Short Answer:

A U-tube manometer is a simple device used to measure the pressure of a fluid at a point by balancing it with a column of another fluid (usually mercury or water) in a U-shaped glass tube. One limb of the U-tube is connected to the pressure point, and the other limb is open to the atmosphere.

In simple words, the U-tube manometer measures pressure by showing the difference in liquid levels in both limbs. The height difference between the columns represents the pressure at the measured point. It can be used for both gauge and differential pressure measurements in liquids and gases.

Detailed Explanation :

U-tube Manometer

A U-tube manometer is one of the most commonly used instruments in fluid mechanics for measuring pressure. It works on the principle of balancing the weight of a liquid column between the point of unknown pressure and a reference (usually atmospheric pressure). The instrument is simple, highly accurate, and reliable for static pressure measurements in both liquids and gases.

It is called a U-tube manometer because the glass tube used in it is bent into a U-shape. One end of the tube is connected to the point where pressure is to be measured, and the other end is usually open to the atmosphere. The manometric liquid (a liquid of known density, like mercury or water) is filled in the tube to a suitable level. The pressure difference causes the liquid to move, and the height difference between the columns gives the measure of pressure.

Construction of U-tube Manometer

A U-tube manometer is very simple in construction. It consists of:

Transparent U-shaped Glass Tube:
A glass tube bent into a U-shape, generally mounted vertically on a wooden or metal frame for support.
Manometric Fluid:
A liquid of known density is used to measure the pressure difference. Mercury, water, or oil can be used, depending on the pressure range. Mercury is preferred for high pressures because of its high density, while water or oil is used for low pressures.
Scale or Ruler:
A scale is fixed along the limbs to measure the height difference between the two liquid columns accurately.
Connection Tube:
One limb is connected to the pressure point (pipe or vessel), while the other is open to the atmosphere (for gauge pressure) or connected to another pressure point (for differential pressure).

Working Principle of U-tube Manometer

The working principle of a U-tube manometer is based on the hydrostatic law, which states that pressure in a static fluid increases with depth due to the weight of the fluid above.

The law can be expressed as:

Where,

= pressure at the point,
= density of the liquid,
= acceleration due to gravity,
= height of liquid column.

The pressure difference between the two limbs of the manometer is proportional to the difference in liquid levels ( ).

Working of U-tube Manometer

Initially, both limbs of the U-tube contain the manometric fluid at the same level when the pressures are equal.
One limb is connected to the point where the pressure is to be measured, while the other remains open to the atmosphere (for gauge pressure) or connected to another pressure point (for differential pressure).
When pressure is applied at the connected limb, the liquid level in that limb moves downward while it rises in the other limb.
The difference in liquid heights ( ) between the two limbs represents the pressure difference.

If the fluid in the pipe has a density and the manometric fluid has a density , the pressure at the measuring point is calculated as:

For a U-tube differential manometer, when both limbs are connected to two different points and :

This equation gives the pressure difference between the two points.

Types of U-tube Manometer

A U-tube manometer can be of two types based on its application:

Simple U-tube Manometer:
- One limb is connected to the point of measurement, and the other is open to the atmosphere.
- Used to measure gauge pressure (pressure above or below atmospheric pressure).
Differential U-tube Manometer:
- Both limbs are connected to two different points in a pipe or two different systems.
- Used to measure pressure difference between two points.

Formula for Pressure Measurement

For a simple U-tube manometer:

Where,

= pressure difference between the two limbs,
= density of the manometric liquid,
= acceleration due to gravity,
= difference in the height of the liquid columns.

If the fluid being measured has a density , the total pressure at the connection point becomes:

Example Calculation

Suppose a U-tube manometer contains mercury ( ) and is used to measure the pressure in a water pipe ( ). The difference in mercury levels between the two limbs is .

Then,

Thus, the gauge pressure at the point is 24.61 kPa.

Advantages of U-tube Manometer

High Accuracy: It gives very accurate results due to direct measurement of pressure head.
Simple Construction: It is easy to make and use.
Low Cost: Inexpensive and requires no calibration.
Can Measure Both Positive and Negative Pressures: Used for both suction and pressure readings.
Durability: No moving parts; hence, maintenance-free and long-lasting.

Limitations of U-tube Manometer

Bulky for High Pressures: Requires a tall tube to measure large pressures.
Temperature Effects: Changes in temperature can affect fluid density and accuracy.
Slow Response: Not suitable for rapidly fluctuating pressures.
Not Portable: It is fixed in place and not convenient for field use.
Not Suitable for High-Pressure Gases: Mercury may evaporate or spill under extreme conditions.

Applications of U-tube Manometer

Laboratory Experiments: Used for accurate measurement of pressure in fluid mechanics experiments.
Pipelines: Used to check pressure in liquid and gas pipelines.
Flow Measurement Devices: Used with Venturi meters and orifice meters to measure pressure differences.
HVAC Systems: Helps in balancing air pressure in ducts and filters.
Calibration: Used for calibration of pressure gauges and other pressure-measuring instruments.

Conclusion

In conclusion, a U-tube manometer is a simple yet effective device for measuring fluid pressure. It operates on the principle of balancing fluid columns of known and unknown pressures. The height difference between the two limbs directly represents the pressure difference. U-tube manometers are accurate, reliable, and widely used in laboratories and industries for both gauge and differential pressure measurements. Despite their limitations, they remain a fundamental and essential instrument in the study of fluid mechanics.