# Bernoulli's Principle explaination

Can someone explain this principle to me in as few words as possible (less than 500) whilst retaining quality?

Doc Al
Mentor
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:

$$P_1 + \frac{1}{2} \rho v_1^2 + \rho g y_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g y_2$$

Last edited:
Is that the same for air flow? ie wind turbines?

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

enigma
Staff Emeritus
Gold Member
Bernoulli applies to all incompressible fluids, which low speed air can be approximated as.

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?

enigma
Staff Emeritus
Gold Member
No, at high speeds the air compresses.

It comes from thermodynamics and the ideal gas law

$$p=\rho*R*T$$

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.

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

Last edited by a moderator:
What is the word equation for this principle?

russ_watters
Mentor
To amplify what enigma said, treating airflow above 220mph as compressible is the rule of thumb I learned.

And what is a "word equation"?

Ummmmm a word equations is an equation in words, or is this priciple to complex to write in words???!!!!

Integral
Staff Emeritus
Gold Member
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.

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

thanks, although that maybe too advanced to tell to the 15/16 year olds that i am trying to find this out for.

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."

enigma
Staff Emeritus
Gold Member

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

Michael D. Sewell
enigma said: