Daniel Bernoulli
HIS THEOREM and CONTRIBUTIONS…..
By: ADITHYA SUNIL
from XI-N
ACKNOWLEDGEMENT
❖I WOULD LIKE TO EXPRESS MY SINCERE
GRATITUDE TO ALL THESE INDIVIDUALS FOR
MENTORING AND SUPPORTING ME…….
❖AND MY TEACHER - MR MANOGARAN
LOGANATHAN FOR GIVING ME THE
GOLDEN OPPORTUNITY TO PRESENT THIS
PROJECT….
❖TO MY PARENTS, THEIR CONSTANT
ENCOURAGEMENT, PATIENCE, AND
UNDERSTANDING HAVE BEEN THE PILLARS
OF MY SUCCESS.
❖I AM GRATEFUL TO MY FRIENDS WHO
CONTRIBUTED IDEAS AND PERSPECTIVES
THAT ENRICHED THE PROJECT.
❖THANK YOU EVERYONE FOR SHAPING THIS
PROJECT AND ENHANCING MY LEARNING
EXPERIENCE…….
➢www.wikipedia.com
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➢www.encylopedia.com
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➢www.brainly_india.com
➢www.britannica.com
• Daniel Bernoulli’s Theorem
• What Is Bernoulli’s Principle ?
• Bernoulli’s Principle Formula
• Derivation Of The Formula
• Applications
• His Contributions For The
World:
i. IN Mathematics
ii.Physics
iii.Economics
• His Legacy
❖ Daniel Bernoulli, a Swiss Standard
German Was A Swiss Mathematician And Physicist
And Was One Of The Many Prominent
Mathematicians In The Bernoulli Family From Basel.
He Is Particularly Remembered For His Applications
Of Mathematics To Mechanics, Especially Fluid
Mechanics, And For His Pioneering Work In
Probability And Statistics. His Name Is
Commemorated In The Bernoulli's Principle, A
Particular Example Of The Conservation Of Energy,
Which Describes The Mathematics Of The
Mechanism Underlying The Operation Of Two
Important Technologies Of The 20th Century: The Carburettor And The Aeroplane Wing.
❑ Bernoulli’s principle formulated by
Daniel Bernoulli states that as the speed of
a moving fluid increases (liquid or gas), the
pressure within the fluid decreases.
Although Bernoulli deduced the law, it was
Leonhard Euler who derived Bernoulli’s
equation in its usual form in the year 1752.
What is Bernoulli’s
Principle ?
➢ Bernoulli’s principle states that,
➢The total mechanical energy of the
moving fluid comprising the gravitational
potential energy of elevation, the energy
associated with the fluid pressure and the
kinetic energy of the fluid motion, remains
constant.
DERIVATION
• First, We Will Calculate The Work Done
(W1) On The Fluid In The Region BC. Work
Done Is
• W1 = P1A1 (V1∆t) = P1∆V
• Moreover, If We Consider The Equation Of
Continuity, The Same Volume Of Fluid Will
Pass Through BC And DE. Therefore, Work
Done By The Fluid On The Right-hand Side
Of The Pipe Or DE Region Is
• W2 = P2A2 (V2∆t) = P2∆V
• Thus, We Can Consider The Work Done On
The Fluid As – P2∆V. Therefore, The Total
Work Done On The Fluid Is
• W1 – W2 = (P1 − P2) ∆V
• The Total Work Done Helps To Convert
The Gravitational Potential Energy And
Kinetic Energy Of The Fluid. Now, Consider
The Fluid Density As Ρ And The Mass
Passing Through The Pipe As ∆M In The
∆T Interval Of Time.
• Hence, ∆M = Ρa1 V1∆t = Ρ∆v
The Bernoulli equation is applied to
all incompressible fluid flow problems.
❖ The Bernoulli equation can be
applied to devices such as the orifice
meter, venturi meter, and pitot tube
and its applications for measuring flow
in open channels and inside tubes.
❖ Venturi meter is a device that is
based on Bernoulli's principle and
used to determine the rate of flow
through a pipe. It works by measuring
the pressure drop across a section
near the pipe. For an incompressible
fluid, reducing the diameter will
increase the fluid flow velocity.
❖
IN PUMPS
IN AEROPLANES
FLUID MECHANICS
HIS
CONTRIBUTIONS
FOR THE WORLD
MATHEMATICS
❑His earliest mathematical work was the
Exercitations (Mathematical Exercises),
published in 1724 with the help of
Goldbach. Two years later he pointed out for
the first time the frequent desirability of
resolving a compound motion into motions
of translation and motion of rotation.
❑His chief work is Hydrodynamica,
published in 1738. It resembles Joseph
Louis Lagrange's Mécanique Analytique in
being arranged so that all the results are
consequences of a single principle, namely,
conservation of energy. This was followed
by a memoir on the theory of the tides, to
which, conjointly with the memoirs by
Euler and Colin Maclaurin, a prize was
awarded by the French Academy: these
three memoirs contain all that was done on
this subject between the publication of
Isaac Newton's Philosophiae Naturalis
Principia Mathematica and the
investigations of Pierre-Simon Laplace.
❑Bernoulli also wrote a large number of
papers on various mechanical questions,
especially on problems connected with
vibrating strings, and the solutions given
by Brook Taylor and by Jean le Rond
d'Alembert.
❖In Hydrodynamica (1738) He Laid
The Basis For The Kinetic Theory
Of Gases, And Applied The Idea
To Explain Boyle's Law.
❖He Worked With Euler On
Elasticity And The Development
Of The Euler–Bernoulli Beam
Equation.
❖Bernoulli's Principle Is Of Critical
Use In Aerodynamics.
❖According To Léon Brillouin, The
Principle Of Superposition Was
First Stated By Daniel Bernoulli
In 1753: "The General Motion Of A
Vibrating System Is Given By A
Superposition Of Its Proper
Vibrations."
➢In His 1738 Book SPECIMEN THEORIAE NOVAE
DE MENSURA SORTIS (Exposition Of A New
Theory On The Measurement Of Risk),Bernoulli
Offered A Solution To The St. Petersburg Paradox As
The Basis Of The Economic Theory Of Risk Aversion,
Risk Premium, And Utility.
➢Bernoulli Often Noticed That When Making
Decisions That Involved Some Uncertainty, People
Did Not Always Try To Maximize Their Possible
Monetary Gain, But Rather Tried To Maximize
"Utility", An Economic Term Encompassing Their
Personal Satisfaction And Benefit. Bernoulli Realized
That For Humans, There Is A Direct Relationship
Between Money Gained And Utility, But That It
Diminishes As The Money Gained Increases…..
➢One Of The Earliest Attempts To Analyse A
Statistical Problem Involving Censored Data Was
Bernoulli's 1766 Analysis Of Smallpox Morbidity And
Mortality Data To ---
DEMONSTRATE THE
EFFICACY OF
INOCULATION.
CONCLUSION
• In 2002,
Bernoulli was
inducted into
the
International Air
& Space Hall of
Fame at the San
Diego Air &
Space Museum.
CERTIFICATE OF
COMPLETION
➢This Is To Certify That Adithya Sunil
From XI-N Has Successfully Completed
The Physics Holiday Homework – The
Project On The Topic
“Bernoulli Theorem”.
Teacher In Charge :- MR MANOGARAN LOGANATHAN
Date Of Issue :- 27/10/24
SIGNATURE :-