# Velocity field

1. Oct 3, 2010

### Santorican

1. The problem statement, all variables and given/known data
Determine whether the velocity field VectorV=(3t)$$\hat{i}$$+(xz)$$\hat{j}$$+(ty^2)$$\hat{k}$$ 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