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Today we will discuss the part 2 of what is manometer and its types, along with its advantages and disadvantages. In case if you haven't read the part 1 check it out here.

Consider the manometer as shown in the figure. Assume that the pressure at point 'a' is greater than point 'b', then the greater pressure at 'a' will force the heavy liquid in U-tube to move downwards, so that heavy liquid will rise in the right limb.

Let,

h = Difference of levels of heavy liquid in right limb and left limb.

s1 = Specific gravity of liquid in the pipes.

s2 = Specific gravity of heavy liquid.

Since the pressure in the right limb and the left limb above the datum line AB are equal, therefore the

(ha - hb) = h (s2 - s1) m head of water.

Similarly, when points a and b are at different levels, as shown in the figure, The pressure in the right limb and the left limb above datum are equal.

Let,

h1 and h3 = Heights of the liquid in the left and right limb.

h2 = Difference of heavy liquid in left and right limb.

ha and hb = Pressure in pipes a and b respectively.

s1 and s3 = Specific gravity of liquids in pipes a and b respectively.

s2 = Specific gravity of heavy liquid.

Then the total pressure in left limb above datum = Total pressure in right limb above datum.

( ha + s1*h1 ) = ( s2*h2 + s3*h3 + hb)

The two ends of U-tube are connected to the point whose difference in pressure is to be measured as shown in the figure. Light liquid is used as manometric liquid; because it may be down and flow in low pressure.

Since the pressure in the left limb and the right limb are equal,

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Today we will discuss the part 2 of what is manometer and its types, along with its advantages and disadvantages. In case if you haven't read the part 1 check it out here.

## Differential Manometer :

Differential Manometer is more of a " pressure comparing " device rather than a " pressure measuring " device. Let me explain by defining differential manometer.

Differential manometer is a type of pressure difference measuring device used for measuring pressure difference between 2 different pipes or 2 points on the same pipe.

Differential U-tube manometer can be classified into 2 types.

- U-tube differential manometer.
- Inverted U-tube differential manometer.

## U-tube differential manometer.

U-tube differential manometer consists of a glass tube bent into U shape. The 2 ends of the U-tube are connected to the points whose pressure is to be measured.

In the U-tube a manometric liquid is filled ( indicated by the shaded portion in the diagram ). This liquid has specific gravity higher than the liquids present in the pipe. Most of the time mercury is used as a manometric liquid as it has desirable characteristics like high specific gravity, clear visible, it does not stick to glass, can be used at wide range of temperature etc.
When the pressurized liquid flows through the pipes, it enters the U-tube manometer. Now depending upon the respective pressure in the pipes, there are 3 possibility.

The manometer fluid in both right and left limb would be equal. This indicates that the pressure in both the pipes would be the same i.e. a = b.

The manometric fluid level in the left limb is low whereas the manometric level in the right level is high. This indicates that the pressure in the left hand pipe is greater i.e a > b.

The manometric fluid level in the right limb is low whereas the manometric level in the left limb is high. This indicates that the pressure in the right hand pipe is greater i.e a < b.

The manometric fluid level in the left limb is low whereas the manometric level in the right level is high. This indicates that the pressure in the left hand pipe is greater i.e a > b.

The manometric fluid level in the right limb is low whereas the manometric level in the left limb is high. This indicates that the pressure in the right hand pipe is greater i.e a < b.

#### Pressure Calculations :

Consider the manometer as shown in the figure. Assume that the pressure at point 'a' is greater than point 'b', then the greater pressure at 'a' will force the heavy liquid in U-tube to move downwards, so that heavy liquid will rise in the right limb.

Let,

h = Difference of levels of heavy liquid in right limb and left limb.

s1 = Specific gravity of liquid in the pipes.

s2 = Specific gravity of heavy liquid.

Since the pressure in the right limb and the left limb above the datum line AB are equal, therefore the

**difference of the pressures**in two points a and b is

(ha - hb) = h (s2 - s1) m head of water.

Similarly, when points a and b are at different levels, as shown in the figure, The pressure in the right limb and the left limb above datum are equal.

Let,

h1 and h3 = Heights of the liquid in the left and right limb.

h2 = Difference of heavy liquid in left and right limb.

ha and hb = Pressure in pipes a and b respectively.

s1 and s3 = Specific gravity of liquids in pipes a and b respectively.

s2 = Specific gravity of heavy liquid.

Then the total pressure in left limb above datum = Total pressure in right limb above datum.

( ha + s1*h1 ) = ( s2*h2 + s3*h3 + hb)

Therefore, ( ha - hb ) = ( s2*h2 + s3* h3 - s1*h1 )

#### You might also like to read:

Centrifugal pump - its construction, working & applications | The Mechanical post.### Inverted U-tube Differential Manometer:

It consists of an inverted U-tube containing a light liquid whose specific gravity is less than the specific gravity of the pipe liquid. Manometric liquid such as oil is used mostly. It is used for measuring the difference of low pressure between two points; where accuracy is important.

The two ends of U-tube are connected to the point whose difference in pressure is to be measured as shown in the figure. Light liquid is used as manometric liquid; because it may be down and flow in low pressure.

Let,

h1 = Height of liquid in left limb below datum AB.

h2 = Difference of levels of the light liquid in right limb and left limb.

h3 = Height of liquid in the right limb below datum AB.

ha = Pressure head in a pipe a.

hb = Pressure head in pipe b.

s2 = Specific gravity of light liquid.

s1, s3 = Specific gravity of liquid in left limb and right limb respectively.

Since the pressure in the left limb and the right limb are equal,

Total Pressure in left limb below datum = Total Pressure in right limb below datum.

(ha - s1*h1) = hb - s2*h2 - s3*h3

( ha - hb ) = ( s1*h1 - s2*h2 - s3*h3 )

### Applications of Differential manometer:

- It can detect leaks in a pipeline as leakage would cause pressure imbalance, thus imbalancing the manometric fluid.
- Differential gauges can detect scale formation and blockages in pipeline using pressure pressure difference.

Image credits - differentialpresssure.com |

- Liquid level in a container can also be measured in a container as shown above.
- Differential manometer is used in laboratory, for calculating flow rates and velocities of different fluids.
- It is also used in industries to measure differential pressures of low velocity fluids.

### Advantages of Differential manometer :

- Simple construction
- Cost effective
- Easy maintainance
- Easy to replace
- Easy to read
- Little to no operating cost.

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