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Radial Component of Velocity

  1. Oct 25, 2014 #1
    1. The problem statement, all variables and given/known data

    In certain hydrodynamic flows the velocity of a liquid is given by v = -grad φ,
    where φ is referred to as the velocity potential. The potential given by:
    'equation'
    corresponds to flow around a solid sphere of radius a. U is a constant.
    Determine the velocity of the fluid throughout the flow. Confirm that the
    radial component of velocity is zero on the surface of the sphere.

    I've successfully found the velocity of the fluid, as my answer is in agreement with the answer given. However, I'm not sure this part of the question means: '
    Confirm that the
    radial component of velocity is zero on the surface of the sphere.'

    Could anyone help me?
     
  2. jcsd
  3. Oct 25, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    A radial component of the velocity would mean something flows into or out of the sphere. This should not happen, and you are supposed to verify this.
    In other words, the flow at the surface has to be parallel to the surface.
     
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