A velocity field is given as $$$\overrightarrow V = 3{x^2}y\widehat i - 6xyz\widehat k$$$
Where $$x,y,z$$ are in $$m$$ and $$V$$ $$m/s.$$ Determine if

(i) It represents an incompressible flow
(ii) The flow is irrotational
(iii) The flow is steady .

The stream function in a two dimensional flow field is given by $$\Psi = {x^2} - {y^2}$$
The magnitude of the velocity at point $$(1,1)$$ is

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

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