This a lab report about finding the Bernoulli theorem demonstration

1. 13
Experiment No. (7)
Bernoulli’s theorem Demonstration
Petroleum Engineering Department
Faculty of Engineering
Koya University
Prepared by:
1-Kaiwan B. HamaSalih 2- Rebin F. Hussien
Supervised by:
Dr. Jaffar A. Ali Mr. Nawrasi
Fluid Mechanics Lab
Lab Report

2. 2
Summary
In this experiment our goal was to find the Demonstrating of Bernoulli’s equation. By measuring the Hm and Ht and then we find
the flow rate, volume, time for each of them. Bernoulli's equation is a powerful tool for understanding and predicting the behaviour
of fluids in various applications to measure flow using devices like weirs, Parshall flumes, and venturimeters, which are commonly
used in hydraulics and civil engineering. It provides valuable insights into the relationship between pressure, velocity, and
elevation in flowing fluids, helping engineers and scientists design and optimize systems that rely on fluid dynamics.

3. 2
Table of Content
Subject Pages
Introduction……………………………………......………………………………………… 4
Aim/Objective of Experiment…….........…………………………………………………… 4
Theory of the experiment…………………………………………………………………… 5
Table of Reading.…………………...………………………………………………………. 6
Sample of Calculation....…………...………………………………………………………. 7-9
Table of Calculation………………...………………………………………………………. 10
Result………………………………………………………………………………………... 11
Discussion (Kaiwan B. HamaSalih) ....……………………………………………………... 12-14
Discussion (Rebin F. Hussien)……………………………………………………………… 15
Conclusion………………………....………………………………………………………... 16
Reference………………………....…………………………………………………………. 17

4. 2
Introduction:
Rhett Allain (Mar 6, 2018) Bernoulli's theorem is a fundamental principle in fluid dynamics that states that the sum of the pressure,
kinetic energy, and potential energy per unit volume remains constant in an incompressible and frictionless flow [1]. Rhett Allain
(Mar 6, 2018) This theorem has numerous real-world applications, such as understanding airplane aerodynamics, calculating wind
load on buildings, and designing water supply and sewer networks [1]. Rhett Allain (Mar 6, 2018) A simple demonstration of
Bernoulli's theorem can be performed using a sheet of paper and a fan. By blowing air onto the paper, the air on the top moves
faster than the air on the bottom, resulting in a lower pressure on the top and a greater force pushing up [1]. Siti Syuhadah (Mar
19, 2016) So, Bernoulli's Principle states that for an inviscid flow of a non-conducting fluid, an increase in the speed of the fluid
occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy [2]. Siti Syuhadah (Mar 19, 2016)
Bernoulli's Principle is named in honor of Daniel Bernoulli who published it in his book Hydrodynamic in 1738 [2]. Siti Syuhadah
(Mar 19, 2016) Suppose a fluid is moving in a horizontal direction and encounters a pressure difference [2]. Siti Syuhadah (Mar
19, 2016) This pressure difference will result in a net force, which is by Newton's Second Law will cause an acceleration of the
fluid [2]. Siti Syuhadah (Mar 19, 2016) Bernoulli's Principle can be demonstrated by the Bernoulli equation [2]. Siti Syuhadah
(Mar 19, 2016) The Bernoulli equation is an approximate relation between pressure, velocity, and elevation [2]. Siti Syuhadah
(Mar 19, 2016) While the Continuity equation relates the speed of a fluid that moving through a pipe to the cross-sectional area
of the pipe [2]. Siti Syuhadah (Mar 19, 2016) It says that as a radius of the pipe decreases the speed of fluid flow must increase
and vice-versa [2].
Aim/Objective of Experiment
 Demonstrating of Bernoulli’s equation.

