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Longitudinal strain rate derivation

  1. Jun 8, 2014 #1
    Hi,

    The attachment below is about strain rate in fluids*. It shows how the strain rate [tex]d\phi/dt[/tex] is related to the velocity field derivative [tex]du/dx[/tex] when you stretch the element in x (i.e. longitudinal strain).

    It has no intermediate steps, and I can't see how the angle has been related to the velocity field (or where the 0.5 factor comes from).

    Thanks very much.

    *From website: http://www.see.ed.ac.uk/~johnc/teaching/fluidmechanics4/2003-04/fluids5/stress.html [Broken]

    Sorry about the small picture - that's how it is on the website.
     

    Attached Files:

    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jun 9, 2014 #2
    I would assume there's a simple trigonometric identity to apply. What makes this difficult for me is that phi is present in both the x and y directions, whilst the equation somehow describes it through the x-axis.
     
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