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Express the shear stress tensor(τ) of a three-dimensional fluid flow element in terms of the velocity vector(v).(a) \(\tau=\mu\left\{(\nabla \vec{v})^T\right\}+\lambda(\nabla.\vec{v})I\)(b) \(\tau=\mu\left\{(\nabla \vec{v})\right\}+\lambda(\nabla.\vec{v})I\)(c) \(\tau=\mu\left\{(\nabla \vec{v})^T+(\nabla.\vec{v})^T\right\}\)(d) \(\tau=\mu\left\{(\nabla \vec{v})^T+(\nabla.\vec{v})^T\right\}+\lambda(\nabla.\vec{v})I\)This question was addressed to me during an online interview.My question is based upon Governing Equations in division Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer»

The correct ANSWER is (d) \(\tau=\mu\left\{(\nabla \vec{v})^T+(\nabla.\vec{v})^T\right\}+\lambda(\nabla.\vec{v})I\)

To explain: The shear stress tensor of a fluid element can be given by \(\tau=\mu\left\{(\nabla \vec{v})^T+(\nabla.\vec{v})^T\right\}+\lambda(\nabla.\vec{v})I\). This is not applicable for practical cases. HOWEVER, common fluids like AIR and WATER are assumed to be Newtonian for USING this relationship.



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