16100lectre21_cg

16100lectre21_cg - Viscous Flow: Stress Strain Relationship...

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Viscous Flow: Stress Strain Relationship Objective: Discuss assumptions which lead to the stress-strain relationship for a Newtonian, linear viscous fluid: j ik ij ij ji k k k u uu x xx v w V y z τµ δ λ  ∂∂ =+ +   =++ = K i where = µ dynamic viscosity coefficient λ = bulk viscosity coefficient Note: 0, 1, ij ij = = 1 shear strain rate in , plane 2 j i ij i j u u ε Thus, written in terms of the strain rates, the stress tensor is: N () viscous stress using indicial notation due to shearing this is of a fluid element viscous stress due to an overall compression or expansion of the fluid element's volume 2 kk ij ij ij xx yy zz τ µε δ λ ε + + ±²²³ ² ²´ ±²²²³²²²´ This stress-strain relationship can be derived by the following two assumptions: 1. The shear stress is independent of a rotation of the coordinate system 2. The shear stress is at most a linear function of the strain rate tensor.
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

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16100lectre21_cg - Viscous Flow: Stress Strain Relationship...

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