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what’s the fundamental theory of manometer

The fundamental theory of a manometer is based on Pascal's law, which states that the pressure applied to a fluid is transmitted equally in all directions. A manometer is a device used to measure the pressure of a fluid, which can be either a liquid or a gas.

In a manometer, a tube is partially filled with a liquid, which is usually mercury or water. One end of the tube is exposed to the fluid whose pressure is being measured, while the other end is open to the atmosphere or connected to a container of known pressure. The difference in pressure between the two ends of the tube causes the liquid to rise or fall in the tube.

The height of the liquid column in the tube is directly proportional to the pressure difference between the two ends of the tube. This relationship is described by the equation:

ΔP = ρgh

where ΔP is the pressure difference between the two ends of the tube, ρ is the density of the liquid, g is the acceleration due to gravity, and h is the height of the liquid column.

Thus, by measuring the height of the liquid column in the manometer, the pressure difference between the two ends of the tube can be determined. This fundamental theory of manometer is widely used in various applications, including in the measurement of blood pressure, fluid pressure in pipes, and air pressure in tires