In metrology, there are different types of measuring instruments such as Linear measuring instruments, comparators, Indicators, interferometers and angular measuring instruments. For the measurement of Pressure in Fluids, we use Manometers and mechanical gauges. In this article, we have discussed the broad classification of the Manometers in a detailed manner.

Before getting into the main topic, we want you to understand the units used for the measurement of Pressure in different unit systems. we use the following units for pressure.

**The units of pressure are :**

In MKS units: kgf/m^{2} and kgf/cm^{2}

In SI units Newton/m^{2} or N/m^{2} and N/mm^{2} (∴ N/m^{2} is known as Pascal and is represented by Pa)**Other commonly used units of pressure are :**

kPa = kilo pascal = 1000 N/m^{2}

bar = 100 kPa = 10^{5} N/m^{2}

Now we know the units of Fluid Pressure. But how we do take measures of the fluid pressure with instruments and how do they work.

## Measurement of Fluid Pressure

The Fluid pressure can be measured by the following instruments:

- Manometers
- Mechanical Gauges.

Let us further classify these two instruments in detail.

### Manometers

Manometers are defined as the devices used for measuring the pressure at a point in a fluid by balancing the column of fluid with the same or another column of the fluid.

Manometers are classified as follows

(i) Simple Manometers

(ii) Differential Manometers

### Mechanical Gauges

Mechanical gauges are defined as the devices used for measuring the pressure by balancing the fluid column by the spring or dead weight. The commonly used mechanical pressure gauges are :

(a) Diaphragm pressure gauge

(b) Bourdon tube pressure gauge

(c) Dead-weight pressure gauge

(d) Bellows pressure gauge

Let us discuss all these manometers in a detailed manner with the schematic diagrams.

## Simple Manometers

A simple manometer consists of a glass tube having one of its ends connected to a point where pressure is to be measured and the other end remains open to the atmosphere. Common types of simple manometers are

- Piezometer,
- U-tube Manometer
- Single Column Manometer

### 1. Piezometer

Piezometer is the simplest form of manometer used to measure gauge pressures. One end of this manometer is connected to the point where pressure is to be measured and another end is open to the atmosphere as shown in the following.

The rise of liquid gives the pressure head at that point. If at point A, the height of liquid say water is h in a piezometer tube, then the pressure at A will be

= ρ × g × h N/m^{2}

### 2. U-tube Manometer

It consists of a glass tube bent in a U-shape, one end of which is connected to a point at which pressure is to be measured and the other end remains open to the atmosphere as shown in the following figure.

The tube generally contains mercury or any other liquid whose specific gravity is greater than the specific gravity of the liquid whose pressure is to be measured.

#### (a) For Gauge Pressure

Let B is the point at which pressure is to be measured, whose value is p.

The datum line is A-A.

Let

h_{1} = Height of light liquid above the datum line

h_{2} = Height of heavy liquid above the datum line

S_{1} = Specific gravity of the light liquid

ρ_{1} = Density of light liquid = 1000 x S_{1}

S_{2} = Specific gravity of the heavy liquid

ρ_{2} = Density of heavy liquid = 1000 × S_{2}

As the pressure is the same for the horizontal surface. Hence pressure above the horizontal datum line A-A in the left column and in the right column of the U-tube manometer should be the same.

Pressure above A-A in the left column = p + ρ_{1} × g × h_{1}

Pressure above A-A in the right column = ρ_{2} × g × h_{2}

As we said above pressure above the horizontal datum line A-A in the left column and in the right column of the U-tube manometer should be the same, we should equate these two pressures

p + ρ_{1} × g × h_{1} = ρ_{2} × g × h_{2}

p = (ρ_{2} × g × h_{2} – ρ_{1} × g × h_{1})

#### (b) For Vacuum Pressure

For measuring vacuum pressure, the level of the heavy liquid in the manometer will be as shown in the following figure

The Pressure above A-A in the left column = ρ_{2} × g × h_{2} + ρ_{1} × g × h_{1} + p

Pressure head in the right column above A-A = 0

We should equate these two equations, we get

ρ_{2} × g × h_{2} + ρ_{1} × g × h_{1} + p = 0

p = – (ρ_{2} × g × h_{2} + ρ_{1} × g × h_{1})

### 3. Single Column Manometer

The single-column manometer is a modified form of a U-tube manometer in which a reservoir, having a large cross-sectional area (about 100 times) as compared to the area of the tube is connected to one of the limbs (say left limb) of the manometer as shown in the following figure.

