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Volume Fluxes and Associated Velocities

  1. Sep 28, 2014 #1
    1. The problem statement, all variables and given/known data
    Suppose that the volume transport associated with the wind-driven circulation's western boundary current (such as the Gulf Stream) is 50 x 10^6 m^3/second. Assume that this volume transport is carried in a current of uniform speed which is 50 km wide and 1 km thick. Calculate the average velocity of the current.

    2. Relevant equations
    Q = v * A
    (volumetric flow rate = velocity*area)

    3. The attempt at a solution
    Reworking the equation Q = v*A to solve for velocity yields the equation, v = Q/A.
    Area has been converted from km to meters.
    So, velocity = (50 x 10^6 m^3/sec) / (50,000,000 m^2) = 1 meter/second.

    So, the answer I've found is a velocity of one meter per second. This is a graduate level course, however, so I am not sure that this correct. The math is not wrong, though; could it be my approach?
     
  2. jcsd
  3. Sep 29, 2014 #2
    Does the answer of 1m/s seem reasonable to you for the Gulf Stream current?

    Chet
     
  4. Sep 29, 2014 #3

    pasmith

    User Avatar
    Homework Helper

    If the cross-sectional area is [itex]50 \times 10^6\,\mathrm{m}^2[/itex] and the volume flux is [itex]50 \times 10^6\,\mathrm{m}^3\,\mathrm{s}^{-1}[/itex] then the average velocity is indeed [itex]1\,\mathrm{m}\,\mathrm{s}^{-1}[/itex].

    Wikipedia says that the maximum velocity in the Gulf Stream is about 2.5 ms-1, so 1 ms-1 is the right order of magnitude for an average.
     
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