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 $=10 \mathrm{~m} \mathrm{~s}^{-2}$

Consider a velocity field $\vec{V}=3 z \hat{i}+0 \hat{j}+C x \hat{k}$, where $C$ is a constant. if the flow is irrotational, the value of C is ________ (rounded off to 1 decimal place).

Let a spherical block of ice at $-7^{\circ} \mathrm{C}$ be exposed to atmospheric air at $30^{\circ} \mathrm{C}$ with the gravitational direction as shown in the figure below. What will be the overall direction of air flow in this situation?

During a welding operation, thermal power of 2500 W is incident normally on a metallic surface. As shown in the figure below (figure is NOT to scale), the heated area is circular. Out of the incident power, $85 \%$ of the power is absorbed within a circle of radius 5 mm while $65 \%$ is absorbed within an inner concentric circle of radius 3 mm . The power density in the shaded area is __________ $\mathrm{Wmm}^{-2}$ (rounded off to 2 decimal places).