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Old   December 17, 2011, 13:01
Default 1D Stress Tensor
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Hi,

What does the second and third terms of the stress tensor reduce to when dealing with the 1D compressible and viscous flow? (So only the pressure term remains)

stress tensor = -P +2*mu*D- 2/3*mu*div(v)
where D = the rate of strain deformation = 1/2*(grad(v)+grad(v)^T)

Thanks in advance!
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Old   December 17, 2011, 13:10
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well, just set all the derivatives wrt y and z to zero, so sth like div(v) will become du/dx...
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Old   December 19, 2011, 08:32
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Hi, Yeah I think I know how to get it mathematically:
stress tensor = -P +1/3*du/dx
I needed to check this as I was not sure what happens physically in a 1D case where a force is applied in the same plane as the fluid velocity (say x-direction).

Also the equation originally involves two viscous stress: the dynamic viscosity which relates stress two linear deformations and the second stress which relates stress to volumetric deformations. And I was not sure if the second one will be present in a 1D case.

I would appreciate any references to 1D shear stress equations. I have found one but I can't quite derive the same equation they have so not sure if its correct.

Thank you in advance!
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Old   December 21, 2011, 05:01
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http://www.jstor.org/pss/2157934

not sure if this is what you are looking for, though....
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