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Bernoulli Equation - Units Question

  1. Apr 2, 2012 #1

    JJBladester

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    1. The problem statement, all variables and given/known data

    My book says that each term in the Bernoulli equation (when divided by ρ, has pressure units). I don't see how.

    2. Relevant equations

    The Bernoulli equation for steady, incompressible flow is:

    [tex]\frac{P}{\rho}+\frac{V^{2}}{2}+gz=constant[/tex]

    3. The attempt at a solution

    Multiplying the Bernoulli equation by density (ρ), we get:

    [tex]P+\rho\frac{V^{2}}{2}+\rho gz=constant[/tex]

    ρ = kg/m3 units

    V2=m6 units

    ρV2=kg*m3 units

    How does the middle term in the Bernoulli equation with the units listed above count as having pressure units?

    Pressure = Force/Area = Newtons/m2= [itex]\frac{\frac{kg\cdot m}{s^2}}{m^2}=\frac{kg}{m\cdot s^2}[/itex]
     
  2. jcsd
  3. Apr 2, 2012 #2

    tiny-tim

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    Hi JJBladester! :smile:
    Nooo :redface:

    V is velocity! :biggrin:

    (btw, Bernouilli's equation is essentially a conservation of energy equation, which is why you get a sort-of mv2/2 term :wink:)
     
  4. Apr 2, 2012 #3

    JJBladester

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    Nooo :redface:

    V is velocity! :biggrin:

    I need more coffee. Wow, I wish I could unpost that last post.

    Thanks for the reply, though. It makes a lot of sense now.
     
  5. Apr 2, 2012 #4

    tiny-tim

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    nooo, you need more sleep! :zzz: :wink:
     
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