# Determination of Pressure by Simple Manometers in Fluid Mechanics

Manometers are devices used to determine the pressure at any point in fluid either by balancing the same fluid column or by using another fluid column. A simple manometer consists of a tubular arrangement where one end of the tube is connected to the point in the fluid, whose pressure is to be determined and the other end is kept open to the atmosphere. Simple manometers can be used to determine the gauge pressure or vacuum pressure.

## Types of Simple Manometers

Common types of simple manometers are:

- Piezometer
- U-tube Manometer
- Single Column Manometer

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### 1. Piezometer

Piezometers are the simplest form of simple manometers that can be employed to measure the gauge pressures. As shown in the figure-1 below, one end of the tube is connected to the point where the pressure is to be found out and the other end is open to the atmosphere.

The rise of the head gives the pressure head with respect to the point under consideration. If so, the pressure at A, with respect to figure-1 is :

**p = density of the fluid **x** g **x** h**—————-Eq.1

The unit of the pressure determined is in N/m^{2}.

### 2. U-Tube Manometer

This manometer consists of a U-Tube as shown in figure-2. One end of the tube is connected to the point of fluid where the pressure is to be determined and the other end is left open to the atmosphere.

The tube consists of a heavy fluid whose density is greater than the fluid whose pressure is to be determined. Mostly, mercury is taken as the heavy fluid other than the test fluid.

**Determination of Gauge Pressure**

The arrangement of a U-tube manometer for the determination of gauge pressure is shown in figure-2.

From the figure,

A-A is the datum line,

S1 and S2 are the specific gravity of test liquid and the heavy liquid respectively,

h1 and h2 are the height of the test and heavy liquids measured above the datum line respectively.

As shown in the figure, the pressure ‘p’ at a point B is to be determined. The pressure acting on the horizontal surfaces are equal. Thus, the pressure acting on the horizontal surface of both the left and right column measured with respect to the datum line A-A is the same.

The pressure at left column above A-A datum line:

= p + density of test liquid x g x h1 ———–Eq.2

The pressure at right column above A-A datum line :

= density of heavy fluid x g x h2 ————-Eq.3

**Determination of Vacuum Pressure**

The level of heavy fluid is as shown in figure-2 while measuring the vacuum pressure. From the figure, the pressure ‘p’ at the point B is to be determined.

Hence,

The pressure at left column above A-A datum line =

p + density of test liquid x g x h1 + density of heavy fluid x g x h2 ——-Eq.5

Pressure at right column above A-A datum line = 0 —————-Eq.6

Thus equating,

### 3. Single Column Manometers

The single column manometer possesses an arrangement similar to that of U-tube manometer. As shown in the figure, a reservoir is connected to one of the limbs and the other end is left open to the atmosphere.

The cross-sectional area of the reservoir is very large (100 times larger) compared to the area of cross-section of the tube. So the change in liquid level of the reservoir is negligible for any pressure variation. Hence, the pressure is contributed from the height of the liquid in the other limbs.

The limbs can be either vertically or horizontally arranged. Hence, there are two types of single column manometers:

**1. Vertical Single Column Manometer**

The arrangement of vertical single column manometer is shown in figure-4 below.

By equating the pressures above the horizontal surfaces, the pressure at point A is given by :

**2. Inclined Single Column Manometer**

The figure below shows the arrangement of inclined single column manometer :

The inclination results in the movement of heavy liquid from the reservoir to a higher distance. Hence, the instrument is very sensitive.

The pressure ‘P’ is determined by the following steps,

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