Explain why the fluid reaches equal levels on either side of a manometer if both sides are open to the atmosphere, even if the tubes are of different diameters.

Fluid statics, often known as hydrostatics, is a branch of fluid mechanics that investigates the state of balance of a floating and submerged body, as well as the pressure in a fluid, or imposed by a fluid, on an immersed body.

The pressure which is exerted by the air or the atmosphere to the earth and to each and every body of the earth is called the atmospheric pressure.Here is this case even if the manometer is of different diameter the fluid are reached at the same position.

Let’s understand the question using the figure

The height of the fluid is same even if the diameter is different because both sides are exposed to the environment, the pressure on top of both fluid columns is the same. If the fluid levels in each column are not the same height, they will change until they are because the pressure at any depth, including the bottom, is only dependent on the pressure on top of the fluid plus ρgh, where, ρ is the density of the fluid, g is gravitational field strength, and h is the height of the fluid when the heights are equal, the pressure at the bottom of each column is equal.

$\mathit{P}\mathbf{=}\mathit{h}\mathit{\rho }\mathit{g}$

Because there is no pressure differential between the two columns now, fluid motion comes to a halt with equal heights.

Hence, there is same height even if the diameter is different, as fluid motion comes to a standstill with equal heights because there is no pressure differential between the two columns.