# Total shear rate in a 3 dimensional flow

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 May 21, 2003, 03:53 Total shear rate in a 3 dimensional flow #1 Bo Busk Jensen Guest   Posts: n/a Hallo All The shear stress on a fluid element in a unidirectional flow is given by du/dy (y the distance from the wall). Is it then correct that the total shear rate on a fluid element in a 3 dimensional flow is expressed by the shear rate tensor (a 3 times 3 matrix)?? Regards Bo

 May 22, 2003, 14:43 Re: Total shear rate in a 3 dimensional flow #2 xueying Guest   Posts: n/a I think it's not completely correct. rate-of-strain tensor 2D = \Delta \vec{v} + (\Delta \vec{v})^T shear rate is equal to sqrt(-II_{2D}). where II_{2D} is the second invariant of the rate of strain tensor,

 May 23, 2003, 03:00 Re: Total shear rate in a 3 dimensional flow #3 Bo Jensen Guest   Posts: n/a Hallo xueying Could you please elaborate on the equations... I cannot make out what they mean.. Regards Bo

 May 23, 2003, 15:26 Re: Total shear rate in a 3 dimensional flow #4 xueying Guest   Posts: n/a Sorry, I wrote it in latex format. To calculate the shear rate, first you need rate-of-strain tensor (let's say 2D); then you need to calculate the second invariant of the tensor 2D (let's say II_2D); finally your shear rate equals to square root of the negative second invariant. Where rate-of-strain equals to gravient v + transpose of gravient v; note gravient is a tensor.

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