Final answer:
Pressure in barometers and manometers is proportional to both the height and the density of the liquid, and is dependent on gravity. Mercury is preferred over water for its high density, allowing for more compact devices.
Step-by-step explanation:
Concerning a barometer or manometer, it is true that pressure is directly proportional to the height of the liquid used in the device. Moreover, pressure is directly proportional to the density of the liquid used as well. However, it is not true that pressure is independent of the acceleration due to gravity; in fact, pressure in these devices is dependent on the acceleration due to gravity. In the equation P = hρg (where P is pressure, h is the height of the liquid column, ρ is the density of the liquid, and g is the acceleration due to gravity), you can see that both the height and the density of the liquid, as well as gravity, play a crucial role. Using a very dense liquid like mercury in barometers allows for a compact design, since less height is needed to balance atmospheric pressure compared to using a liquid like water, which is less dense and would require a much taller device.