ABSTRACT
Pressure change analysis is an analysis to observe the effect of specific parameters on the
fluid velocity and pressure at various points. The objective of this experiment carried out is to
relate the effect of each parameter with the Bernoulli's principle. Bernoulli’s principle states
that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or a
decrease in the fluid's potential energy. The principle is named after Daniel Bernoulli who
published it in his book Hydrodynamica in 1738. Bernoulli’s principle also states that within
an ideal fluid, the sum of thermal energy, kinetic energy, and potential energy must be
constant. Thus, the relationship between pressure and velocity can be made, where points
with higher velocity will have lower pressure in comparison with points with lower velocity.
The data obtained is used to relate the effect of each parameter with Bernoulli’s principle by
comparing the time taken for the fluid to reach the desired points. In this experiment, the
chemicals used were oil and water. The experiment begins with the preparation of three
mineral water bottles which were labeled and nailed with a nail size of 2mm at the 200ml
mark. Then, the bottles were filled with 1000ml of water, and the nail was removed to record
the time taken for every 200ml reduction in volume. The experiment was repeated with nail
sizes of 3mm, and 4mm, and oil as the fluid in the bottle for all nail diameters. Based on the
results, it is observed that the bottles with larger diameters took less time to reach 800, 600,
400, and 200ml, respectively. The fluid type also resulted in different results, where oil took
more time on average to reach the targeted volume. Hence, it proved Bernoulli’s principle
correlates well with pressure change analysis, where external factor such as height, area, and
density affects the pressure resulting in a higher velocity of the fluids. In certain cases,
viscosity has also been considered since density affects the velocity of fluids insignificantly
when both fluids have different viscosity.
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METHODOLOGY
3
RESULTS
Table 1.1: Time taken for the liquid to flow out from the bottle for every 200 ml for 2mm
sized nail.
Time Taken (s)
Volume (ml)
Diameter = 2mm
Water
Oil
1000
0.00
0.00
800
24.36
26.94
600
55.48
62.98
400
94.76
113.04
200
270.00
303.08
Table 1.2: Time taken for the liquid to flow out from the bottle for every 200 ml for 3mm
sized nail.
Time Taken (s)
Diameter = 3mm
Water
Oil
0
0
8.81
12.54
20.59
25.05
34.61
36.49
70.56
122.41
Volume (ml)
1000
800
600
400
200
Table 1.3: Time taken for the liquid to flow out from the bottle for every 200 ml for 4mm
sized nail.
Time Taken (s)
Diameter = 4mm
Water
Oil
Volume (ml)
0
6
16.13
29.55
62.37
1000
800
600
400
200
4
0
10.61
20.91
34.77
73.81
DISCUSSION
The relationship between the pressure and speed of an incompressible fluid moving through a
pipe or channel is known as Bernoulli's principle. It claims that pressure within a fluid falls as
the fluid's velocity rises and vice versa. The 18th-century Swiss mathematician Daniel
Bernoulli, who made this discovery, is honored with the name of this principle.
Bernoulli's principal equation, which is stated as follows, may be used to quantitatively
represent the relationship between the dynamic pressure, velocity, and cross-sectional area.
1 2 𝑃
𝑣 + + 𝑔ℎ = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
2
𝜌
Where :
v: velocity
P: pressure
ρ: density
g: gravity acceleration
h: height
Therefore, as the cross-sectional area of the pipe or channel is reduced, the velocity of the
water will increase, and the pressure within the water will decrease. This decrease in pressure
will cause an increase in dynamic pressure
1) How does the change in the cross-sectional area affect the dynamic pressure?
Bernoulli's principle states that a fluid's dynamic pressure is inversely proportional to the
cross-sectional area of the pipe or channel through which it is flowing. Dynamic pressure,
commonly referred to as velocity pressure, is the pressure brought on by a fluid's motion and
is described as:
1
Dynamic pressure (Pd) = 2 𝜌𝑣 2
where q is the dynamic pressure, ρ is the density of the fluid, and v is the velocity of the fluid.
