Question

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

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

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

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

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

Answer 1

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

The explanation: For non-diagonal elements,

( au=muleft{∇vec{v}+(∇vec{v})^T ight})

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