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Physics/Fluid Mechanics Problem - need help badly

  1. Mar 27, 2012 #1
    1. The problem statement, all variables and given/known data

    I have been staring at these two problems for a LONG time now and keep getting stuck. Please help me, and try to explain so I can understand.

    ro = density
    p = pressure
    g = gravity
    h = height/elevation
    A = area
    v = velocity

    1a) Use the principal of dimensional consistency, show that bernoulli's equation written as:

    P + (1/2)(ro)(v²) + (ro)gh = constant

    has the dimension of pressure.

    1b) When it is written as:

    (ro)/[(ro)*g] + (v²)/(2g) + h = constant

    show that each term has the dimension of length.




    2) Using equations

    a) A*v = A*v
    Left side both have subscript 1, right side have subscript 2.

    and the version of Bernoulli's equation:

    P/(ro) + (v²)/2 + gh = constant

    show that

    v(subscript 2) = sqrt((2*[p(sub1)-p(sub2)])/ (ro(1-[(A(sub2)/A(sub1))²])

    Sorry if it's hard to read. I can't do this on my own and my roommate isn't here to tutor me like he usually does.


    3. The attempt at a solution

    I don't even understand 1a and 1b. For 2, I can get as far as

    v[sub2] = [ro =(ro)gh - p]/[(ro)*(A(sub2)/A(sub1))²]

    and that's just by creating similar denominators for the second equation and substituting for v[sub2] with what i solved for the other v in the other equation.

    Help?
     
  2. jcsd
  3. Mar 27, 2012 #2

    NascentOxygen

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    Staff: Mentor

    Hi Kalookakoo! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

    For starters, can you show that the terms on each side of the "+" signs all have units identical to the units of pressure?
     
    Last edited by a moderator: May 5, 2017
  4. Mar 27, 2012 #3
    Well. p is already pressure.

    ro*gh I guess could be kg/m^3 * (g) = N/m^3 * m = N/m^2 which is pressure.

    I don't see how the middle term can be pressure,
     
  5. Mar 27, 2012 #4

    NascentOxygen

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    Hint: F=ma
     
  6. Mar 27, 2012 #5
    Ohhhh.

    I pull out a m on the v² to be (m/s²) which is acceleration times the mass of the density so it's Force/m^3 * m = F/A.

    Wow, overlooked that, thanks.

    1a) Down!

    Can you help me with 2? I think I can get 2b down by myself, I'll ask if I get stuck again.
     
  7. Mar 27, 2012 #6
    I got 1b. :)

    It's really simple once I realized the F=ma part lol.

    Part 2 is troublesome...
     
  8. Mar 28, 2012 #7

    NascentOxygen

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    You shouldn't have a "p" here; it will be p1 or p2. As for the "h" terms, assume h remains constant.

    Your use of the "=" equal sign is too carefree. It is supposed to mean equals. Now would be a good time to start to use it more carefully, before you get into more complicated maths or science exercises. What is on the left of the "=" should be equal to what is on the right.
     
  9. Mar 28, 2012 #8
    Sorry that second equal sign is supposed to be a subtraction sign.

    Does that mean I have to use that second formula twice using p1 and v1 then v2 and p2?
     
  10. Mar 28, 2012 #9

    NascentOxygen

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    Staff: Mentor

    Use this equation for P1,v1 then for P2,v2
     
  11. Mar 28, 2012 #10
    And then what?

    Do I solve for p1 and p2 and set it up as (p1-p2) like it is in the end equation?

    Because I get (-ro)[(v²[sub1]/2) + (v²[sub2]/2)]

    Where does that come into play?
     
  12. Mar 28, 2012 #11
    And then what?

    Do I solve for p1 and p2 and set it up as (p1-p2) like it is in the end equation?

    Because I get (-ro)[(v²[sub1]/2) + (v²[sub2]/2)]

    Where does that come into play?
     
  13. Mar 28, 2012 #12

    NascentOxygen

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    This relates v1 to v2.
     
  14. Mar 28, 2012 #13
    How does that fit in? I just can't see it for some reason.

    I plugged in p1,v1 and p2,v2 in the bernoulli equation and solved for v2 and got:

    v²[sub2] = 2(p[sub1]-p[sub2])/(ro) + v²[sub1]

    It's almost right..but I'm stuck
     
  15. Mar 29, 2012 #14

    NascentOxygen

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    Staff: Mentor

    Replace this v1 with v1 from this equation:
     
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