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Continuum Mechanics: Check if fluid flow is real

  1. Sep 13, 2011 #1
    1. The problem statement, all variables and given/known data

    see attachment.


    2. Relevant equations

    Navier Stokes continuity equation:



    762462cbd19e9bf6d392e1d5636193d7.png

    3. The attempt at a solution

    So what I tried to do was to use the above equation to see if it equals zero.

    del(rho)/del(t)=del(xyz-t)/del(t)
    =-1

    then to make the deriving easier I multiplied the density by each of the velocity components

    rho*vx=x^3yz-tx^2
    rho*vy=y^3xz+2txyz-y^2t-2t^2
    rho*vz=x^2y^2z^2-2txyz+t^2

    then I did the derivative part of the equation

    grad.(rho*v)= del(rho*vi)/del(xi)
    =del(rho*vx)/del(x) + del(rho*vy)/del(y) + del(rho*vz)/del(z)
    =3x^2yz-2tx+3y^2xz+2txz-2yt+0+2x^2y^2z-2txy+0


    ^^this isn't zero :/
     

    Attached Files:

  2. jcsd
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