The $$2$$ - $$D$$ flow with, velocity $$\overrightarrow v = \left( {x + 2y + 2} \right)\overrightarrow i + \left( {4 - y} \right)\overrightarrow j $$ is

The velocity components in the $$x$$ and $$y$$ directions are given by $$u = \lambda x{y^3} - {x^2}y,$$ $$v = x{y^2} - {3 \over 4}{y^4}.$$ The value of $$\lambda $$ for a possible flow field involving an incompressible fluid is

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