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Applications of Bernoullis

PrincipleGeorgia 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 knownfor his work in fluid mechanics and for his boom Hydrodynamica.

Bernoulli came up with the equitation

where:

is the fluid flow speedat a point on a streamline,

is the acceleration due to gravity,

is the elevationof the point above a reference plane, with the

positive z-direction pointing upward so in the direction opposite tothe gravitational acceleration,

is the pressureat the point, and

is the densityof the fluid at all points in the fluid.

http://en.wikipedia.org/wiki/Speedhttp://en.wikipedia.org/wiki/Earth%27s_gravityhttp://en.wikipedia.org/wiki/Elevationhttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Elevationhttp://en.wikipedia.org/wiki/Earth%27s_gravityhttp://en.wikipedia.org/wiki/Speed

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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 fluidincreases, the pressurewithin (the force per unit area applied toan object) the fluid decreases.

Bernoullis principle is used in aerodynamics and help explains howairplane get lift, and how race cars stay on the ground. It also hasuses in lots of different machines such as a Hozon for agriculturaluse.

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HozonSiphon 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 intothe water.

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HozonSiphon Mixer (cont)

This is where Bernoullis principle steps in.

Because the water is flowing over the topof the fertilizer tube it creates pressure

around the stream of moving water.

This pressure around the stream of watercauses the fertilizer to be projected

upwards towards the stream of water.

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HozonSiphon 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!

Racecars designs such as the ones the perform in the Indianapolis 500 use Bernoullisprinciple to keep the car on the ground, and allow the car to make sharper turns.

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.

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Airplanes

Notice the shape of the

airplanes wings.

They are shapedopposite 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 tocause fertilizer to mix with water by the pressure of the water it isbeing mixed with.

Racecars use a spoiler shaped so that pressure stays on top of thecar holding down.

Airplane wings are shaped opposite of racecars to have pressure onthe bottom of the wing to give it lift.