1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Water Flowing through U-tubes (Velocity Given Cross-Sectional Areas)

  1. Jan 28, 2013 #1
    1. The problem statement, all variables and given/known data
    See question 23

    A' = 1/2A

    2. Relevant equations
    Av = A'v'

    3. The attempt at a solution
    I thought this was just a simple Av = A'v' problem
    which would lead to v' = 2v. But there is apparently more to it, as the answer is √2v.
    It could have to do with the momentum because F_net = 0 so it is conserved.
    In that case,
    mv = mv but I'm confused about how to use that to solve the problem.
  2. jcsd
  3. Jan 28, 2013 #2
    Any thoughts?
  4. Jan 28, 2013 #3
    Use conservation of momentum. In terms of the fluid density, the area, and the velocity v, what is the rate of change of momentum of the fluid passing through the U tube on the left? Same question for the U tube on the right.
  5. Jan 28, 2013 #4
    momentum = mv
    dp/dt = m/t(v)
    dp/dt = (ρAv)v
    dp/dt = ρAv^2 - This is the left

    dp/dt = pA'v'^2
    A' = .5A
    dp/dt = ρAv'^2/2

    The two rate changes are equal ( net forces are zero).
    v^2 = v'^2/2
    2v^2 = v'^2
    v' = √2v

    This is the right answer. Thanks.

    Just a question; from where did you get the motivation to use rate change of momentum?
  6. Jan 28, 2013 #5
    The problem said that the assembly of u tubes is in equilibrium. That means that the forces exerted by the fluids on the u tubes must be equal. The force exerted by each fluid on each u tube is equal to the force exerted by the u tube on the fluid. The latter is equal to the rate of change of momentum of the fluid.
  7. Jan 28, 2013 #6
    Ok I see where you were going.
    Essentially, the conceptual link is:
    Equlibrium → ƩF = 0 → FL = FR
    F = dp/dt
    dp/dt = mv/dt
    Given, that v is constant, m is changing
    dp/dt = dm/dt*v
    dm/dt = ρAv
    dp/dt = ρAv^2
    And that's it right.

    I'm just making sure so I don't end up memorizing scenarios.
  8. Jan 28, 2013 #7
    Yes. Well done. I hold in very high regard a student like you who focuses on fundamentals. You can look forward to a bright future.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook