A channel of width $$450$$ $$mm$$ branches into two sub-channels having width $$300$$ $$mm$$ and $$200$$ $$mm$$ as shown in figure. If the volumetric flow rate (taking unit depth) of an incompressible flow through the main channel is $$0.9$$ $$3$$ $$m/s,$$ and the velocity in the sub-channel of width $$200$$ $$mm$$ is $$3$$ $$m/s,$$ the velocity in the sub-channel of width $$300$$ $$mm$$ is _____________ $$m/s$$.

Assume both inlet and outlet to be at the same elevation.

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 , $${a_x} = {{ - \left( {x + y} \right)} \over {{{\left( {{x^2} + {y^2}} \right)}^2}}}$$

The water jet exiting from a stationary tank through a circular opening of diameter $$300$$ $$mm$$ impinges on a rigid wall as shown in the figure. Neglect all minor losses and assume the water level in the tank to remain constant. The net horizontal force experienced by the wall is ___________ $$kN.$$

Density of water is $$1000\,\,kg/{m^3}.$$

Acceleration due to gravity $$g = 10\,\,m/{s^2}.$$

Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $$\mu $$ through a circular pipe of radius $$R.$$ Given that the velocity at a radial location of $$R/2$$ from the center-line of the pipe is $${U_1},$$ the shear stress at the wall is $$K\mu {U_1}/R,$$ where $$K$$ is _________________.