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Velocity field

  1. Oct 3, 2010 #1
    1. The problem statement, all variables and given/known data
    Determine whether the velocity field VectorV=(3t)[tex]\hat{i}[/tex]+(xz)[tex]\hat{j}[/tex]+(ty^2)[tex]\hat{k}[/tex] is incompressible, irrotational, both, or neither. Also obtain expressions for the linear and shear strain rates.


    2. Relevant equations

    V=(u,v,w)

    omega=1/2[(delw/dely)-(delv/delz)]i + 1/2[(delu/delz)-(delw/delx)]j + 1/2[(delv/delx)+(delu/dely)]k

    epsilonxx=delu/delx
    epsilonyy=delv/dely
    epsilonzz=delw/delz

    epsilonxy=1/2[(delu/dely)+(delv/delx)]

    epsilonzx=1/2[(delw/delx)+(delu/delz)]

    epsilonyz=1/2[(delv/delz)+(delw/dely)]



    3. The attempt at a solution

    Okay so I said u=3t, v=xz, w=ty

    When I did the partial derivative of the original equation I got a rate of rotation equal to 1/2[(t-x)i+(z)k]

    then when I did the linear strain rate I got zero for all of them so when I added up all of the linear strain rates for the volumetric strain rate it comes out to be incompressible?

    Then for the Shear Strain rates I got epsilon xy = z/2 and epsilon yz = (x+t)/2?

    I don't know this doesn't seem very right...

    Help? lol
     
  2. jcsd
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