16100lecture3_cg

# 16100lecture3_cg - Stress-Strain Relationship for a Newtonian Fluid First the notation for the viscous stresses are y yy yz x y xz z y zz yx xx x

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Stress-Strain Relationship for a Newtonian Fluid First, the notation for the viscous stresses are: x y z τ xx τ xy τ xz τ zx τ zy τ zz τ yx τ yy τ yz τ ij = stress acting on the fluid element with a face whose normal is in + x i direction and the stress is in + x j direction. Common assumption is that the net moment created by the viscous stresses are zero. ij = ji

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Stress-Strain Relationship for a Newtonian Fluid Let’s look at this in 2-D: dx dy x y τ xx τ xy τ yx τ yy τ yy τ yx τ xy τ xx M z dx dy τ xy 2 dy yx dx 2 M = Net moment about center= z dx + xy dy yx dx 2 2 M = ( x y ) dxdy z y x 2 Thus, for M = 0, x = z y Assumptions for Newtonian fluid stress-strain: 1) ij is at most a linear function of ε ij . 2) The fluid is isotropic, thus its properties are independent of direction stress-strain relationship cannot depend on choice of coordinate axes. 3) When the strain rates are zero, the viscous stresses must be zero. 16.100 2002 2
Stress-Strain Relationship for a Newtonian Fluid
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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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16100lecture3_cg - Stress-Strain Relationship for a Newtonian Fluid First the notation for the viscous stresses are y yy yz x y xz z y zz yx xx x

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