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.

Steady, compressible flow of air takes place through an adiabatic converging-diverging nozzle, as shown in the figure. For a particular value of pressure difference across the nozzle, a stationary normal shock wave forms in the diverging section of the nozzle. If $E$ and $F$ denote the flow conditions just upstream and downstream of the normal shock, respectively, which of the following statement(s) is/are TRUE?

The velocity field of a certain two-dimensional flow is given by

V(𝑥, 𝑦) = 𝑘(𝑥𝑖̂ − 𝑦𝑗̂)

where 𝑘 = 2 s^-1. The coordinates 𝑥 and 𝑦 are in meters. Assume gravitational effects to be negligible.

If the density of the fluid is 1000 kg/m³ and the pressure at the origin is 100 kPa, the pressure at the location (2 m, 2 m) is _____________ kPa.

(Answer in integer)