The relationship between the dynamic pressure and cross-sectional area can be understood by
examining the continuity equation in the example below, which states that the mass flow rate
of a fluid is constant along a pipe or channel, provided the fluid is incompressible and there
are no leaks.
(𝐴1)(𝑣1) = (𝐴2)(𝑣2)
where v1 and v2 are the fluid velocities at those places, and A1 and A2 are the cross-sectional
areas of the pipe or channel at those points.
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From this equation, it can be seen that as the cross-sectional area of a pipe or channel
decreases, the velocity of the fluid must increase to maintain a constant mass flow rate. As
the velocity increases, the dynamic pressure of the fluid also increases, according to the
formula for dynamic pressure.
Conversely, as the cross-sectional area of a pipe or channel increases, the velocity of the fluid
must decrease to maintain a constant mass flow rate. As the velocity decreases, the dynamic
pressure of the fluid also decreases.
2) How does the height and density of the liquid affect the velocity?
Bernoulli's principle states that in a fluid flow, an increase in velocity is accompanied by a
decrease in pressure and vice versa, assuming that the flow is steady and incompressible. The
principle applies to all fluids, including liquids and gases, and is based on the conservation of
energy.
Regarding the effect of height and density on velocity in Bernoulli's principle, we can
consider the following:

Height: In a vertical flow, the height of the fluid column can affect the velocity of the
fluid. The higher the column, the greater the potential energy of the fluid, and
therefore the greater the velocity. This is due to the fact that the potential energy is
converted into kinetic energy as the fluid falls, and the velocity increases accordingly.
Conversely, as the height decreases, the velocity of the fluid decreases.

Density: The density of the fluid can also affect the velocity of the fluid in a flow. As
the density of the fluid increases, the pressure decreases, according to Bernoulli's
principle. This decrease in pressure can result in an increase in velocity, assuming that
the flow rate remains constant. Conversely, if the density of the fluid decreases, the
pressure increases, and the velocity decreases.
It is important to note that the effect of height and density on velocity in Bernoulli's principle
can be more complicated in practical situations, where there are additional factors to
consider, such as viscosity, turbulence, and boundary effects. Nonetheless, the basic
relationship between height, density, and velocity holds true, and Bernoulli's principle
remains a valuable tool for understanding fluid flows.
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3) Plot the graph for volume (V)* or height (H) versus time (t) at different crosssectional area.
Figure 1.1: Volume (mL) versus time taken (s) for 4π mm2
Graph of Volume (mL) versus time taken (s) for 4π mm2
1100
1000
Volume (mL)
900
800
700
600
Water
500
Oil
400
300
200
0
50
100
150
200
250
300
350
Time Taken (s)
Fig 1.2: Volume (mL) versus time taken (s) for 9π mm2
Graph of Volume (mL) versus time taken (s) for 9π mm2
1100
1000
Volume (mL)
900
800
700
600
Water
500
Oil
400
300
200
0
20
40
60
80
Time Taken (s)
7
100
120
140
Figure 1.3: Volume (mL) versus time taken (s) for 16π mm2
Graph of Volume (mL) versus time taken (s) for 16π mm2
1100
1000
Volume (mL)
900
800
700
600
Water
500
Oil
400
300
200
0
10
20
30
40
50
60
70
80
Time Taken (s)
4) Find the relation between velocity of the liquid and cross-sectional area from plot V
vs t.
According to Figures 1.1, 1.2 and 1.3, it can be observed that the velocity of the liquid
increases as the cross-sectional area of the nail increases. For example, the time taken for the
water level to reach 200ml are 270, 62.37 and 70.56. Comparing the results obtained from
Figure 1.1 and Figure 1.3, we can see that the time taken for volume of water to decrease at
each 200ml mark are 18.36, 39.35, 65.21 and 207.63, longer for the nail with 2mm diameter
than the nail with 4mm diameter. At the same time, the time taken in Figure 1.1 were 15.55,
34.89, 60.15 and 199.44 seconds longer than the time taken in Figure 1.2 for every 200ml.
