1. Bernoulli’s Principle
Theory and Applications

2. Daniel Bernoulli
Bernoulli was a Swiss mathematician and physicist.
He discovered this principle while conducting experiments about the conservation of energy.
His results were published in Hydrodynamica (1738).
Leonhard Euler ( ), a German mathematician, generalized Bernoulli’s findings into what we know as the Bernoulli principle.

3. What does Bernoulli’s principle state?
When the speed of a fluid increases, the internal pressure in the fluid decreases
P α 1/v
Pressure is defined as the force per unit area.
The units of pressure in the SI system are pascals: 1 Pa = 1 N/m2

4. conservation of energy
P+ ρgy + ½ ρv2 = constant
If no change in height:
P + ½ρv2 = constant
faster speed
slower speed
more pressure
less pressure

5. conservation of energy
kinetic
energy
Motion of fluid
Pressure in fluid
potential
energy
KE + PE is constant

6. Bernoulli & Flight
Bernoulli’s Principle is what allows birds and planes to fly.
The secret behind flight is ‘under the wings.’

7. Applications of Bernoulli’s Principle
Lift on an airplane wing is due to the different air speeds and pressures on the two surfaces of the wing.

8. On top: greater air speed and less air pressure
AIRPLANE WING
On top: greater air speed and less air pressure v2 v1
On bottom: less air speed and more air pressure

9. AIR Creates Lift In Other Words . . . .
The air on top of the wing must travel a longer distance than the air below the wing. But, air on both sides must reach the end of the wing at the same time. Therefore, the air on top of the wing traveling faster = less air pressure.
Creates Lift
AIR

10. AIRPLANE WING
LIFT

11. Applications of Bernoulli’s Principle
The Spoiler on a race car provides better traction and avoids lift

12. Spoiler – airfoil reversed
less air speed
more pressure
greater air speed
less pressure
net force: downward

13. Applications of Bernoulli’s Principle
In a serve storm how does a house loose its roof?
Air flow is disturbed by the house. The "streamlines" crowd around the top of the roof  faster flow above house  reduced pressure above roof than inside the house  room lifted off because of pressure difference.
Why do rabbits not suffocate in the burrows?
Air must circulate. The burrows must have two entrances. Air flows across the two holes is usually slightly different  slight pressure difference  forces flow of air through burrow. One hole is usually higher than the other and the a small mound is built around the holes to increase the pressure difference.

14. Wind over a roof
Patm = Proof + ½ ρv2 v
proof
v = 0
patm

15. Applications of Bernoulli’s Principle
Air flow over multiple openings can provide the needed circulation in underground burrows.

16. Winds over a mountain
Wind and Weather

17. Atomizer – As air passes at top of tube,
the pressure decreases and fluid is drawn up
the tube.

18. What happens to the paper when you blow across the top?
Paper rises
Why?
Breath speeds air molecules which decrease pressure on top of paper
The pressure under the paper pushes the paper up

19. Shower Curtain
Use Bernoulli’s principle to explain why your shower curtain blows inward with a hot shower.
Hot inside shower
Air molecules speed up inside shower; therefore, pressure decreases inside shower
Air outside shower with more pressure pushes shower curtain in

20. Another Example
What could you do to get the ping pong balls to move toward each other?
Increase speed of air between the ping pong balls
This would decrease the pressure
Air outside ping balls would have more pressure and push them toward each other

21. Bernoulli’s Principle at Home
Wind blowing across the top of a chimney lowers the air pressure, therefore the higher air pressure at the bottom pushes the air and smoke up the chimney.

22. Atmospheric Pressure and Gauge Pressure
At sea level the atmospheric pressure is about ; this is called one atmosphere (atm).
Another unit of pressure is the bar:
Standard atmospheric pressure is just over 1 bar.
This pressure does not crush us, as our cells maintain an internal pressure that balances it.

23. Atmospheric Pressure and Gauge Pressure
Most pressure gauges measure the pressure above the atmospheric pressure – this is called the gauge pressure.
The absolute pressure is the sum of the atmospheric pressure and the gauge pressure.

24. Measurement of Pressure; Gauges and the Barometer
This is a mercury barometer, developed by Torricelli to measure atmospheric pressure. The height of the column of mercury is such that the pressure in the tube at the surface level is 1 atm.
Therefore, pressure is often quoted in millimeters (or inches) of mercury.

25. Flow Rate and the Equation of Continuity
If the density doesn’t change – typical for liquids – this simplifies to Where the pipe is wider, the flow is slower.

26. Applications of Bernoulli’s Principle
A venturi meter can be used to measure fluid flow by measuring pressure differences.

27. Summary Phases of matter: solid, liquid, gas.
Liquids and gases are called fluids.
Density is mass per unit volume.
Pressure is force per unit area.
Pressure at a depth h is ρgh.
External pressure applied to a confined fluid is transmitted throughout the fluid.

28. Summary Atmospheric pressure is measured with a barometer.
Gauge pressure is the total pressure minus the atmospheric pressure.
Where the velocity of a fluid is high, the pressure is low, and vice versa.