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Calibration of Bourdon Apparatus: a Report

Categories: Physics

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1. Objectives

The primary objectives of this experiment are as follows:

To gain a comprehensive understanding of the working principle of the Bourdon apparatus.
To perform calculations and explore the fundamental concepts of pressure.
To determine the percentage of error in the Bourdon scale readings and ensure the accuracy of pressure measurement
through calibration using a calibration cylinder.

2. Theory

The Bourdon tube manometer is a crucial instrument in fluid mechanics and pressure measurement. It operates on the principle that as pressure is applied to the inside of a curved, flattened tube (the Bourdon tube), it tends to straighten out.

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This deformation is proportional to the pressure, and it is what allows us to measure pressure.

The formula for pressure (P) can be defined as:

P = F / A

Where:

F represents the force (N).
A denotes the cross-sectional area of the Bourdon tube (m²).

In this experiment, we aim to calibrate a Bourdon tube manometer using various known weights, measuring pressure in units of KPa (Kilopascals) and Pa (Pascals) with the unit N/m² (Newtons per square meter).

3. Experiment Apparatus and Setup

3.1 Apparatus

The following apparatus were utilized for this experiment:

A pressure calibration device.
A Bourdon scale manometer.
Different weights with known masses.

3.2 Setup

The setup for this experiment involved the following steps:

The apparatus was thoroughly cleaned to ensure accuracy.
The Bourdon gauge was reset to zero, eliminating any initial offset.
The device's cylinder was filled with water, and the plunger was carefully inserted.
Valve V1 was opened, and the vent valve was used to remove any trapped air inside the system, after which the vent valve was closed.
The readings on the scale were noted as the initial readings.
We loaded the piston incrementally with known weights, starting with 1 kg, and recorded the corresponding gauge readings at each weight increment.

4. Observations & Calculations

Throughout the experiment, we recorded the following data:

Mass (m, kg)	Deformation (D, cm)	Pressure Up (P_gauge(up), KPa)	Pressure Down (P_gauge(down), KPa)	Measurement Number
1	2	0.34	0.3	1
1.5	2	0.48	0.4	2
2	3	0.62	0.57	3
2.5	4	0.8	0.73	4
3	5	0.91	0.83	5
3.5	6	1.1	1.1	6

The cross-sectional area (A) of the Bourdon tube was calculated as:

A = πr² = π(0.022 m)² = 0.000314 m²

The weight (W) applied to the piston was calculated as:

W = m × 9.81 N

The calibrated pressure (P_cal) was determined as the average of the pressure readings obtained when the weights were added and removed:

P_cal = (P_gauge(up) + P_gauge(down)) / 2

The calibration error (Error) was calculated as the absolute difference between P_cal and the Bourdon gauge reading (P_gauge), divided by P_cal:

Error = |P_cal - P_gauge| / P_cal

The percentage error (Error%) was calculated as:

Error% = (Error / P_cal) × 100%

Error%	Error	P_cal	P_gauge(up)	P_gauge(down)	Measurement Number
-0.02426%	-0.00758	0.31242	0.32	0.34	1
0.061094%	0.025631	0.468631	0.44	0.48	2
0.047757%	0.029841	0.624841	0.595	0.62	3
0.02055%	0.016051	0.781051	0.765	0.8	4
0.071764%	0.067261	0.937261	0.87	0.91	5
-0.00597%	-0.00653	1.093471	1.1	1.1	6

5. Results and Discussion

The results obtained during the experiment indicate that the laboratory measurements closely align with the expected values.

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The small percentage errors demonstrate the successful calibration of the Bourdon apparatus, confirming its accuracy in measuring pressure. Any minor deviations observed can be attributed to factors such as experimental conditions, environmental changes, or manufacturing tolerances in the equipment.

This experiment underscores the importance of calibration in ensuring the reliability of pressure measurements. Accurate pressure readings are crucial in various fields, including fluid dynamics, engineering, and industrial applications. Any inaccuracies in pressure measurement can lead to significant errors in calculations and potentially impact the safety and performance of systems that rely on precise pressure control.

6. Conclusion

The Bourdon gauge, a thin-walled metal tube, proves to be a highly accurate but delicate instrument for pressure measurement. Its sensitivity allows for precise readings, but it also makes it vulnerable to damage. Additionally, the Bourdon gauge may malfunction when subjected to rapidly fluctuating pressures.

As a solution to these limitations, alternative pressure measurement devices have been developed, including electronic sensors and transducers that are less prone to physical damage and offer rapid response times. Nevertheless, the Bourdon gauge remains a valuable tool in situations where its accuracy and reliability are paramount.