Due to the large cross-sectional area of the reservoir, for any variation in pressure, the change in the liquid level in the reservoir will be very small which may be neglected and hence the pressure is given by the height of liquid in the other limb. The other limb may be vertical or inclined.

Thus there are two types of single-column manometers as

- Vertical Single Column Manometer
- Inclined Single Column Manometer

#### Vertical Single Column Manometer

The above-given figure is the vertical single-column manometer. Let X-X be the datum line in the reservoir and in the right limb of the manometer when it is not connected to the pipe. When the manometer is connected to the pipe, due to high pressure at A, the heavy liquid in the reservoir will be pushed downward and will rise in the right limb.

Let

Δh = Fall of heavy liquid in the reservoir

h_{2} = Rise of heavy liquid in the right limb

h_{1} = Height of centre of pipe above X-X

P_{A} = Pressure at A, which is to be measured

A = Cross-sectional area of the reservoir

a = Cross-sectional area of the right limb

S_{1} = Specific gravity of liquid in the pipe

S_{2} = Specific gravity of heavy liquid in reservoir and right limb

ρ_{1} = Density of liquid in the pipe

ρ_{2} = Density of liquid in the reservoir

The fall of heavy liquid in the reservoir will cause a rise in heavy liquid levels in the right limb.

A × ∆h = a × h_{2}

∆h = (a × h_{2})/A

Now consider the datum line Y-Y as shown in the above figure.

The pressure in the right limb above Y – Y = ρ_{2} × g × (∆h + h_{2})

The Pressure in the left limb above Y – Y = ρ_{1} × g × (∆h + h_{1}) + P_{A}

Equating these pressures, we have

ρ_{2} × g × (∆h + h_{2}) = ρ_{1} × g × (∆h + h_{1}) + P_{A}

P_{A} = ρ_{2} × g × (∆h + h_{2}) – ρ_{1} × g × (∆h + h_{1})

P_{A} = ∆h(ρ_{2}g – ρ_{1}g) + h_{2}ρ_{2}g – h_{1}ρ_{1} g

P_{A} = [(a × h_{2})/A] (ρ_{2}g – ρ_{1}g) + h_{2}ρ_{2}g – h_{1}ρ_{1} g

This is the equation to

As area A is very large as compared to a, hence ratio a/A becomes very small and can be neglected.

Then

P_{A} = h_{2}ρ_{2}g – h_{1}ρ_{1} g

From this equation, it is clear that as h_{1} is known and hence by knowing h_{2} or rise of heavy liquid in the right limb, the pressure at A can be calculated.

#### Inclined Single Column Manometer

The following figure shows the inclined single-column manometer. This manometer is more sensitive. Due to inclination, the distance moved by the heavy liquid in the right limb will be more.

Let

L= Length of heavy liquid moved in the right limb from X-X

θ = Inclination of the right limb with horizontal

h_{2} = Vertical rise of heavy liquid in the right limb from X-X = L × sin θ

From the above equation, the pressure at A is

P_{A} = h_{2}ρ_{2}g – h_{1}ρ_{1} g

Substituting the value of h_{2} we get

P_{A} = L × sin θ × ρ_{2}g – h_{1}ρ_{1} g

From these relations, we can find the fluid pressure.

## Differential Manometers

Differential manometers are the devices used for measuring the difference in pressures between two points in a pipe or in two different pipes. A differential manometer consists of a U-tube, containing a heavy liquid, whose two ends are connected to the points, whose difference in pressure is to be

measured.

