(adsbygoogle = window.adsbygoogle || []).push({}); 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

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# Velocity field

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