# BERNOULLI'S PRINCIPLE

Photo by: 2jenn

Bernoulli's principle, sometimes known as Bernoulli's equation, holds that for fluids in an ideal state, pressure and density are inversely related: in other words, a slow-moving fluid exerts more pressure than a fast-moving fluid. Since "fluid" in this context applies equally to liquids and gases, the principle has as many applications with regard to airflow as to the flow of liquids. One of the most dramatic everyday examples of Bernoulli's principle can be found in the airplane, which stays aloft due to pressure differences on the surface of its wing; but the truth of the principle is also illustrated in something as mundane as a shower curtain that billows inward.

The Swiss mathematician and physicist Daniel Bernoulli (1700-1782) discovered the principle that bears his name while conducting experiments concerning an even more fundamental concept: the conservation of energy. This is a law of physics that holds that a system isolated from all outside factors maintains the same total amount of energy, though energy transformations from one form to another take place.

For instance, if you were standing at the top of a building holding a baseball over the side, the ball would have a certain quantity of potential energy—the energy that an object possesses by virtue of its position. Once the ball is dropped, it immediately begins losing potential energy and gaining kinetic energy—the energy that an object possesses by virtue of its motion. Since the total energy must remain constant, potential and kinetic energy have an inverse relationship: as the value of one variable decreases, that of the other increases in exact proportion.

The ball cannot keep falling forever, losing potential energy and gaining kinetic energy. In fact, it can never gain an amount of kinetic energy greater than the potential energy it possessed in the first place. At the moment before the ball hits the ground, its kinetic energy is equal to the potential energy it possessed at the top of the building. Correspondingly, its potential energy is zero—the same amount of kinetic energy it possessed before it was dropped.

Then, as the ball hits the ground, the energy is dispersed. Most of it goes into the ground, and depending on the rigidity of the ball and the ground, this energy may cause the ball to bounce. Some of the energy may appear in the form of sound, produced as the ball hits bottom, and some will manifest as heat. The total energy, however, will not be lost: it will simply have changed form.

Bernoulli was one of the first scientists to propose what is known as the kinetic theory of gases: that gas, like all matter, is composed of tiny molecules in constant motion. In the 1730s, he conducted experiments in the conservation of energy using liquids, observing how water flows through pipes of varying diameter. In a segment of pipe with a relatively large diameter, he observed, water flowed slowly, but as it entered a segment of smaller diameter, its speed increased.

It was clear that some force had to be acting on the water to increase its speed. Earlier, Robert Boyle (1627-1691) had demonstrated that pressure and volume have an inverse relationship, and Bernoulli seems to have applied Boyle's findings to the present situation. Clearly the volume of water flowing through the narrower pipe at any given moment was less than that flowing through the wider one. This suggested, according to Boyle's law, that the pressure in the wider pipe must be greater.

As fluid moves from a wider pipe to a narrower one, the volume of that fluid that moves a given distance in a given time period does not change. But since the width of the narrower pipe is smaller, the fluid must move faster in order to achieve that result. One way to illustrate this is to observe the behavior of a river: in a wide, unconstricted region, it flows slowly, but if its flow is narrowed by canyon walls (for instance), then it speeds up dramatically.

The above is a result of the fact that water is a fluid, and having the characteristics of a fluid, it adjusts its shape to fit that of its container or other solid objects it encounters on its path. Since the volume passing through a given length of pipe during a given period of time will be the same, there must be a decrease in pressure. Hence Bernoulli's conclusion: the slower the rate of flow, the higher the pressure, and the faster the rate of flow, the lower the pressure.

Bernoulli published the results of his work in Hydrodynamica (1738), but did not present his ideas or their implications clearly. Later, his friend the German mathematician Leonhard Euler (1707-1783) generalized his findings in the statement known today as Bernoulli's principle.

