bernoullis-THEOREM application and its derivations

bernoullis theorem and its applications with derivations with pictorial representation

1. A PRESENTATION ON BERNOULLI’STHEOREM
Preparedby
RINKU JANGRA
ASSISTANTPROFESSOR
CivilEngineeringDepartment
Ganga Institute of Technology & Management,Kablana
Jhajjar(Haryana)

2. BERNOULLI’SPRINCIPLE
ANDITS
APPLICATIONS
y
1
y
2
x
1
x
2 p
2
A
2
A
1
v
1
v
2

p
1
X
Y
time1
time2
m
m

3. DERIVATION OFBERNOULLI’S
EQUATION

4. DERIVATION OF BERNOULLI’S EQUATION

5. DERIVATION OF BERNOULLI’S EQUATION
Since work
has been
done, there
has been a
change in
the
mechanical
energy of
the fluid
segment.
Thisenergy
change is
found with
the help of
the next
diagram.

6. DERIVATION OF BERNOULLI’S EQUATION

7. Bernoulli’sEquation
A fluid can also change its
height. By looking at thework
done as it moves, wefind:
This is Bernoulli’s equation.
One thing it tells us is thatas
the speed goes up, the
pressure goesdown.

8. Applications of Bernoulli’s Principle:Torricelli,
Airplanes, Baseballs, BloodFlow
Using Bernoulli’s principle, we find that the speed offluid
coming from a spigot on an open tankis:
This is calledTorricelli’s
theorem.

9. Applications of Bernoulli’s Principle:Torricelli,
Airplanes, Baseballs, BloodFlow
Lift on an airplane wing is due to the different airspeeds
and pressures on the two surfaces of thewing.

10. Applications of Bernoulli’s Principle:Torricelli,
Airplanes, Baseballs, BloodFlow
A sailboat can moveagainst
the wind, using thepressure
differences on each side of
the sail, and using the keel
to keep from going
sideways.

11. Applications of Bernoulli’s Principle:Torricelli,
Airplanes, Baseballs, BloodFlow
A ball’s path will curvedue
to its spin, which results in
the air speeds on the two
sides of the ball not being
equal.

12. Applications of Bernoulli’s Principle:Torricelli,
Airplanes, Baseballs, BloodFlow
A person with
constricted arterieswill
find that they may
experience atemporary
lack of blood to the
brain as blood speeds
up to get past the
constriction, thereby
reducing thepressure.

13. Applications of Bernoulli’s Principle:Torricelli,
Airplanes, Baseballs, BloodFlow
Aventurimetercanbeusedtomeasurefluidflowby
measuring pressuredifferences.

14. Applications of Bernoulli’s Principle:Torricelli,
Airplanes, Baseballs, BloodFlow
Air flow across the top helps smoke go up a chimney,and
air flow over multiple openings can provide the needed
circulation in undergroundburrows.

15. THANKSFORWATCHING!