The most common types of differential manometers are

- U-tube differential manometer and
- Inverted U-tube differential manometer

### 1. U-tube Differential Manometer

The following figure shows the differential manometers of the U-tube type

Let the two points A and B are at a different level and also contains liquids of different

Specific Gravity These points are connected to the U-tube differential manometer. Let the pressure at A and B be P_{A} and P_{B}.

Let

h= Difference of mercury level in the U-tube.

y = Distance of the centre of B, from the mercury level in the right limb.

x = Distance of the centre of A, from the mercury level in the right limb.

ρ_{1} = Density of liquid at A.

ρ_{2} = Density of liquid at B.

ρ_{g} = Density of heavy liquid or mercury

P_{A} = pressure at A

P_{B} = Pressure at B

Let us take the datum line at X-X.

Pressure above X-X in the left limb = ρ_{1}g(h + x) + P_{A}

Pressure above X-X in the right limb = (ρ_{g} × g × h) + (ρ_{2} × g × y) + P_{B}

Equating the two pressure, we have

ρ_{1}g(h + x) + P_{A} = (ρ_{g} × g × h) + (ρ_{2} × g × y) + P_{B}

P_{A} – P_{B} = (ρ_{g} × g × h) + (ρ_{2} × g × y) – ρ_{1}g(h + x)

P_{A} – P_{B} = h × g(ρ_{g} – ρ_{1}) + ρ_{2}gy – ρ_{1}gx

Difference of pressure at A and B if they are at different levels P_{A} – P_{B} = h × g(ρ_{g} – ρ_{1}) + ρ_{2}gy – ρ_{1}gx

If A and B are at the same level and contain the same liquid of density ρ_{1}.

Then the Pressure above X-X in right limb = (ρ_{g} × g × h) + (ρ_{1} × g × x) + P_{B}

Pressure above X-X in left limb = ρ_{1}g(h + x) + P_{A}

Equating the two pressure, we get

(ρ_{g} × g × h) + (ρ_{1} × g × x) + P_{B} = ρ_{1}g(h + x) + P_{A}

P_{A} – P_{B} = (ρ_{g} × g × h) + (ρ_{1} × g × x) – ρ_{1}g(h + x)

P_{A} – P_{B} = h × g(ρ_{g} – ρ_{1}) + ρ_{1}gy – ρ_{1}gx

P_{A} – P_{B} = h × g(ρ_{g} – ρ_{1})

Difference of pressure at A and B if they are at the same level P_{A} – P_{B} = h × g(ρ_{g} – ρ_{1}).

### 2. Inverted U-tube Differential Manometer

It consists of an inverted U-tube, containing a light liquid. The two ends of the tube are connected to the points whose difference in pressure is to be measured. It is used for measuring the difference between low pressures.

The following figure shows an inverted U-tube differential manometer connected to the two points A and B. Let the pressure at A is more than the pressure at B.

Let

h_{1} = Height of liquid in left limb below the datum line X-X

h_{2} = Height of liquid in the right limb

h = Difference between light liquid

ρ_{1} = Density of liquid at A.

ρ_{2} = Density of liquid at B.

ρ_{s} = Density of light liquid

P_{A} = pressure at A

P_{B} = Pressure at B

Let us take the datum line at X-X.

Pressure above X-X in the left limb = P_{A} – ρ_{1} × g × h_{1}

Pressure above X-X in the right limb = P_{B} – (ρ_{2} × g × h_{2}) – (ρ_{s} × g × h)

Equating the two pressure, we have

P_{A} – ρ_{1} × g × h_{1} = P_{B} – (ρ_{2} × g × h_{2}) – (ρ_{s} × g × h)

P_{A} – P_{B} = (ρ_{1} × g × h_{1}) – (ρ_{2} × g × h_{2}) – (ρ_{s} × g × h)

Difference of pressure at A and B is P_{A} – P_{B} = (ρ_{1} × g × h_{1}) – (ρ_{2} × g × h_{2}) – (ρ_{s} × g × h)

## Conclusion

We have discussed all the types of manometers used to measure fluids. Let us know what you think about these in the comment section below.

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