Hi,

I am trying to determine the value of strain in a fluid. A literature review leads me to:

Sij = 1/2 (duj/dxi + dui/dxj)

Some papers have

|S| = sqrt(2 * Sij Sij)

whilst others have

|S| = sqrt (Sij Sij)

Can anyone tell me which is correct.

Thanks

Tim.

The first one seems familiar and correct

Hi,

The first formula gives you the rate of strain as commonly defined, in tensor notation and hence with direction. I've seen, as you, both the other two defintions for the total strain. I would prefer people to use the one without 2.

The first one is the strain rate tensor (3x3 matrix) while the latter is the magnitude of the strain rate tensor (a scalar value). Both are correct depending on what you want to evaluate.