Bernoulli’s Principle 11.5 Group 6

PREFACE

Alhamdulillah gratitude for the blessings and mercy of Allah SWT so in the end I can accomplish the task of Physics about the making of this paper well and on time. I also say a big thank you to all those who have helped me so that this task can be resolved properly and smoothly without any significant obstruction. In this paper I lifted the title of the Bernoulli principle In making this paper are of course still many shortcomings. Therefore, I expect criticism and suggestions from readers for the development of this paper. Hopefully what I have presented can be useful to readers and can be used as a reference for the development works better.

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Bernoulli’s Principle 11.5 Group 6

CONTENTS

PREFACE...................................................................................................1

CONTENTS................................................................................................2

INTRODUCTION........................................................................................4

About Daniel Bernoulli..........................................................................4

A. Bernoulli’s principle.........................................................................5

B. Bernoulli’s Formula..........................................................................6

C. Aplication of Bernoulli’s Principle....................................................7

D. EXAMPLES........................................................................................9

CONCLUTION.........................................................................................10

REFERENCE............................................................................................11

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Bernoulli’s Principle 11.5 Group 6

INTRODUCTION

About Daniel Bernoulli

His discovery was the first time that an analysis of water flowing from a hole in a container was correct. His discovery was that, as iterated above, that a rise in pressure would cause a decrease in speed and a decrease in pressure would cause an increase in speed. Bernoulli largely created his principal based on the theory of conservation of energy. (The law of conservation of energy states that energy can be neither created nor destroyed, and therefore the sum of all the forms of energy in the system is constant.) He used the conservation of energy as well as pumps and other machines that are used to raise water to come up with this principle. Daniel Bernoulli (1700-82), son of Johann I, was born on Groningen, Netherlands. Of all the Bernoullis, he was perhaps the greatest mathematician. Daniel also had the widest interests which includes medicine, biology, physics, mechanics, and astronomy. Daniel originally planned a career business and medicine. Like other family members, however, he was drawn to the field of mathematics. Between 1725 and 1732, he taught mathematics at the Academy of Science in St. Petersburg, Russia. He then went to the University of Basel, where he taught anatomy, botany and then physics. Daniel's most important work was in mechanics. He was the founder of the science of hydrodynamics, the study of moving fluids. One of his main contributions in this area is Bernoulli's Principle, which states that the pressure in a fluid decreases as its velocity, or speed, increases. Daniel is also noted for his work in calculus and probability theory, especially as it applies to games. He's also considered one of the founders of the kinetic theory of gases, which helps explain the property and behavior of gases. Between 1725 and 1749, Daniel won many prizes for his work on astronomy, gravity, tides, magnetism, and ocean currents.

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Bernoulli’s Principle 11.5 Group 6

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Bernoulli’s Principle 11.5 Group 6

CONTENTS

A. Bernoulli’s principle

In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy. Bernoulli's principle is named after the Swiss scientist Daniel Bernoulli who published his principle in his book Hydrodynamica in 1738.

Bernoulli's principle can be applied to various types of fluid flow, resulting in what is loosely denoted as Bernoulli's equation. In fact, there are different forms of the Bernoulli equation for different types of flow. The simple form of Bernoulli's principle is valid for incompressible flows (e.g. most liquid flows) and also for compressible flows (e.g. gases) moving at low Mach numbers. More advanced forms may in some cases be applied to compressible flows at higher Mach numbers (see the derivations of the Bernoulli equation).

Bernoulli's principle can be derived from the principle of conservation of energy. This states that, in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. Thus an increase in the speed of the fluid occurs proportionately with an increase in both its dynamic pressure and kinetic energy, and a decrease in its static pressure and potential energy. If the fluid is flowing out of a reservoir, the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per unit volume (the sum of pressure and gravitational potential ρ g h) is the same everywhere.

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Bernoulli’s Principle 11.5 Group 6

Bernoulli's principle can also be derived directly from Newton's 2nd law. If a small volume of fluid is flowing horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than in front. This gives a net force on the volume, accelerating it along the streamline.