## User Contributions:

Maddie
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Maddie Evans
Dazz
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reddd 44
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andrew s
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Luke M
Surely if boyles law states that volume is inversely proportional to pressure then because at any given point the volume of the wider part will be greater than that of the narrower part then the pressure in the wider part will be less than that of the narrower part. Also Boyles law is only true for ideal gases so why have you stated that it is true for water, a liquid?
I would like to learn more about this principle. I'm sure it will be on my semester exam. Try and help me please and thank-you. I'm in the 12th grade and passing my physics class means the world to me right now.
pearl shukla
I am having a doubt.
If pressure and velocities are inversely proportional then how it is possible in the case of water flowing through a pipe. If we increase the pressure ,water come out at higher speed. I need more information
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i need more examples.. but it is nice to have like this .. i learn about this topic ..
I am designing a jet meant for spraying water.How can I mix atmospheric air into the pressurized water so that water air mixture is expelled through the nozzle.
Sarah
Thank you so much for this great info on where and Bernoulli's princple i have been searching every where for info. And thats becuase in my Science class we have a group projet and I wantedto just basically understand what is Daneil Bernoulli's princlpe all about:)
Katie
Hey im in grade 6 and Im doing some final studying fore a since test on wends and I'm getting confused on what bernoullis principal is I'm thinking it's pretty much gravitational force? Please ancer ASAP

Thanks,
Katie
mikey
I am in Grade 8 and im confused on the whole idea can someone please explain what it is can u guys help me figure out what this is? someone email back asap
Grace
As fluid is being split (for example aeroplane wing and air) the density varies, the side with the less surface area has more density (because the doesn't have to move fast to meet the air it was split from)while the side with more surface area has less density (because it has to move quickly) so the object takes the space where there is less density.For planes this creates lift.

P. S. This is how it effects gas not liquid.
Reginald Mejio
thanks for clarification. It helps me a lot especially I will have my report in physics.
Nathaniel Vivero
Maybe this will be more understandable if you will insert videos for more explanations,. . . .
shantanu agrawal
i understood little bit about the article..but my question to you is why not heat energy and sound energy not considered in bernoulli's equation? because there may be some transfer oh heat in pipe flows...and if u have any further information on this topic then mail me...
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IncrediblyH.ard
Amazing! I am learning about this in my physics class right now
Nice attempt to explaining the principle except for the part where u talked about Boyle's Law. Boyle's Law is for ideal gasses. Ideal gasses are compressible but Bernoulli's principle is for non compressible fluids. U can't bring Boyle's Law in this.

So here is how the principle works. When a liquid passes through thinner pipe, its kinetic energy increases as its speed increases. But where is this extra kinetic energy coming from? The answer is Potential energy arising due to pressure. Due to non-compressibility, the fluid exerts lateral force/pressure on the walls of the pipe . This force or pressure can be used to do work. So we can say that this pressure gives rise to potential energy. And this potential energy is converted to kinetic energy when liquid passes through thin pipe. Since the pressure is being used to do increase speed of liquid, the pressure of liquid (pressure exerted on pipe wall) falls when speed rises in thin pipe.
lennox lanquaye
i need more pictures about bernoulli's equation,thank you.
zob ashfaq
can u please tell me how the carburetor is an application of bernoulli's equation?
I really have a doubt
How the pressure decreases when the velocity of water at the narrower section increases?
Pressure means force per unit area,correct?
Now,when the velocity of water increases at the nozzle means the force of the water particles increases i.e the pressure should increase,right? comparing with the wider area,that section has less velocity water molecules,so it should be low pressure.
Correct me if I'm wrong.
molly
thanks!!! now i know about bernoullie's principle i am gonna go on this site know and learn about it again
sam
Can u explain bernoilli principle more intuitively? i mean how does this effect come about by a statistical treatment of molecular motions? how can we understand it from a molecular level?
Razz
Nice! I really needed help with this for school and now I got it, but I wish you would explain a little more.
binari
hey I need more information about that topic.what are some real world applications of bernoulli's principle? please send me an email?
Wild
Why do we learn about Bernoulli's Principle? I really need to know this
nice
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Somebody
Hi!

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