Bernoulli's Principle explaination

In summary, Bernoulli's principle is a statement of conservation of energy along a fluid, which relates the pressure, velocity, and height between two points under certain conditions. It can be represented by the Bernoulli equation and applies to all incompressible fluids, including low-speed air. At high speeds, the more complicated thermodynamic properties must be used. The principle can be summarized as: as the velocity of a flow increases, the pressure drops and the pressure will not go any higher than the pressure of a stagnant flow.
  • #1
rattis
41
0
Can someone explain this principle to me in as few words as possible (less than 500) whilst retaining quality?
 
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  • #2
Bernoulli's principle relates the pressure, velocity, and height between two points along a fluid under certain conditions (such as incompressible, steady flow, non-viscous). It is a statement of conservation of energy along the fluid.

Bernoulli's equation looks like this:

[tex]P_1 + \frac{1}{2} \rho v_1^2 + \rho g y_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g y_2[/tex]

Want more? Google. :smile:
 
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  • #3
Is that the same for air flow? ie wind turbines?

I don't like google, i get too much useless information, spam, porn, untruths, bad attempts and general waffle.
 
  • #4
Bernoulli applies to all incompressible fluids, which low speed air can be approximated as.
 
  • #5
enigma said: Bernoulli applies to all incompressible fluids, which low speed air can be approximated as.

I don't think approximating low speed air as an incompressible fluid is a very good approximation. Don't you mean high speed?
 
  • #6
No, at high speeds the air compresses.

It comes from thermodynamics and the ideal gas law

[tex]p=\rho*R*T[/tex]

If you restrict the space which air can take up (by putting a wing in its path, for instance), the temperature rises, the density increases, and the pressure rises. According to thermodynamic properties, how much each changes depends entirely on the Mach number.

For low Mach number flows (less than .3), the density changes less than 5%, so it can be safely modeled as incompressible. For high Mach numbers (modern aircraft or rocket nozzles), using Bernoulli will give you very wrong numbers. In those cases, the more complicated thermodynamic properties must be used. If you're interested, Introduction to Flight, by John D. Anderson is a very well written textbook which has a chapter or three on it.
 
  • #7
rattis,
Enigma and Doc Al are absolutely steering you in the right direction. A good book on fluid mechanics would help, and google too(send us some porn links).
-Mike
 
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  • #8
What is the word equation for this principle?
 
  • #9
To amplify what enigma said, treating airflow above 220mph as compressible is the rule of thumb I learned.

And what is a "word equation"?
 
  • #10
Ummmmm a word equations is an equation in words, or is this principle to complex to write in words?! :confused:
 
  • #11
rattis said:
What is the word equation for this principle?
Read Doc Al's post, he gives the key information.

Examine the equation the first thing to note is that the 2 sides only differ by the subscripts, this means it is relating the same properties in different regions.

The first term is a P or pressure, since all the terms are added they must all have the units of pressure. The second term is the density times the square of the velocity, this looks suspiciously like a kinetic energy. Notice that Doc Al mention conservation of energy? So this expression corresponds to a pressure due to the motion of the fluid. The last expression is a similar to a potential energy, this is a pressure due to fluid depth.
 
  • #12
rattis said:
What is the word equation for this principle?

Absolute pressure plus kinetic energy per unit volume plus potential energy per unit volume has the same value at all points along a streamline.

or if you like:

Absolute pressure plus dynamic pressure plus potential energy per unit volume has the same value at all points along a streamline.

or in a level system(no gravitational potential energy):
The sum of absolute pressure plus dynamic pressure remains constant along a streamline.

I hope that this is what you were looking for.
-Mike
 
  • #13
thanks, although that maybe too advanced to tell to the 15/16 year olds that i am trying to find this out for.
 
  • #14
I found a better version in an encyclopedia.

"Bernoulli’s principle states that as the velocity of a moving fluid (liquid or gas) increases, the pressure within the fluid decreases."
 
  • #15
Alright... how about:

As the velocity of a flow increases, the pressure drops. The pressure will not go any higher than the pressure of a stagnant (zero velocity) flow.

EDIT: crosspost
 
  • #16
enigma said:
Alright... how about:

As the velocity of a flow increases, the pressure drops. The pressure will not go any higher than the pressure of a stagnant (zero velocity) flow.


Absolutely.
-Mike
 

1. What is Bernoulli's Principle?

Bernoulli's Principle is a scientific law that states that as the speed of a fluid increases, its pressure decreases. This principle is named after Swiss mathematician and physicist Daniel Bernoulli, who first described it in the 18th century.

2. How does Bernoulli's Principle work?

Bernoulli's Principle works by taking into account the conservation of energy in a fluid. As the fluid's speed increases, its kinetic energy also increases, causing a decrease in its potential energy. This decrease in energy results in a decrease in pressure, as described by the equation P + 1/2ρv2 = constant, where P is pressure, ρ is density, and v is velocity.

3. What are some real-life applications of Bernoulli's Principle?

Bernoulli's Principle can be observed in many everyday situations, such as the lift force on an airplane wing, the flow of air over a curved surface, and the movement of water through a pipe. It is also used in the design of carburetors, atomizers, and other fluid-based systems.

4. How does Bernoulli's Principle relate to the concept of lift?

Bernoulli's Principle is a key factor in explaining the phenomenon of lift in aerodynamics. As air flows over the curved surface of an airplane wing, its velocity increases, causing a decrease in pressure according to Bernoulli's Principle. This creates a pressure difference between the top and bottom of the wing, resulting in an upward force (lift) that allows the plane to fly.

5. Are there any limitations to Bernoulli's Principle?

While Bernoulli's Principle is a fundamental principle in fluid dynamics, it has some limitations. It assumes an ideal, non-viscous fluid and does not take into account factors such as turbulence or boundary layer effects. Additionally, it is only valid for incompressible fluids, meaning that it cannot be applied to gases such as air at high speeds. However, it is still a useful concept for understanding and predicting fluid behavior in many practical applications.

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