5. 2
Theory of the experiment:
For ideal fluid flow the total energy at a point on the same streamline is equal:
Total energy head (H1) at point (1) = Total energy head (H2) at point (2) = Total energy head (H3) at point (3) = Constant
& Total energy head (H)=
𝑃
𝛾
+
𝑣2
2𝑔
+ 𝑍
∴
P1
γ
+
v1
2
2g
+ Z1 =
P2
γ
+
v2
2
2g
+ Z2 =
P3
γ
+
v3
2
2g
+ Z3 = H ……………… [Bernoulli’s Equation]
Where:
𝑝
𝛾
: Static pressure head (pressure energy per unit weight).
𝑣2
2𝑔
: Velocity head (kinetic energy per unit weight).
Z: Potential head (Potential energy per unit weight).

6. 2
Unit description
The apparatus of the experiment is called Bernoulli’s theorem demonstration apparatus. The measurement object is a venturi tube
with 6 pressure measurement points. The 6 static pressures are displayed on a board with 6 water pressure gauges. The overall
pressure can also be measured at various locations in the venturi tube and indicated on a second water pressure gauge.
Measurement is by way of a probe which can be moved axially with respect to the venturi tube. The probe is sealed by way of a
compression gland. Water is supplied from the hydraulic bench.
1- Assembly boar. 2- Single water pressure gauge. 3- Discharge pipe. 4- Outlet ball cock
5- Venturi tube with 6 measurement points. 6- Compression gland.7- Probe for measuring
overall pressure (can be moved axially). 8- Hose connection, water supply. 9- Ball cock at
water inlet.10- 6-fold water pressure gauge (pressure distribution in venturi tube)

7. 2
Experimental Work:
No.
Q
(m
3
/s)
Hs (cm) Ht (cm) Hdyn (cm)
A B C D E F A B C D E F A B C D E F
1
222.2
24.5
23.5
6
14.5
19.5
20
34
33.5
33.3
32.7
31.2
30.3
9.5
10
27.3
18.2
11.7
10.3
2
217.3
21.5
20
4
12
16.5
17.5
30
29.3
29.2
28.6
28
27.5
8.5
9.3
25.2
16.6
11.5
10

8. 2
Table of Calculation:
NO
Q
Cm3
/s
hs= ps/y (cm) hd=v2
/2g(cm) Hcal (cm) Hm (cm)
hs1 hs2 hs3 hs4 hs5 hs6 hd1 hd2 hd3 hd4 hd5 hd6 Hcal1 Hcal2 Hca3l Hcal4 Hcal5 Hcal6 Hm1 Hm2 Hm3 Hm4 Hm5 Hm6
1 222.
883
24.5 23.5 6 14.5 19.5 20 313.9
Cm
500.
139
cm
1291.
81
cm
855.
85
cm
432.
334
cm
313.
912
cm
338.4
cm
523.
639
cm
1297.
81
cm
870.
35
cm
451.834
cm
347.
912
cm
34 33.5 33.3 32.5 31.1 30.3
2 217.
391
21.5 20 4 12 16.5 17.5 298.
669
Cm
475.
811
cm
1228.
93
cm
814.
191
cm
411.
285
cm
298.
64
cm
320.
169
cm
495.
811
cm
1232.
93
cm
826.
191
cm
427.
785
cm
316.
14
cm
30 29.3 29.2 28.6 28 27.5

9. 2

10. 2

11. 13
Results:
The results of the Bernoulli's theorem demonstration experiment can be summarized as
follows:
1. The experiment, conducted using the Bernoulli's Theorem Demonstration Apparatus,
aimed to demonstrate the validity of Bernoulli's theorem.
2. The apparatus consisted of a tapered duct (venturi), a series of manometers tapped into
the venturi to measure the pressure head, and a hypodermic probe that could be
traversed along the Centre of the test section to measure the flow velocity.
3. During the experiment, water was fed through a hose connector, and students could
control the flow rate of the water using a pump.
4. The objective of the experiment was to investigate the validity of Bernoulli's equation,
which was verified using the tapered duct (venturi) system.
5. The experiment demonstrated that when fluids move from a region of higher pressure
to a lower pressure, their velocity increases.
6. There were slight differences in the speed of the flow and pressure when using
Bernoulli's equation and the Continuity equation to calculate velocity.
Overall, the demonstration experiment successfully showed the principles of Bernoulli's
theorem in action and provided insights into its applications in fluid dynamics.

