# Differential Manometer: its types, equations, uses with PDF

Welcome back to The Mechanical post. Today we will discuss the Differential manometer, its types, applications, and advantages.

Also, we would be looking at the equations of each of the differential manometer.

We have divided the topic of Manometer into 2 parts, the first one being the simple U tube manometer and the other part being on the differential manometer.

In case if you haven't read the first part on U tube Manometer you can check it out here.

## What is a Differential Manometer?

A differential Manometer is more of a " pressure comparing " device rather than a " pressure measuring " device.

The differential manometer is used to measure the difference of pressure between two points.

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 manometers can be mainly classified into 2 types.
• U-tube differential manometer.
• Inverted U-tube differential manometer.

### U-tube differential manometer.

A U-tube differential manometer consists of a glass tube bent into a 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 green 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, clearly visible, does not stick to glass, can be used at a wide range of temperature, etc.

#### Working :

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 possibilities.

#1) The manometer fluid in both the right and left limbs would be equal.

This indicates that the pressure in both the pipes is the same i.e. a = b.

#2) 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.

#3) 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 equations of U tube differential manometer:

Case 1 ) Both pipes are at the same level.

Assume that the pressure at point 'a' is greater than point 'b'. Refer to the above figure of the manometer.

Since the pressure at point 'a' is greater than point 'b', the greater pressure at 'a' will force the heavy liquid in the left limb downwards, as a result, the heavy manometric 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 the heavy liquid.

Since the pressure in the right limb and the left limb above the datum line X-X are equal, therefore the difference of the pressures in two points "a" and "b" will be given as:

Note that ha - hb is the pressure difference in terms of meter head of water.

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

Case 2) The pipes are at different levels.

Similarly, when points a and b are at different levels, as shown in the figure below, the pressure in the right limb and the left limb above the 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 the heavy liquid.

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

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

∴ ( ha - hb ) = ( s2*h2) + (s3* h3) - (s1*h1 ) {alertSuccess}

### Inverted U-tube Differential Manometer:

The Inverted differential manometer consists of an inverted U-tube containing a light liquid whose specific gravity is less than the specific gravity of the pipe liquid.

The inverted differential manometer is used for measuring the difference of low pressure between two points.

For inverted manometers, light liquids like oil are preferred.

The light liquid is used as a manometric liquid because if a heavier manometric liquid is used, it will flow down and enter the pipes and contaminate the liquid in the pipe.

The two ends of the U-tube are connected to the point whose difference in pressure is to be measured as shown in the above figure.

Let,

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

h2 = Difference of levels of the light liquid in the 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 a 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 ) {alertSuccess}

### Applications of Differential manometer:

• A differential manometer can be used to 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 pipelines using pressure difference.
 Image credits -  differentialpresssure.com
• Liquid level in a container can also be measured in a container as shown above.
• It can be used as a water level indicator in a boiler as a boiler mounting.
• A differential manometer is used in the 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 :

• Manometers have a simple construction
• They are cost-effective
• It is easy to maintain.
• They can be easily replaced.
• A manometer is easy to use.
• They have little to no operating cost.
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That's an overview of the Differential manometer. If you like this post or have any suggestions do let us know in the comments we would love to hear from you.