Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fluid mechanics: defition of shear flow [rate of deformation tensor]

  1. Dec 28, 2012 #1
    fluid mechanics: defition of "shear flow" [rate of deformation tensor]

    I'm studying old undergraduate chemical engineering notes for an exam in grad school. Can't recall what this really means, can anyone explain to me what "off-diagonal elements" means and why the trig function velocities would be or not be "off-diagonal elements". And can you explain what the question is talking about in general.

    Problem statement: Consider the velocity field u = ([/x],[/y],[/z]), where: [/x](x,y,z)=constant*y*z*sin(constant*x)...(similar functions for y and z velocities)

    and question: "Recall that the definition of "shear flow" is one for which the rate of deformation tensor [Δ][/ij] has only off-diagonal elements. Is this shear flow?" (y or n)
  2. jcsd
  3. Dec 28, 2012 #2
    Re: fluid mechanics: defition of "shear flow" [rate of deformation tensor]

    And those are velocities like u (sub x,y,z) just in each direction. Not sure how to write the notation in the posts
  4. Dec 29, 2012 #3
    Re: fluid mechanics: defition of "shear flow" [rate of deformation tensor]

    If you are a chemical engineer, your first step should be to go back to Bird, Stewart, and Lightfoot, and look up the definition of the rate of deformation tensor. The components of the rate of deformation tensor in cartesian coordinates can be arranged in a 3x3 matrix. The diagonal elements of this matrix are equal to the partial derivatives of the three velocity components with respect to distance in the coordinate direction of the velocity components. If these three components of the matrix are equal to zero, the flow is considered to be a pure shear flow. The rate of deformation tensor does not specifically relate to the trigonometric functions, although, for a particular flow in which the spatial variation of the velocity components are expressed in terms of the trigonometric functions, they will of course come into play.
  5. Dec 29, 2012 #4
    Re: fluid mechanics: defition of "shear flow" [rate of deformation tensor]

    Welcome to Physics Forums, KD215.

    As regards to your queries about posting in the forum, you have obviously noticed the quick symbols on the right of the edit box.

    Have you also seen the formatting option icons on the toolbar above the box?

    Subscript and superscript can be accessed from the X2 and X2 icons.

    A wider range of maths and other symbols are available by clicking on the Ʃ at the end.

    This forum recognises a form of typographical language or input called LaTex. You access this in a wisywig mode by obtainign a free or commercial program to enter it directly.
    I (try to) use Mathtype.

    As regards the technical part of your question. There are several mechanical properties that have the principal or normal property as diagonal elements of their matrix or tensor and other properties (parallel or cross products) as off diagonal. Examples as Inertia, stress, strain, displacement.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook