Help with Bernoulli's Equation

[Csv321]

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I am studying from TPR books and listening to the Audio Osmosis CD's. In the TPR book, it says Bernoulli's Equation is

P1 + (1/2)(density1)(velocity1)^2 + (density1)(gravity)(height1) =

P2 + (1/2)(density2)(velocity)^2 + (density2)(gravity)(height2)

But listening to Audio Osmosis, the 3rd CD, they say the left side of the equation is all equal to some constant K....

Could someone please explain this? Or do I need to keep listening and they will explain it and eventually tell me the same thing?

Thanks!

 

[ASDIC]

what EK is trying to say is that with ideal fluids pressure on the left side always equals the pressure on right side. So the constant K.

Sometimes they might ask you solve for some variable, say fluid speed, the you use the equation to solve.

 

[inshanesworld]

First, for sure the question will be about a liquid cause if it is a gas, very specific criteria must be met to use that equation with a gas...

So... If it is a liquid, there is no density2 'cause liquids are pretty much incompressible.

With that said the best way to remember the equation is

DeltaP + 1/2*density*DeltaV^2 + density*g*Deltah = 0

Where DeltaP is P2-P1, Delta V is V2-V1 and Delta h is Height2-Height1

I am not sure what the nonsense about K is 'cause the point of the equation is that it is equal to zero. Perhaps they are referring to Q's where the upstream info is all given thus when you plug it in you get a value on the left. who knows?

 

[MoosePilot]

The bottom line is you might need to know the formula, but more likely you need to know the gist of what the formula's telling you.

If you change one variable, how do the others react? That's really the key to Bernoulli's.

 

[Csv321]

Thanks! I think I was just thinking too hard....

 

[N-toxicologist]

The bottom line is you might need to know the formula, but more likely you need to know the gist of what the formula's telling you.

If you change one variable, how do the others react? That's really the key to Bernoulli's.

Always the voice of reason, and so succinct! 👍

The left side = constant thing is just what Moosie said. If P1 stays the same, and you increase your PE term, what happens to your KE term? Remember, Bernoulli's is the statement of conservation of TOTAL mechanical energy. 😎

 

[Jack Swift]

could someone explain what the equation means? I read the EK and princeton but i never could reallly understand what the equation is for.

 

[ASDIC]

the equation assumes ideal fluid behavior.

What the equation is saying is that there will be no loss of pressure in a pipe in which there is an ideal fluid. In other words, if there is a loss of pressure, the fluid will pick more velocity and if there is an increase in pressure, the fluid velocity will slow down.

 

[Fusion]

the equation assumes ideal fluid behavior.

What the equation is saying is that there will be no loss of pressure in a pipe in which there is an ideal fluid. In other words, if there is a loss of pressure, the fluid will pick more velocity and if there is an increase in pressure, the fluid velocity will slow down.

Yes, this is the take-home concept of Bernoulli's equation. As (ideal) fluid velocity increases, pressure decreases, and vice-versa. Remember, fluid velocity and pressure forces are perpendicular. Thus, as one increases, the other must decrease in order to 'offset' the disturbance.

 

[inshanesworld]

Must not neglect the PE part of the equation!! If your there is a significant Delta H then that will effect both pressure and/or velocity.

 

[Code Brown]

The one thing that may clear up any confusion is to remember that there are two ways that people write the equation. The first is to add up the energy density and equal this to some number, and the other is to have all of the deltas of the energy density equal up to zero. The main point is this, you need to end up with what you started with and just need to account for where it went. Physics is about the conservation of stuff (be it force, momentum, energy, energy density).

 

[willthatsall]

If height remains constant, velocity and pressure are inversely related. I bet that's how Bernoulli's shows up 80% of the time.