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Math Help - Bernoulli's principle

  1. #1
    Senior Member TriKri's Avatar
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    Bernoulli's principle

    Hi!

    Can someone please explain to me: What does Bernoulli's principle really mean? I don't get the formula.

    First of all, velocity has a direction. And second velocity is relative. Let me explain what I mean: Bernoulli's principle says that

    \frac{v^2}{2}+gh+\frac{p}{\rho}=\text{constant}

    if we derive this by some variable x, we get:

    v\frac{\delta v}{\delta x}+g\frac{\delta h}{\delta x}+\frac{1}{\rho}\cdot\frac{\delta p}{\delta x}=0

    This would mean that if the velocity is high from the beginning, the value of \frac{\delta v}{\delta x} is of big importance to the equation, but if the velocity is zero, the value of \frac{\delta v}{\delta x} doesn't matter at all? Can a liquid be "still"? In that case, in relation to what is the velocity of the liquid measured?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by TriKri View Post
    Hi!

    Can someone please explain to me: What does Bernoulli's principle really mean? I don't get the formula.

    First of all, velocity has a direction. And second velocity is relative. Let me explain what I mean: Bernoulli's principle says that

    \frac{v^2}{2}+gh+\frac{p}{\rho}=\text{constant}

    if we derive this by some variable x, we get:

    v\frac{\delta v}{\delta x}+g\frac{\delta h}{\delta x}+\frac{1}{\rho}\cdot\frac{\delta p}{\delta x}=0

    This would mean that if the velocity is high from the beginning, the value of \frac{\delta v}{\delta x} is of big importance to the equation, but if the velocity is zero, the value of \frac{\delta v}{\delta x} doesn't matter at all? Can a liquid be "still"? In that case, in relation to what is the velocity of the liquid measured?
    Bernoulli's principle is conservation of energy spelled sideways. (Essentially we are using the conservation of the mechanical energy density.)

    If you are moving along with the fluid then it appears that the fluid is not moving. However I have a hard time visualizing myself in stationary fluid and the pipe is moving by me! Typically the velocity flow of a fluid is measured with respect to the surface of the pipe it is in. If the pipe is in a vehicle (or something) that is performing rapid directional changes I'm not sure what to use for a coordinate system.

    -Dan
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  3. #3
    Junior Member Singular's Avatar
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    Quote Originally Posted by TriKri View Post
    Hi!
    Can a liquid be "still"? In that case, in relation to what is the velocity of the liquid measured?
    In what sense, macroscopic or microscopic ?
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