Froude number and wave speed

Discussion in 'Hydrodynamics and Aerodynamics' started by Chuck Bodeen, Oct 22, 2013.

  1. Chuck Bodeen
    Joined: Oct 2013
    Posts: 1
    Likes: 0, Points: 0, Legacy Rep: 10
    Location: Panama City Beach, FL

    Chuck Bodeen New Member

    For shallow water, the Froude number is defined as object speed / wave speed
    or V/c where c=sqrt(g d) and d is water depth and g is acceleration of gravity.

    For a boat, Froude number is boat speed / sqrt(g L)
    where L is the waterline length.

    My question is: What is the physical meaning of sqrt(g L)?
    Is this some kind of wave speed?
     
  2. jehardiman
    Joined: Aug 2004
    Posts: 3,069
    Likes: 572, Points: 113, Legacy Rep: 2040
    Location: Port Orchard, Washington, USA

    jehardiman Senior Member

    Yes it is related to wave speed (c) where c = sqrt ((g/k) * tanh (k*d)) and where k is wave number (2*pi/wave length) and d is water depth. It has to do with the mass spring of a wave of length L and is required to make the Fn dimensionless. Get out a copy of Oceanographical Engineering by Weigel or Principles of Naval Architecture for a full discussion of the development of Fn and how it is related to the different k's via water depth.
     
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