# 1D Stress Tensor

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 December 17, 2011, 13:01 1D Stress Tensor #1 Senior Member   Join Date: Jun 2010 Posts: 107 Rep Power: 7 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!

 December 17, 2011, 13:10 #2 Senior Member   cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 11 well, just set all the derivatives wrt y and z to zero, so sth like div(v) will become du/dx...

 December 19, 2011, 08:32 #3 Senior Member   Join Date: Jun 2010 Posts: 107 Rep Power: 7 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!

 December 21, 2011, 05:01 #4 Senior Member   cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 11 http://www.jstor.org/pss/2157934 not sure if this is what you are looking for, though....

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