# MEASUREMENT OF PRESSURE

The pressure of a fluid is measured by the fallowing devices.

1. Manometers

2. Mechanical gauges.

## 1. Manometers:

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

a) Simple Manometers

b) Differential Manometers.

## 2. 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.

## 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. The common types of simple manometers are:

1. Piezo meter.

2. U-tube manometer.

3. Single column manometer.

## 1. Piezometer:

It is a simplest form of manometer used for measuring gauge pressure. One end of this manometer is connected to the point where pressure is to be measured and other end is open to the atmosphere. The rise of liquid in the Piezometer gives pressure head at that point A.

The height of liquid say water is ‘h’ in piezometer tube, then

Pressure at A = **𝛒 g h** **𝐍/Square ****𝐦eter**

## 2. U- tube Manometer:

It consists of a glass tube bent in u-shape, one end of which is connected to a point at which pressure is to be measured and other end remains open to the atmosphere. 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 A – A

Let h1 = height of light liquid above datum line h2 =height of heavy liquid above datum line

S1 = sp. gravity of light liquid

ρ1= density of light liquid = 1000 S1 S2 = sp. gravity of heavy liquid

ρ2= density of heavy liquid = 1000 S2

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

Pressure above A—A ion the left column = p + 𝜌1 gh1 Pressure above A – A in the left column = 𝜌2gh2 Hence equating the two pressures p + 𝜌1 gh1 = 𝜌2gh2

p = 𝝆𝟐gh2 – 𝝆𝟏 gh1

(b) For Vacuum Pressure:

For measuring vacuum pressure, the level of heavy fluid in the manometer will be as shown in fig. Pressure above A A in the left column = 𝜌2g h2 + 𝜌1g h1+ P

Pressure head in the right column above A A = O

𝜌2g h2 + 𝜌1g h1 + P = O

p = – (𝝆𝟐g h2 + 𝝆𝟏g h1)

## SINGLE COLUMN MANOMETER:

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 tube is connected to one of the limbs (say left limb) of the manometer. Due to 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 the liquid in the other limb. The other limb may be vertical or inclined. Thus, there are two types of single column manometer

1. Vertical single column manometer.

2. Inclined single column manometer.

## 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 connected to the pipe, when the Manometer is connected to the pipe, due to high pressure at A The heavy in the reservoir will be pushed downwards and will rise in the right limb.

Let, Δ h= fall of heavy liquid in the reservoir h2= rise of heavy liquid in the right limb

h1= height of the centre of the pipe above X – X pA= Pressure at A, which is to be measured.

A = Cross- sectional area of the reservoir a = cross sectional area of the right limb S1= Specific. Gravity of liquid in pipe

S2= sp. Gravity of heavy liquid in the reservoir and right limb

𝜌1 = density of liquid in pipe

𝜌2= density of liquid in reservoir

Fall of heavy liquid reservoir will cause a rise of heavy liquid level in the right limb

## INCLINED SINGLE COLUMN MANOMETER:

The manometer is more sensitive. Due to inclination the distance moved by heavy liquid in the right limb will be more.

## DIFFERENTIAL MANOMETERS:

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

1. U- Tube differential manometer

2. Inverted U- tube differential manometer.

## 1. U- Tube differential manometer:

a) Let the two points A and B are at different levels and also contains liquids of different sp.gr.

## 2. Inverted U – Tube differential manometer

It consists of a inverted U – tube, containing a light liquid. The two ends of the tube are connected to the points whose difference of pressure is to be measured. It is used for measuring difference of low pressures. Let an inverted U – tube differential manometer connected to the two points A and B. Let pressure at A is more than pressure at B.

Let h1 = Height of the liquid in the left limb below the datum line X-X h2 = Height of the liquid in the right limb.