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Bernoulli? Difference in water pressure between floors

  1. Nov 26, 2011 #1
    1. The problem statement, all variables and given/known data

    A water line enters a house 2.0 m below the ground. A smaller diameter pipe carries water to a faucet 5.0 m above the ground, on the second floor. Water flows at 2.0 m/s in the main line and at 7.0 m/s on the second floor. Take the density of water to be 1.0 x 103 kg/m3. The difference in pressure between the main line and the second floor is:

    A. 7.15 x 104 Pa with the main line at the higher pressure
    B. 2.65 x 104 Pa with the main line at the higher pressure
    C. 7.15 x 104 Pa with the main line at the lower pressure
    D. 2.65 x 104 Pa with the main line at the lower pressure
    E. 9.4 x 104 Pa with the main line at the higher pressure


    2. Relevant equations

    p + 1/2ρv2 + ρgy

    3. The attempt at a solution

    main line = second floor

    p1 + 1/2ρv21 + ρgy1 = p2 + 1/2ρv22 + ρgy2

    p1 + (.5)(1000)(4) + (1000)(9.8)(0) = p2 + (.5)(1000)(49) + (1000)(9.8)(7)

    p1 + 2000 + 0 = p2 + 24500 + 68600

    p1 - p2 = 24500 + 68600 - 2000

    = 9.11 X 104

    I was told this answer was incorrect. I think I'm doing something wrong with my y (elevation). I've tried using 0 and 7 and -2 and 5 without success.

    Per a search on the internet, it looks like 7.15 x 104 with the main line at the higher pressure is the right answer, but I can not find an explanation why.

    Any idea where I'm going wrong?

    Thanks!
     
  2. jcsd
  3. Nov 27, 2011 #2
    I think your answer is correct. The main pressure is definitely higher or you couldn't move the water to the upstairs. I don't see any math or conversion errors.
     
  4. Nov 27, 2011 #3
    What answer do you get when you use 5m as the change in elevation, rather than 7m?
    A. 7.15 x 104 Pa with the main line at the higher pressure
    But 5m is the elevation change between the ground and the second floor.

    Your question asks for pressure difference between main line and the second floor, which is what you calculated using 7m. Your answer seems correct.
     
  5. Nov 27, 2011 #4
    Who says the answer is wrong, H?
     
  6. Nov 28, 2011 #5
    It was a question that I had to answer in an online format so it told me that the answer was incorrect once I submitted it.

    I’m going to check with my professor today to see why the answer was marked incorrect. I’ll let y’all know what I learn.
     
  7. Nov 28, 2011 #6
    Well, turns out my answer was right and the computer was wrong. Who would have thought! :)

    Thanks all!
     
  8. Nov 29, 2011 #7
    Wow, how cool is that? See? I didn't steer you wrong for physics advice. :smile:
     
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