12. 2
Discussion-Kaiwan B. HamaSalih
1. Plot the pressure head (
𝑷𝒔
𝜸
) along the venture tube.
In this plot we see the distinctions between the tensions in (ps/y) in static heads in first
stream is higher than the subsequent stream and this due to the heads.
2. Plot the velocity head (
𝒗𝟐
𝟐𝒈
) along the venture tube.
In this plot we see the distinctions between the unique heads in (v2/2g) the subsequent
stream is lower than the first and y this as a result of heads
0
5
10
15
20
25
30
h1 h2 h3 h4 h5 h6'
𝑷𝒔/𝜸
hs
Curve between pressure head along the venture tube
0
500
1000
1500
2000
2500
3000
h1 h2 h3 h4 h5 h6
𝒗𝟐/𝟐𝒈
hs
Curve velocity & along the venture tube

13. 2
3. Plot the total energy head Hcal & Hm along the venturi tube.
4. what is the difference between the sum of the pressure kinetic energy density, and
gravitational potential energy density in Bernoulli equation demonstration?
In the Bernoulli's equation demonstration, the sum of pressure, kinetic energy density, and
gravitational potential energy density represents the total energy per unit volume of a fluid.
Each term has a specific meaning and impact on the fluid's behavior:
 Pressure: Pressure is the force per unit area exerted by a fluid on a surface. In
Bernoulli's equation, pressure is represented as ρgh, where ρ is the fluid density, g is
the acceleration due to gravity, and h is the height difference between two points in
the fluid. Pressure is an essential factor in determining the behavior of fluids and is a
key component of the Bernoulli's equation.
 Kinetic Energy Density: Kinetic energy density is the amount of energy associated
with the fluid's motion. In the context of Bernoulli's equation, it is represented as
ρv²/2, where ρ is the fluid density and v are the fluid velocity. Kinetic energy density
is a crucial term in understanding the relationship between the fluid's velocity and
pressure, as it represents the energy transferred to the fluid due to its motion.
80%
82%
84%
86%
88%
90%
92%
94%
96%
98%
100%
h1 h2 h3 h4 h5 h6
hs
Curve Hcal & Hm

14. 2
 Gravitational Potential Energy Density: Gravitational potential energy density is the
energy stored in a fluid due to its elevation or height difference. In Bernoulli's
equation, it is represented as ρgh, where ρ is the fluid density, g is the acceleration
due to gravity, and h is the height difference between two points in the fluid. This
term accounts for the energy transferred to the fluid due to its elevation and is
essential for understanding the behavior of fluids in gravity-driven systems.
The Bernoulli's equation demonstrates that the sum of these three terms remains constant along
a streamline for an incompressible, frictionless fluid. This relationship is a statement of the
conservation of energy, stating that the energy needed to increase the fluid's velocity comes at
the expense of the pressure energy. Understanding the behavior of these terms is crucial for
analyzing and predicting the flow of fluids in various applications, such as hydraulics,
aerospace, and environmental engineering.
5. What is the relationship between Bernoulli's equation and the conservation of
energy principle?
Bernoulli's equation is a statement of the conservation of energy principle for a flowing fluid.
It states that the sum of pressure, kinetic energy density, and gravitational potential energy
density at any two points in a steady streamline flowing fluid remains constant.
6. What are the assumptions behind Bernoulli's equation?
Bernoulli's equation relies on several assumptions, including steady flow, incompressible fluid,
and no losses from fluid friction.
7. How does Bernoulli's equation account for the effects of viscosity?
Bernoulli's equation is based on an idealized system, which assumes zero viscosity. Real fluids
have some viscosity, which can affect the flow and the accuracy of the equation. However, the
equation can still be used as a good approximation for many practical purposes, as the effects
of viscosity are often negligible.
8. How does the velocity of a fluid affect the Bernoulli’s equation demonstration?

