Parabolic mirrors are the practical application of the mathematical concept of a parabola to construct a reflective surface. One of the earliest forms of this type of mirror was the…

## The Working Principle, Types, And Applications of a Manometer

A device used to measure the pressure at any point in a fluid, manometers are also used to measure the pressure of gas and air. This ScienceStruck article explains the working principle of a manometer, and provides a review of different types of manometers and their applications.

### Quick Fact

A sphygmomanometer, a type of manometer, is commonly used to check blood pressure in humans. Systolic pressure reading is the mercury reading on the pressure gauge when the pulse is first heard, while diastolic pressure reading is when the pulse can first no longer be heard.

‘Pressure’ or the intensity of pressure is defined as force per unit area, or **P = F/A**, where P is measured in N/m^{2}. Fluid pressure is measured with respect to varying individual reference that is device or procedural specific. When it is measured with respect to absolute zero (or complete vacuum), it is called absolute pressure. When it is measured either above or below atmospheric pressure, it is called gauge pressure.

The term manometer is derived from the ancient Greek words ‘manós’, meaning thin or rare, and ‘métron’. A manometer works on the principle of hydrostatic equilibrium and is used for measuring the pressure (static pressure) exerted by a still liquid or gas. Hydrostatic equilibrium states that the pressure at any point in a fluid at rest is equal, and its value is just the weight of the overlying fluid. In its simplest form, a manometer is a U-shaped tube consisting of an incompressible fluid like water or mercury. It is inexpensive and does not need calibration.

As seen in the figure, the U-shaped tube filled with liquid measures the differential pressure, i.e., the difference in levels ‘h’ between the two limbs gives the pressure difference (p_{1} – p_{2}) between them. When pressure is applied at limb 1, the fluid recedes in limb 1, and its level rises in limb 2. This rise continues till a balance is struck between the unit weight of fluid and the pressure applied. If the pressure applied at one opening; say limb 1 of the U-tube, is atmospheric pressure, the difference gives the gauge pressure at limb 2.

**h = (p _{1} – p_{2}) ρ g**

where, **ρ** = density of the liquid used in manometer

Hence, **ρg** = specific weight of the liquid

Manometers are generally classified into **simple manometers** and **differential manometers**. Let us take a closer look at the each individual type and their working principle in detail.

## Types of Simple Manometers

### ▶ Piezometer

As shown in the figure, one end of the piezometer is open to atmospheric pressure, and the other end is connected to the point A, where pressure is to be measured. The rise of liquid will be in accordance with the pressure at point A. If h is the height of liquid in the piezometer, pressure at point A is given by:

**Pressure in N/m ^{2} = ρ × g × h**

### ▶ U-Tube Manometer

It consists of a glass tube bent like the letter ‘U’. In this type of manometer, balancing a column of liquid is done by another column of same or other liquid. One end of the U-tube is attached to the point where pressure is to be measured, while the other end is open to atmospheric pressure. The pressure at point B in the figure is given by:

**P = ρ _{2} g h_{2} – ρ_{1}g h_{1}**

where, **ρ _{2}** = density of heavy liquid

**h**= height of heavy liquid above reference line

_{2}**ρ**= density of light liquid

_{1}**h**= height of light liquid above reference line.

_{1}### ▶ Cistern or Well Type Manometer:

As shown in the figure, the well area is larger than the area of the tube, denoted by A. The rise in liquid level in the tube is considered while that in the well is ignored. If p_{1} and p_{2 }are absolute pressures applied as shown in figure:

**h p _{1} A – p_{2} A = Ahρg**

**h = (p**

_{1}– p_{2})/ρg### ▶ Inclined Type Manometer

It is similar to a well type manometer in construction. The only difference being that the vertical column limb is inclined at an angle θ. Inclined manometers are used for accurate measurement of small pressure.

## Types of Differential Manometers

Differential Manometers are used to measure the pressure difference between two points in a pipe or between two different pipes. The principle and working of the types of differential manometers are given below.

### ▶ U- tube Differential Manometer

In the adjoining figure, the two points A and B are in liquids having different specific gravity. Also, A and B are at different levels. A liquid which is denser than the two fluids is used in the U tube, which is immiscible with the other fluids. Let the pressure at point A be P_{A} and that at point B be P_{B}.

**P _{A} – P_{B} = g × h (ρ_{g} – ρ_{1})**

where, **h** = difference in mercury level in the U-tube**ρ _{g}** = density of heavy liquid

**ρ**= density of liquid A.

_{1}### ▶ Inverted U-tube Differential Manometer

This type of manometer is used when the difference between the densities of the two liquids is small. Similar to the previous type, A and B are points at different levels with liquids having different specific gravity. It consists of a glass tube shaped like an inverted letter ‘U’ and is similar to two piezometers connected end to end. Air is present at the center of the two limbs. As the two points in consideration are at different pressures, the liquid rises in the two limbs. Air or mercury is used as the manometric fluid. If P_{A} is the pressure at point A and P_{B} is the pressure at point B;

**P _{A} – P_{B} = ρ_{1} × g × h_{1} – ρ _{2} × g × h_{2} – ρ g × g × h**

where, **ρ _{1}** = density of liquid at A

**ρ**= density of liquid at B

_{ 2}**ρ**= density of light liquid

_{ g}**h**= difference of light liquid

## Digital Manometer

A digital manometer uses a microprocessor and pressure transducer to sense slight changes in pressure. It gives the pressure readout on a digital screen. It measures differential pressure across two inputs. An analog/digital output in proportion to the instantaneous pressure can be obtained.

Digital manometers report positive, negative, or differential measurements between pressures. With the integration of an anemometer, flow readings can also be recorded on a digital manometer.

## Manometer Accuracy

Current standards for accuracy require that manometers be within +/- 3 mm Hg (mm of mercury) of the reference or within +/- 3 mm Hg or 2% of the reading (whichever is greater) for extended temperature ranges.

*Accuracy in Liquid Manometers*

- U-tube type: +/- ½ of minor scale graduation
- Well type: +/- ½ of minor scale graduation
- Inclined type: +/- ½ of minor scale graduation

*Accuracy in Digital Manometers*

- General purpose: +/- 0.025 – 0.1% F.S.
- Calibrating: +/- 0.025 – 0.1% F.S.

## Manometer Applications

- Used in the maintenance of heating, ventilation, and air conditioning (HVAC) systems, low pressure pneumatic or gas systems.
- Construction of bridges, installing swimming pools and other engineering applications.
- Climate forecasting.
- Clinical applications like measuring blood pressure and in physiotherapy.
- Piezometers are used to measure the pressure in pipes where the liquid is in motion.

A manometer is one of the earliest and simplest devices used for measurement of gauge pressure and differential pressures. As mentioned in this discourse, it has myriad uses in different fields.