Expressing \(\tau:\Delta \vec{V}\) in terms of flow variables, we get λφ+μψ. What are φ and ψ?

• A. \(\phi=(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z})^2 \,and\, \psi=(\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x})^2+(\frac{\partial v}{\partial z}+\frac{\partial w}{\partial y})^2+(\frac{\partial u}{\partial z}+\frac{\partial w}{\partial x})^2\)
• B. \(\psi=(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z})^2 \,and\, \phi=(\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x})^2+(\frac{\partial v}{\partial z}+\frac{\partial w}{\partial y})^2+(\frac{\partial u}{\partial z}+\frac{\partial w}{\partial x})^2\)
• C. \(\psi=(\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z})^2 \,and\, \phi=2(\frac{\partial u}{\partial x})^2 + 2(\frac{\partial v}{\partial y})^2 +2(\frac{\partial w}{\partial z})^2+(\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x})^2 +\) \( (\frac{\partial v}{\partial z} + \frac{\partial w}{\partial y})^2 + (\frac{\partial u}{\partial z} + \frac{\partial w}{\partial x})^2\)
• D. \(\phi=(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z})^2 \,and\, \psi=2(\frac{\partial u}{\partial x})^2+2(\frac{\partial v}{\partial y})^2+2(\frac{\partial w}{\partial z})^2+(\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x})^2+\) \((\frac{\partial v}{\partial z}+\frac{\partial w}{\partial y})^2+(\frac{\partial u}{\partial z}+\frac{\partial w}{\partial x})^2\)