Manometer

Any fluid (be it liquid or gas) exerts pressure. Fluid pressure is the force exerted by a fluid per unit area on any object. This fluid pressure can be measured by a simple device, known as a manometer. The simplest kind of manometer is a U-shaped tube. Sometimes, a reference liquid is used to measure the pressure, and sometimes we can choose to skip adding the reference liquid. It depends on how we want to conduct our experiment. A manometer can be of different types, all of which will be covered in this article in detail. You would also get to know who invented the manometer, and what are its uses in day to day life.

U-Shaped manometer

As mentioned above, it is the simplest type of manometer. It is made up of glass.

Case 1: Both ends of the tube are open

When we pour a liquid into an open glass U-tube, then the liquid adjusts itself in a way that the height in both the columns is equal. This happens because the atmospheric pressure is equal at both columns, since the glass tube is open from both ends. 

Case 2: One end of the tube is closed

There can be two further possibilities to be explored in this case. 

Let us suppose that the left column is closed, and that there is some gas entrapped in that column. The gas also has some pressure.

When we pour the liquid into the tube, it gets into both the columns. Now, if the gas in the left column has a pressure greater than the atmospheric pressure, the level of liquid in the left column would be lower as compared to the level of liquid in the right column. The difference in the atmospheric pressure and the pressure of the gas is represented by the difference in the heights of the liquid in the two columns. The more the height difference, the more the pressure difference, and vice versa.

If the gas in the left column has a pressure lower than the atmospheric pressure, then the level of liquid in the left column would be higher as compared to the level of liquid in the right column. If there is no gas in the left column, then the atmospheric pressure would lead to an even further lowering of the liquid level in the right column. The more the liquid goes down in height, the more the atmospheric pressure is.

If there is absolutely no gas present in the left column, i.e., there is a vacuum, then there would be no pressure exerted on the liquid in the left column. The atmosphere would exert all the pressure only on the liquid present in the right column. Hence, the liquid in the right column gets pushed down, and the level of liquid in the left column rises. This difference in height is equivalent to the value of atmospheric pressure. In such a case, it acts like a barometer, a device that measures atmospheric pressure. 

Calculation

A very simple formula is applied to calculate the fluid pressure inside the manometer at any given point.

We know that P = 𝛒gh, 

where,

P is the pressure, 

𝛒 is the fluid’s density,

g is acceleration due to gravity, 

h is the height.

It is fairly easy to derive this formula, and it requires the application of the basic physics concepts.

Let the liquid be present in the form of a cylindrical tube of height h and area of cross-section A.

Now, the liquid of cylindrical shape would obviously exert some force. This force would be equal to the product of its mass and acceleration due to gravity.
Mathematically, F = m.g

Force per unit area gives pressure, so P = F/A
Replacing the value of force in the above equation, we get

P = mg/A

But, mass is nothing but the product of the density of liquid and volume of liquid. So, m = 𝛒V

P = 𝛒Vg/A

Now, the volume of the cylinder is equal to the product of the cross-sectional area of the cylinder and its height. So, V = A.h

Hence, P = 𝛒gh

This is the derivation of the formula used to measure the fluid pressure in a manometer.

Uses of Manometer

One of the primary uses of a manometer is to measure fluid pressure. It is so easy to measure fluid pressure using this device that it can be used in any laboratory with little assistance. Moreover, this device is not very expensive, which makes the process economical as well.

It is used to estimate pressure inside the pipelines. 

The most common type of manometer is the sphygmomanometer. It is a medical device used to measure blood pressure in patients, and was invented by Karl Samuel Ritter von Basch in 1881.

Conclusion

A manometer is an important scientific device, and its construction is very simple. The simplest manometer is a U-shaped glass tube whose one end can be connected by a pressure device and the other end can be kept open to the atmosphere. The height difference in the levels of liquid in the two columns can give atmospheric pressure. A manometer can measure the pressure of both gases and liquids. We use a reference liquid (most commonly mercury) to do the required calculations.