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- Thread starter rattis
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Doc Al

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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.

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.

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I dont like google, i get too much useless information, spam, porn, untruths, bad attempts and general waffle.

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enigma

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Bernoulli applies to all incompressible fluids, which low speed air can be approximated as.

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I don't think approximating low speed air as an incompressible fluid is a very good approximation. Don't you mean high speed?

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enigma

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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,

- #7

Michael D. Sewell

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

Enigma and Doc Al are

-Mike

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What is the word equation for this principle?

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russ_watters

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And what is a "word equation"?

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Integral

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Read Doc Al's post, he gives the key information.rattis said:What is the word equation for this principle?

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

Michael D. Sewell

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

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"Bernoulli’s principle states that as the velocity of a moving fluid (liquid or gas) increases, the pressure within the fluid decreases."

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enigma

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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

Michael D. Sewell

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.

-Mike

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