Water with a density of $1000 \mathrm{~kg} / \mathrm{m}^3$ comes out of an industrial condenser through a horizontal pipe of 15 cm radius at the flow rate of $4.5 \mathrm{~m}^3 / \mathrm{min}$. The outlet of the pipe is connected to a coaxial diffuser of 0.5 m length using a flange to raise the pressure of water to atmospheric condition without any backflow. The inner radius ( $r$, in m ) of the diffuser cross-section is expressed as

$$ r=0.15+0.4 x^2 $$

where, $x$ represents the axial distance of the diffuser in m , from its inlet. Considering frictionless flow, the magnitude of the force exerted by the diffuser on the flange is

$\_\_\_\_$ N (rounded off to 2 decimal places).

A pitot tube connected to a U-tube mercury manometer measures the speed of air flowing in the wind tunnel as shown in the figure below. The density of air is $1.23 \mathrm{~kg} \mathrm{~m}^{-3}$ while the density of water is $1000 \mathrm{~kg} \mathrm{~m}^{-3}$. For the manometer reading of $h=30 \mathrm{~mm}$ of mercury, the speed of air in the wind tunnel is __________ $\mathrm{m} \mathrm{s}^{-1}$ (rounded off to 1 decimal place).

Assume: Specific gravity of mercury $=13.6$

Acceleration due to gravity $=10 \mathrm{~m} \mathrm{~s}^{-2}$

In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting points W, N, and S with point J have an equal length L. The pipe connecting points J and E has a length 10L. The pressures at the ends N, E, and S are equal. The flow rate in the pipe connecting W and J is Q. Assume that the fluid flow is steady, incompressible, and the pressure losses at the pipe entrance and junction are negligible. Consider the following statements:

I : The flow rate in pipe connecting J and E is Q/21.

II: The pressure difference between J and N is equal to the pressure difference between J and E.