# Fluids/tensors problem

davcrai

## Homework Statement

Going through a proof of uniqueness for stokes flow for a fluids class I'm taking. Part of it involves replacing the strain tensor (e) with the stress tensor (a), ie going from

(2u)*int(eij*eij)dV

to

int(eij*aij)dV

## Homework Equations

aij = -p*dij + 2u*eij

dij = 1 if i=j, 0 otherwise.

## The Attempt at a Solution

I can see you simply substitute for 2u*eij to the integral as follows,

int(eij*(eij*(p*dij + aij))dV

but why does eij*p*dij = 0 ????????

## The Attempt at a Solution

foxjwill

Please try reposting this in the physics part of the forum.

Homework Helper

Because the strain tensor e is traceless. The pressure term is exactly minus the trace of the stress tensor a.

Last edited:
davcrai

Thank you very much!