What is the wavelength of the wave, the pressure of the trapped gas, and the definition of streamline flow?

From the figure, the first crest is at $0.5 \text{ m}$ and the second crest is at $2.5 \text{ m}$.

The wavelength ($\lambda$) is the distance between two consecutive crests.

The wavelength of the wave is $\boxed{\text{2.0 m}}$.

Atmospheric pressure, $P_{atm} = 100000 \text{ Pa}$.
Height difference in mercury, $h = 5 \text{ cm} = 0.05 \text{ m}$.
Density of mercury, $\rho_{Hg} = 13600 \text{ kg/m}^3$.
Acceleration due to gravity, $g = 9.8 \text{ m/s}^2$.

Since the mercury level in the sealed arm (trapped gas side) is higher, the pressure of the trapped gas is less than the atmospheric pressure.

The pressure of the gas is $\boxed{\text{93336 Pa}}$.

a) Streamline flow: This is a type of fluid flow where the fluid particles move in smooth, parallel layers without mixing. The velocity of the fluid at any given point remains constant over time, and the paths of individual fluid particles do not cross each other.

b) Turbulent flow: This is a type of fluid flow characterized by irregular, chaotic, and unpredictable motion of fluid particles. It involves the formation of eddies and vortices, leading to significant mixing and rapid variations in velocity and pressure at any given point.

As air flows through the pipe, its speed changes with the cross-sectional area. According to the principle of continuity, where the cross-sectional area is smaller (at pipe B), the speed of the air is higher. Conversely, where the cross-sectional area is larger (at pipe A), the speed of the air is lower.

Bernoulli's principle states that for a horizontal flow, an increase in fluid speed is accompanied by a decrease in pressure. Therefore, the pressure of the air at pipe B (higher speed) is lower than the pressure of the air at pipe A (lower speed).

The lower air pressure at pipe B causes the atmospheric pressure acting on the surface of the water in the container to push the water higher into pipe B. Conversely, the higher air pressure at pipe A exerts more downward force, resulting in a lower water level in pipe A. This difference in pressure causes the observed difference in water levels.