A steady two-dimensional flow field is specified by the stream function

ψ = kx3y,

where x and y are in meters and the constant k = 1 m-2s-1. The magnitude of acceleration at a point (x, y) = (1 m, 1 m) is ________ m/s2 (round off to 2 decimal places).

For a steady flow, the velocity field is $$\overrightarrow V = \left( { - {x^2} + 3y} \right)\widehat i + \left( {2xy} \right)\widehat j.$$ The magnitude of the acceleration of the particle at $$(1, -1)$$ is

For a two-dimensional flow, the velocity field is $$\overrightarrow u = {x \over {{x^2} + {y^2}}}\widehat i + {y \over {{x^2} + {y^2}}}\widehat j,$$ where $$\widehat i$$ and $$\widehat j\,\,$$ are the basis vectors in the $$x$$-$$y$$ Cartesian coordinate system .
Identify the CORRECT statements from below.
(1) The flow is incompressible
(2) The flow is unsteady
(3) $$y$$-component of acceleration, $${a_y} = {{ - y} \over {{{\left( {{x^2} + {y^2}} \right)}^2}}}$$
(4) $$x$$-component of acceleration , $${a_x} = {{ - \left( {x + y} \right)} \over {{{\left( {{x^2} + {y^2}} \right)}^2}}}$$

Match the following pairs: