Question

Express \(\tau_{yz}\) in terms of velocity gradients.

(a) \(\tau_{yz}=μ(\frac{\partial v}{\partial z}+\frac{\partial w}{\partial y})\)

(b) \(\tau_{yz}=μ(\frac{\partial u}{\partial z}+\frac{\partial u}{\partial y})\)

(c) \(\tau_{yz}=μ(\frac{\partial v}{\partial x}+\frac{\partial w}{\partial x})\)

(d) \(\tau_{yz}=μ(\frac{\partial w}{\partial z}+\frac{\partial v}{\partial y})\)

The question was asked during an online exam.

I need to ask this question from Governing Equations topic in chapter Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

Correct option is (a) \(\tau_{yz}=μ(\frac{\partial v}{\partial z}+\frac{\partial w}{\partial y})\)

The explanation: For non-diagonal elements,

\(\tau=\mu\left\{∇\vec{v}+(∇\vec{v})^T\right\}\)

\(\tau_{yz}=\mu(\frac{\partial v}{\partial z}+\frac{\partial w}{\partial y})\).