Fluid particles are subject only to pressure and their own weight. If a fluid is flowing horizontally and along a section of a streamline, where the speed increases it can only be because the fluid on that section has moved from a region of higher pressure to a region of lower pressure; and if its speed decreases, it can only be because it has moved from a region of lower pressure to a region of higher pressure. Consequently, within a fluid flowing horizontally, the highest speed occurs where the pressure is lowest, and the lowest speed occurs where the pressure is highest.

B. Bernoulli’s Formula

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Besar usaha untuk memindahkan fluida sejauh x1 :

Besar usaha untuk memindahkan fluida sejauh x2 :111 .xFW 111 xAP

VxA 11

222 .xFW 222 xAPVxA 22

VPW 11

Volume of fluid

volume of fluid

VPW 22

Bernoulli’s Principle 11.5 Group 6

C. Aplication of Bernoulli’s Principle

1 . The carburetor used in many reciprocating engines contains a venturi to create a region of low pressure to draw fuel into the carburetor and mix it thoroughly with the incoming air. The low pressure in the throat of a venturi can be explained by Bernoulli's principle; in the narrow throat, the air is moving at its fastest speed and therefore it is at its lowest pressure

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So the W total was to do is : VPVPW 21

m

V Because :

m

PPW 21 so :

Changing of mecanic energy when the fluid move to the right:

2

12

212 2

1vvmhhmgEM

Because the work equals energy :

MEW

21

221221 2

1vvmhhmg

mPP

m

vvmhhmgPP

2

1221221 2

1

21

221221 2

1vvhhgPP

21

221221 2

1

2

1vvghghPP

2222

2111 2

1

2

1vghPvghP

tan2

1 2 konsvghP

so :

Bernoulli’s Principle 11.5 Group 6

2 . The Pitot tube and static port on an aircraft are used to determine the airspeed of the aircraft. These two devices are connected to the airspeed indicator which determines the dynamic pressure of the airflow past the aircraft. Dynamic pressure is the difference between stagnation pressure and static pressure . Bernoulli's principle is used to calibrate the airspeed indicator so that it displays the indicated airspeed appropriate to the dynamic pressure.

3. Airflight

• Bernoulli’s Principle is what allows birds and planes to fly.

• The secret behind flight is ‘under the wings.’• The air on top of the wing must travel a longerdistance than the air below the wing. But, air onboth sides must reach the end of the wing at thesame time. Therefore, the air on top of the wing traveling faster = less air pressure.

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Creates Lift

AIR

Bernoulli’s Principle 11.5 Group 6

D. EXAMPLES

Water circulates throughout a house in a hot-water heating system. If water is pumped out at a speed of 0.50 m/s through a 4.0 cm diameter pipe in the basement under a pressure of 3.0 atm, what will be the flow speed and pressure in a 2.6 cm diameter pipe on the second floor 5.0 m above? Assume pipes do not divide into branches.

Known : v1 = 0.50 m/s d2 = 2.6 cmd1 = 4.0 cm h2 = 5.0 mr1 = 2.0 cmP1 = 3.0 atm

Ask : v2 ?P2?

Answer :

First calculate the flow speed on the second floor, calling it v2, using the equation of continuity. We can call the basement point 1.

v2 = (v1A1) / (A2) = (v1π(r1)2) / (π(r2)2) = (0.50 m/s)(0.020 m)2 / (0.013 m)2 = 1.2 m/sTo find pressure, we use Bernoulli’s equation:P2 = P1 + ρg(h2– h1) + ½ρ((v2)2 – (v1)2)P2 = (3x105) + (1x103)(10)(5-0) + ½(1x103)[(1.2)2-(0.50)2]P2 = (3x105) + (5x104) + 595P2 = 3.5x105 N/m2

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Bernoulli’s Principle 11.5 Group 6

CONCLUTION

BERNOULLI’S PRINCIPLE :

“as the velocity of a fluid increases, the pressure exerted by that fluid decreases”

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Bernoulli’s Principle 11.5 Group 6

REFERENCE

http://bernoullisprinciple.weebly.com/applications.html

http://www.csp.science.ubc.ca/life/StudentSamples/Website2/examples.html

http://www.efm.leeds.ac.uk/CIVE/CIVE1400/Section3/bernoulli.htm

http://bernoullisprinciple.weebly.com/quotes.html

http://www.yourdictionary.com/bernoulli-s-principle

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