Applications of Bernoulli

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Applications of Bernoullis Principle

• Georgia CTAE Resource Network
• Curriculum Office
• Philip Ledford and Dr. Frank Flanders

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Daniel Bernoulli

• Daniel Bernoulli was a Dutch-Swiss mathematician
  who is most known for his work in fluid mechanics
  and for his boom Hydrodynamica.
• Bernoulli came up with the equitation
• where
• is the fluid flow speed at a point on a
  streamline,
• is the acceleration due to gravity,
• is the elevation of the point above a reference
  plane, with the positive z-direction pointing
  upward so in the direction opposite to the
  gravitational acceleration,
• is the pressure at the point, and
• is the density of the fluid at all points in
  the fluid.

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Bernoullis Equation

• What does it mean?
• In a simplified non-mathematical explanation,
  Bernoullis equation basically means that if
  velocity (the speed of motion) of a fluid
  increases, the pressure within (the force per
  unit area applied to an object) the fluid
  decreases.
• Bernoullis principle is used in aerodynamics and
  help explains how airplane get lift, and how race
  cars stay on the ground. It also has uses in lots
  of different machines such as a Hozon for
  agricultural use.

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Hozon Siphon Mixer
A Hozon siphon mixer is used agriculturally to
fertilize plants. This device operates somewhat
with Bernoullis principle. Water flows
through the device at a certain velocity. As you
can see the water flows over tube where
fertilizer is projected into the water.
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Hozon Siphon Mixer (cont)
This is where Bernoullis principle steps in.
Because the water is flowing over the top of the
fertilizer tube it creates pressure around the
stream of moving water. This pressure around
the stream of water causes the fertilizer to be
projected upwards towards the stream of water.
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Hozon Siphon Mixer (cont)
Why doesnt the water just spray into the
fertilizer tube? The pressure of the stream is
very low since its velocity is very high. But,
the velocity around the out side of the stream of
water is very low, thus causing the pressure
outside the stream of water to be very high. The
high pressure that is projecting fertilizer into
the water doesnt allow the water to enter the
fertilizer tube.
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Racecars!
Notice the shape of the spoiler.
? The spoiler starts out thin and gradually
curves upward. This causes the velocity to
decrease and pressure to increase on the top.
Racecars designs such as the ones the perform in
the Indianapolis 500 use Bernoullis principle to
keep the car on the ground, and allow the car to
make sharper turns.
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Racecars! (contd)
The spoiler of the car is shaped so that the
velocity of air on the top of the spoiler is
moving slower, thus creating more pressure on the
top of the car pushing the car downward. The
velocity of air on the bottom of the spoiler is
much faster, thus having less pressure pushing
upward on the car.
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Airplanes

• Notice the shape of the airplanes wings.
• They are shaped opposite of a racecars spoiler.

The top of an airplanes wings are shaped so that
the velocity of air moves faster over the top and
slower on the bottom. Since the velocity of air
is faster on top that means the pressure on top
is low. The velocity of air is slower on the
bottom so the pressure on bottom is greater
helping give lift (the force that pulls an object
outward, or upward.) to the airplane keeping it
up in the air.
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Airplane Wing
The top of an airplanes wing is shaped so that
the velocity of air moves faster over the top and
slower on the bottom. Since the velocity of air
is faster on top that means the pressure on top
is low. The velocity of air is slower on the
bottom so the pressure on bottom is greater
helping give lift to the airplane keeping it up
in the air.
The same concept of low velocity and high
pressure on the bottom of an airplanes wings
also applies to the wings of flying birds.
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Summary

• What did we learn?
• Daniel Bernoulli was a Dutch-Swiss mathematician
  who came up with the principle of fluid mechanics
  known as Bernoullis Principle.
• Bernoullis principle basically states that as a
  fluids velocity increases the pressure within
  that fluid decreases.

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Summary (cont)

• Devices such as Hozon siphon mixers use
  Bernoullis principle to cause fertilizer to mix
  with water by the pressure of the water it is
  being mixed with.
• Racecars use a spoiler shaped so that pressure
  stays on top of the car holding down.
• Airplane wings are shaped opposite of racecars to
  have pressure on the bottom of the wing to give
  it lift.