A similar observation can be made for when oil is used as the liquid in the bottle, where
the time taken by oil to reach the 200ml level for 2, 3 and 4mm nail diameter were 303.08,
122,41 and 73.81 seconds, respectively. When comparing the time taken from data in 2mm
with 4mm, the time taken would be 16.33, 45.07, 78.27 and 229.27 seconds slower, whereas
the data of 2mm, when compared with 3mm, were slower by 14.40, 37.93, 76.55 and 190.67
seconds.
The result obtained from both liquids proves the hypothesis that where larger the crosssectional area, the greater the velocity of the liquid. This phenomenon is due to Bernoulli’s
principle, where a larger area results in lower pressure, which causes higher velocity.
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CONCLUSION AND RECOMENDATION
In conclusion, cross sectional area has been affecting the fluid velocity which means
the smaller the cross-sectional area, the higher the fluid velocity. Moreover, level with higher
pressure will give a higher fluid velocity. Fron the result of this pressure change analysis
experiment, for the smallest diameter 2mm has the highest velocity compared to hole in the
diameter of 3mm and 4mm. Based on the results, it is observed that the bottles with larger
diameters took less time to reach 800, 600, 400, and 200ml, respectively. The parameters of a
bottle and holes that will affect the Bernoulli’s principle are the density, cross sectional area
and also the pressure of the liquid at various points. The fluid type also resulted in different
results, where oil took more time on average to reach the targeted volume compared to water.
Hence, its proved Bernoulli’s principle correlates well with pressure change analysis, where
external factors such as height, area, and density affect the pressure resulting in a higher
velocity of the fluids. In certain cases, viscosity has also been considered since density affects
the velocity of fluids insignificantly when both fluids have different viscosity.
However, we were not able to certain that the hole of nails has a diameter of exactly
2mm, 3mm, 4mm as reported above. In addition, we are not even able to claim that the
“hole” is circular in shape. There were small, jagged edges around the edge of the opening
that were a result of the non-perfect drill. Therefore, the velocity of the liquid is too difficult
to determine accurately for this experiment. Hence, it clearly shows that our method of
creating the hole is by using a nail into a plastic bottle will not result in perfect size as we
desired. Therefore, the results of the experiment might not be precise. As recommendation to
improve and get precise values for the experiments results, the diameter of the nails must be
measure accurately using an apparatus like Vernier Caliper to get a more accurate crosssectional area which is one of the parameters in Bernoulli’s principle. The largest error in this
lab is that we wished to find the instantaneous flow rate of the liquid given a height.
Therefore, an average flow rate should also require using the average height, or Height =
height initial – height final. This could potentially provide more accurate data, especially as
the height increases. The most convenient way to fix this error would be to decrease the
amount of time that the water drains. Besides, the time taken for the water or oil to stop
flowing out must be recorded accurately
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REFERENCE
1. Khan Academy: What is Bernoulli's
principle?https://www.khanacademy.org/science/physics/fluids/fluid-dynamics/a/what-isbernoullis-equation
2. Habib Ahmari and Shah Md Imran Kabir; Open Educational Resources (OER), by the
University of Texas at Arlington Libraries (UTA Libraries), Applied Fluid Mechanics
Lab Manual
https://uta.pressbooks.pub/appliedfluidmechanics/chapter/experiment-2/
3. Anup Kumar Dey, 2023, Assumption in Bernoulli’s Equation:
https://whatispiping.com/bernoullis-equation-principle-examples/
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APPENDIX
Figure 1: Mark a scale every 200 ml on the bottle (starting from the bottom of the bottle) until
1000 ml.
Figure 2: By using a nail sized 2 mm, make a hole at the scale of 200 ml
Figure 3: Observe and record the time when the water decrease every 200ml
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