Final answer:
The fluid levels in a manometer equalize on both sides when open to the atmosphere due to the equal atmospheric pressure exerted on each side, leading to equilibrium irrespective of tube diameters.
Step-by-step explanation:
The fluid in a manometer reaches equal levels on either side when both sides are open to the atmosphere because the atmospheric pressure is the same on both sides. Regardless of the tubes' different diameters, the pressures at the bottom of both sides must be equal, or else the fluid will flow from the side with higher pressure to the side with lower pressure until equilibrium is reached.
This is guided by the principle that pressure at a certain depth, in fluids at rest, depends only on the height and not on the shape of the container. Hence, if the manometer is open to the atmosphere on both ends, the atmospheric pressure exerts the same force on both columns of fluid, so the fluid levels out to the same height on both sides.