Short Answer:

An inclined tube manometer is a modified form of the U-tube manometer used to measure very small pressure differences accurately. In this device, one limb of the U-tube is inclined at a small angle to the horizontal, which increases the length of the liquid column for the same pressure difference.

In simple words, an inclined tube manometer gives a more precise reading of small pressure changes by spreading the liquid movement over a longer scale. It is mainly used for measuring low pressures in air ducts, gas pipelines, and laboratory experiments where high accuracy is required.

Detailed Explanation :

Inclined Tube Manometer

An inclined tube manometer is a pressure measuring instrument that is used for determining very small pressure differences in fluids, especially in gases. It is a more sensitive type of manometer compared to the vertical U-tube manometer.

It works on the principle of hydrostatic equilibrium, which states that the pressure difference in a fluid column is directly proportional to the height and density of the fluid. In this instrument, the tube is inclined at a known angle, so that even a small change in pressure causes a noticeable movement of the liquid along the tube, improving measurement precision.

The inclined design makes it particularly useful for low-pressure measurements in systems like ventilation ducts, airflows, or gas lines where traditional U-tube manometers are not sensitive enough.

Construction of Inclined Tube Manometer

The inclined tube manometer consists of the following main parts:

Transparent Glass Tube:
The main part of the device is a narrow glass tube mounted on a graduated scale. The tube is inclined at a small angle (usually between 10° to 20°) to the horizontal to increase the accuracy of readings.
Manometric Fluid:
A liquid of known density is filled in the tube, commonly water, oil, or mercury, depending on the type of pressure being measured.
- For small pressure differences, low-density liquids (like water or oil) are used.
- For higher pressures, mercury is used.
Reservoir or Base Limb:
One end of the tube is connected to a small reservoir that contains the manometric liquid. This ensures a stable reference level for measuring pressure changes.
Pressure Connection:
The other end of the tube is connected to the point in the fluid system where pressure is to be measured.
Scale or Graduated Markings:
A scale is provided along the inclined limb to measure the movement of the liquid column. It is usually calibrated in terms of pressure head (mm or inches of water or mercury).

Working Principle

The working principle of an inclined tube manometer is based on the hydrostatic law, which states:

The pressure difference between two points in a static fluid is equal to the product of the fluid density, gravitational acceleration, and vertical height difference between the points.

Mathematically,

Where,

= Pressure difference (Pa)
= Density of the liquid (kg/m³)
= Acceleration due to gravity (9.81 m/s²)
= Vertical height difference of liquid column (m)

However, in an inclined manometer, the actual length of the liquid column (L) is measured along the inclined limb, and the vertical height difference is related to by:

where is the inclination angle of the tube.

Thus, the pressure difference becomes:

Since the angle is small, is much greater than , and therefore, the movement of the liquid for a small pressure change becomes more noticeable. This increases the sensitivity and accuracy of the measurement.

Working of Inclined Tube Manometer

Initially, when no pressure difference exists, the liquid in the inclined tube and the reservoir remains at the same level.
When the inclined limb is connected to a point having pressure greater than atmospheric, the pressure pushes the manometric liquid, causing it to move upward along the inclined tube.
The difference in height (or length along the inclined scale) represents the pressure difference.
The corresponding pressure is calculated using the relationship:

If the pressure at the connection point is less than atmospheric pressure, the liquid level in the inclined limb will fall, and readings are taken in the opposite direction.

Advantages of Inclined Tube Manometer

High Sensitivity:
Due to the inclination, a small pressure difference causes a large movement of the liquid, making it suitable for very low-pressure measurements.
Better Accuracy:
Provides more precise readings for small pressure variations compared to a vertical manometer.
Simple Construction:
Easy to construct and operate without any moving parts.
Cost-Effective:
Economical and durable compared to electronic pressure gauges.
Clear Visual Indication:
The large movement of the liquid provides a clear visual indication of pressure changes.

Limitations of Inclined Tube Manometer

Limited to Low Pressures:
Cannot measure very high pressures due to small height differences.
Temperature Sensitivity:
Variations in temperature can change fluid density, affecting readings.
Fixed Installation:
It cannot be easily moved or used in portable applications.
Fragile:
The glass tube is delicate and requires careful handling.
Manual Reading Error:
Human error may occur while reading the inclined scale.

Applications of Inclined Tube Manometer

Air and Gas Flow Measurement:
Used to measure small pressure differences in air ducts, filters, and gas pipelines.
Ventilation and HVAC Systems:
Helps to monitor air pressure in heating, ventilation, and air-conditioning systems.
Laboratory Experiments:
Commonly used in fluid mechanics labs for precise low-pressure measurements.
Calibrating Low-Pressure Gauges:
Serves as a standard for calibrating sensitive pressure measuring devices.
Scientific and Research Work:
Used in wind tunnels, aerodynamics, and environmental monitoring setups.

Example Calculation

Suppose the length of liquid movement along the inclined tube is and the tube is inclined at . The density of the manometric fluid (water) is .

The vertical height difference is:

Therefore, the pressure difference is:

Hence, the pressure difference is approximately 507.7 Pa, showing that very small pressures can be measured accurately with an inclined manometer.

Conclusion

In conclusion, an inclined tube manometer is a highly sensitive instrument designed to measure small pressure differences with greater accuracy. It works on the principle of hydrostatic pressure and enhances the sensitivity of readings by inclining the measuring limb. The increased length of the liquid movement allows even minute pressure changes to be observed clearly. This makes the inclined tube manometer especially useful in applications such as air pressure measurement, HVAC systems, and laboratory experiments where precision is important.