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Bernoulli/Continuity, Water flowing at different heights/radii

  1. Apr 12, 2013 #1
    1. The problem statement, all variables and given/known data
    Water flows in the pipe below as an ideal fluid where:
    P1 = 1.95*10^5 Pa ; Rad @ P1 = 3cm
    P2 = 1.20*10^5 Pa ; Rad @ P2 = 1.50 cm
    P2 is above P1, but the height difference is UNKNOWN.

    Questions:
    1. What are the velocities at P1 and P2?
    2. Find volume flow rate through the pipe.

    I don't have a diagram, but it's pretty simple - known pressures with known radii at UNKNOWN heights.


    2. Relevant equations
    P1 = P2 + dgh -- doesn't this assume the areas are the same? (which they aren't)
    Bernoulli's.
    A1V1 = A2V2


    3. The attempt at a solution
    1. I used A1V1 = A2V2 to solve the ratio between V1 and V2 (since rad can be used to find A) and solved for v1.

    2. I substituted answer for v1 into v1 of bernoulli's equation. This way I can get v2.
    BUT, I can't solve Bernoulli's eq. without knowing the heights, h1 and h2.

    3. I though P1 - P2 = dgh could work, but I thought this was only for change in height with the same area. Am I wrong?

    Help would be much appreciated. I'm so stuck on this whole different areas/heights/pressures thing and my brain is shutting down a bit from the frustration. Haha help?
     
  2. jcsd
  3. Apr 12, 2013 #2
    Sometimes people us a capital P to represent the sum of the pressure p (lower case) plus ρgz:

    P = p + ρgz

    Is it possible that that is the case here? Even then, you still need to know the density in order to get the kinetic energy per unit volume.
     
  4. Apr 12, 2013 #3
    thanks for responding -- sorry that i used dgh, it's just what my teacher uses

    Anyway, I don't think so, she definitely means p1 and p2 being the pressure at the bottom and top of the pipe. And we're allowed to use d = 1000 kg/m3 for water so I know the density. I'm just not sure if I can solve for the height (z) with the information given.

    I'm thinking that she needs to give us that in order to solve it.

    I found a problem that uses the same diagram and all the same information, except this one has a height difference given:
    q1376760"]http://www.chegg.com/homework-help/questions-and-answers/water-moves-constricted-pipe-steady-ideal-flow-lower-point-pressure-171-105-pa-pipe-radius-q1376760
    [/URL]

    I'm guessing this is why I can't solve this, but is there something I'm missing?
     
  5. Apr 12, 2013 #4
    I agree with you. You need to know the height difference.

    Chet
     
  6. Apr 12, 2013 #5
    Thanks, once I know that this problem will be pretty easy. Thanks!
     
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