15. 2
The volume of a fluid does not directly affect Bernoulli's equation. Instead, Bernoulli's
equation relates the pressure, velocity, and elevation of a fluid at a particular point along its
flow. The equation states that the sum of the pressure, kinetic energy density, and gravitational
potential energy density at any two points in a steady, streamline flowing fluid remains
constant. This relationship holds true for a small volume of fluid as it moves along its path.
Therefore, while the volume of the fluid is an important characteristic, it is not a direct factor
in the Bernoulli's equation demonstration. The equation is based on the conservation of energy
for an incompressible fluid in the absence of dissipative forces, and it is broadly applicable in
fluid dynamics.
9. How does Bernoulli's equation relate to the Venturi effect?
Bernoulli's equation is related to the Venturi effect, which states that as fluid velocity increases,
pressure decreases, and vice versa. This relationship is used in various applications, such as
wing design and pipe flow.
10.What are the factors that could effect on the experiment?
Several factors can affect the Bernoulli's equation demonstration experiment, which is used
to study the relationship between pressure, velocity, and elevation of a flowing fluid. Some
of these factors include:
1. Assumptions: The validity of Bernoulli's equation relies on certain assumptions, such as
steady flow, incompressible fluid, and no losses from fluid friction. If these assumptions
are not met, the accuracy of the equation may be compromised.
2. Viscosity: Bernoulli's equation is based on an idealized system, which assumes zero
viscosity. Real fluids have some viscosity, which can affect the flow and the accuracy
of the equation.
3. Flow Conditions: The experiment may not accurately represent real-world flow
conditions, such as turbulent flow or three-dimensional flow. This can limit the
applicability of the equation in certain situations.
4. Measurement Errors: The accuracy of the experiment depends on the precision of the
measurements taken, such as the pressure, velocity, and height of the fluid at different

16. 2
points along the flow. Errors in these measurements can affect the validity of the
equation.
5. Experimental Setup: The design and execution of the experiment can also impact the
results. For example, the tapered duct (venturi) used in the experiment should be
properly constructed and connected to manometers to measure the pressure head and
total head. Any errors in the setup can lead to inaccurate results.

17. 2
Discussion-Rebin F. Hussien
1. What is the main principle behind Bernoulli's theorem, and how does it relate to the
behavior of fluids in motion?
Bernoulli's principle relies on the conservation of energy in fluid dynamics, asserting that
when a fluid's velocity rises, its pressure decreases, and conversely. This connection
elucidates occurrences such as Venturi effect in narrowed pipes.
2. How does the Venturi meter utilize the principles of Bernoulli's theorem, and what is
its practical application in fluid measurement?
The Venturi meter employs Bernoulli's principle through a narrowed section in a pipe. As
fluid velocity rises in the constricted area, following Bernoulli's theorem, pressure decreases.
This pressure variance is utilized to gauge fluid flow rates in pipes, rendering Venturi meters
essential for measuring water and gas flows in diverse industrial applications.
3. What is relation between pressure and density in Bernoulli theorem experiment?
density and pressure are inversely proportional to each other's means high density fluid will
apply more pressure while moving than the low-density fluids.

18. 2
Conclusion:
Bernoulli's theorem is a fundamental principle in fluid dynamics, stating that the sum of
pressure, kinetic energy, and potential energy per unit volume remains constant in an
incompressible and frictionless flow. This theorem has various real-world applications, such
as in aerodynamics, calculating wind load on buildings, and designing water supply networks.
A simple demonstration of Bernoulli's theorem can be performed using a sheet of paper and a
fan, where the air blown onto the paper causes it to move up, illustrating the principle in action.
The theorem's applications are wide-ranging, from understanding airplane aerodynamics to
designing water supply networks.

19. 2
Reference:
1. Rhett Allain (Mar 6, 2018), Demonstration of Bernoulli’s principle You can try it at
home, Available at https://www.wired.com, Accessed at 7/12/2023.
2. Hasan Raby (Nov 30, 2020), Bernoulli’s principle Demonstration lab report, Available
at https://www.scribd.com, Accessed at 7/12/2023.
3. Siti Syuhadah (Mar 19, 2016), Lab report 3, Available at https://www.scribd.com,
Accessed at 8/12/2023.