Question

The Newtonian fluid has the following velocity field:
$\overrightarrow{V}=x^{2}y\hat{i}+2x{y}^{2}z\hat{j}-y{z}^3\hat{k}$

The rate shear deformation ${\epsilon }_{yz}$ at the point x = -2, y = -1 and z = 2 for given flow is

• A. -6
• B. -2
• C. -12
• D. 4

Answer 1

The correct option is A -6

$\overrightarrow{V}=x^{2}y\hat{i}+2x{y}^{2}z\hat{j}-y{z}^3\hat{k}$

Shear strain,

${\epsilon }_{yz}=\frac{1}{2}(\frac{\partial v}{\partial z}+\frac{\partial w}{\partial y})=\frac{1}{2}(2x{y}^2-z^3)$

$At(-2,-1,2),weget$

${\epsilon }_{yz}=\frac{1}{2}(-4-8)=-6$