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The DEVIATORIC STRESS TENSOR $\sigma_{ij}^d$ in N-S is the part:
A{'text': 'Identical to total stress', 'label': 'A'}
B{'text': 'Total stress MINUS the isotropic pressure: $\\sigma_{ij}^d = \\sigma_{ij} + p\\delta_{ij}$ — captures the shear/viscous part', 'label': 'B'}
C{'text': 'Equal to pressure only', 'label': 'C'}
D{'text': 'Zero for any fluid', 'label': 'D'}
Answer & Solution
Correct answer: B. {'text': 'Total stress MINUS the isotropic pressure: $\\sigma_{ij}^d = \\sigma_{ij} + p\\delta_{ij}$ — captures the shear/viscous part', 'label': 'B'}
Total stress = $-p\delta_{ij} + \sigma_{ij}^d$. Deviatoric (shear) stress encodes the viscous part. For a Newtonian fluid it depends linearly on strain rate. Pressure (the isotropic part) is a separate thermodynamic variable.
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