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Homework Help: Show that the units for all 3 terms in bernouliis equation are the same

  1. Jan 9, 2010 #1
    1. The problem statement, all variables and given/known data

    bernouliis equaton

    P + 1/2 Rho v^2 + Rho g h = constant

    find the units of the three terms on the left hand side & show they are the same and then the units of the constant on the right

    3. The attempt at a solution

    all i can think to do here is check the SI units for each term

    units for pressure = Pa or NM^-2
    units for density = kg/m^3
    units for velocity =m/s
    units for g = m/s
    units for h = m

    but i cant see how i combine them or how they all come out the same ?
  2. jcsd
  3. Jan 9, 2010 #2


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    Homework Helper

    Pressure P = NM^-2 = kg*M*s^-2*M^-2 = kg*M^-1*s^-2.
    Similarly work out for the other two expression. You can see that all the tree terms have the same dimensions.
  4. Jan 9, 2010 #3

    Doc Al

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    Staff: Mentor

    Express each factor in terms of the basic units: m, kg, s. Then work out the units of each term in the equation by multiplying the units of each factor.
    Hint: Express the pressure in terms of those three basic units.
    Those units should be ms^-2.
  5. Jan 11, 2010 #4
    Ok so pressure becomes kgm^-1 s^-2, then the other terms expressed in
    M , kg, s are

    ½ pv^2 is Kg m^-3 m/s^-1
    Pgh is kg m^-3 m/2^2

    I think I am still having a problem with the powers thou, I am not combining the units correctly
  6. Jan 11, 2010 #5

    Doc Al

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    Staff: Mentor

    Show how you got these.

    What are the units for density? For v?
  7. Jan 11, 2010 #6
    density is mass / volume so its units are Kg m^-3
    for velocity units are m/s^-1

    so combined you get Kg m^-3 m/s^-1

    and for the second part
    density - Kg m^-3
    units for g = m/s^-2
    units for h - m

    combines to give Kg m^-3 m/s^-2

    i must be getting this wrong but i have re read my text book and i cant see where to correct it,
  8. Jan 11, 2010 #7
    The dimensions of velocity are [tex][L]^1\times [T]^{-1}[/tex]

    The dimensions of velocity squared are [tex][L]^2 \times [T]^{-2}[/tex]
  9. Jan 11, 2010 #8

    Doc Al

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    Staff: Mentor

    The density units are correct, but velocity has units of m/s or m*s^-1.

    Not quite. The units for ½ρv² would be:
    [kg*m^-3]*[m*s^-1]² = [kg*m^-3]*[m*s^-1]*[m*s^-1]

    See if you can simplify that by collecting all the powers of m and s. (For example, what's m^-3*m*m simplify to?)
  10. Jan 12, 2010 #9
    Ok I think I see it now,

    So m^-3*m*m simplifies to m^-1
    And s^-1*s^-1 simplifies to s^-2

    So the units for ½ρv² would be kg m^-1s^-2

    Then for the second term
    Units for density are kg*m^-3
    Units for g are m*s^-2
    Units for h are m

    This is


    Collecting the m terms gives m^-1 so the units are

    Kg m^-1s^-2

    Then all I need is the units for the constant at the end, if the three terms all have the same units then the constant must be in the same units to the power 3, like if you have a volume then m*m*m the result is m^3 ?

    if so how do I do this for kg m^-1s^-2 ?
  11. Jan 12, 2010 #10

    Doc Al

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    Staff: Mentor


    Don't confuse three terms (which add) with three factors (which multiply). All the terms have the same units, including the constant. So you're done.
  12. Jan 13, 2010 #11
    thanks so much for your help !!
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