CALIBRATION OF A BOURDON PRESSURE GAUGE

PRINCIPLE:

The mechanism of the gauge may be seen through the transparent dial of the instrument. A tube having a thin wall of oval cross-section is bent to a circular arc encompassing about 270 degrees. It is rigidly held at one end where the pressure is admitted to the tube and is free to move at the other end. When the pressure is admitted, the tube tends to straighten. The movement at the free end operates a mechanical system, which moves a pointer around the graduated scale. The movement of the pointer is proportional to the pressure applied. The sensitivity of the gauge depends on the material and dimensions of the Bourdon tube.

OBJECTIVES

The objectives are as given below:-

1. a) A Bourdon pressure gauge calibration
2. b) To generated proper tabulated data by performing experiment.
3. c) Discussion on graph which was plotted gauge pressure vs. increasing pressure and gauge pressure vs. decreasing pressure.
4. d) Generation of linear regression equation and discussion on it.
5. e) Calculation of standard error of the data.
6. f) Conduction of error analysis as per the possible sources of errors.

PROCEDURE

1. Ensure that the cylinder is vertical. Record the weight of the piston and the cylinder area
2. Add the weights provided in about eight increments up to a maximum of 6.2 kg. Under no circumstances should more weights than the ones supplied be added. Always load the weights gradually and do not drop them on the platform
3. Record the mass added to the piston and the pressure gauge reading to the nearest 1.0 kPa (this will require some interpolation) at each increment of loading on the attached data sheet. Rotate the piston gently at each loading to prevent the piston from sticking.
4. Reverse the above procedure. Remove the weights in the same increments that they were added and record the weight subtracted and the corresponding pressure gauge reading in the column labeled “decreasing pressure”.
5. Repeat steps (2) through (4) for a second trial.
6. After obtaining all the data, remove the piston. Dry the piston and the cylinder with a lint free cloth.
7. Finally, smear the piston with oil before putting the instrument away.

MATERIALS

1. The below apparatus have been provided for carrying out the experiment.

Figure 1 Schematic of the Bourdon Pressure Gauge Calibrator

2. Series of Weights like 0.5kg, 1kg etc

ANALYSIS

GIVEN DATA: –

Acceleration due to gravity (g) = 9.807 m/s²

Piston weight = 1.000 kg

Cylinder area = 3.173 x 10^-4 m²

Table1 and 2 represents a typical set of results. The weights are converted from units of kilogram-force (kg-f) to Newton (N) simply by multiplying by the factor 9.807 The actual pressure were calculated as per below formula:-

After that, gauge error has been calculated by simply subtracting the gauge reading to actual pressure reading.

Table 1 Data for pressure gauge trial 1

Table 2 Data for pressure gauge trial

RESULT AND DISCUSSION

The exactness of the current alignment, and a sure condition concerning the adjustment was defined by contrasting pressure gauge reading and pressure inside the chamber. The explanation for this was on the grounds that all the readings from the Bourdon Gauge were arrived at the midpoint of out dependent on their weight, and legitimately contrasted with the determined an incentive for the weight at a similar weight. The motivation behind why the determined worth’s utilization was crucial here was on the grounds that that worth was the hypothetical/genuine worth. That was the worth the Bourdon Gauge ought to have been perusing if its adjustment had no mistake. While certainly feasible, it is impossible any sort of estimating apparatus is 100 percent exact. The standard deviation indicated the separation between the purposes of the Bourdon Gauge readings, and the determined worth being the weight in the chamber.

The graph has been plotted between increasing gauge pressure vs. actual gauge pressure and decreasing gauge pressure vs. actual gauge pressure as per the results given in table 1 and 2 for the trial 1 and 2. These plots were shown in the Fig.2, 3, 4 and 5. The nature of curve is almost straight line.

Figure 2 Plot increasing gauge pressure vs. actual gauge pressure for table 1

The linear regression equation for the above readings is Y = 0.9930*X – 0.6987.

The R square value obtained is 0.9992. The standard error data (Sy.x) is 1.403.

While comparing them, the decreasing gauge pressure curve almost same as the increasing gauge pressure.

Figure 3 Plot decreasing gauge pressure vs. actual gauge pressure for table 1

The linear regression equation for the above readings is Y = 0.9565*X + 5.072.

The R square value obtained is 0.9976. There is a large difference in the in the constant value of the equation. The standard error data (Sy.x) is 2.394.

Figure 4 Plot increasing gauge pressure vs. actual gauge pressure for table 2

The linear regression equation for the above readings is Y = 0.9986*X + 0.9249.

The R square value obtained is 0. 9969. The standard error data (Sy.x) is 2.826.

Figure 5 Plot decreasing gauge pressure vs. actual gauge pressure for table 2

The linear regression equation for the above readings is Y = 0.9874*X + 4.410.

The R square value obtained is 0. 9970. The standard error data (Sy.x) is 2.744.

While comparing the standard error of all the four liner regression equation they are approximately same.

Two different kinds of error may normally be expected in a gauge of this type. First (there is the possibility of hysteresis due to friction and backlash (so that the gauge will tend to read lower values then the pressure is increasing than when decreasing. The gauge tested here has not more than 1KN/m2 of this kind of error. Secondly (there is the graduation error due to the scale being marked off incorrectly. In this gauge( the graduation error increases fairly steadily zero to approximately 4 KN/m2 at a reading of around 175KN/m2 This error( of about 2.3% ( would be acceptable small for many engineering purposes( although bourdon gauge with a much higher accuracy are available for accurate work.

1. What suggestions do you have for improving the apparatus?

1. a) Try to eliminate human error. As we put weight above the piston by hand.
2. b) The transmission of water should be visible throughout the experiment. If any bubble is present in water, it may error in the reading.

1. No correction was made to the results for the difference in elevation of the piston of the dead weight tester and of the pressure gauge. If the center of the gauge were 200 mm higher than the base of the piston, should a correction be made? If so, how big of a correction is needed?

As we increase the height of the piston, so the water inside the need to travel more.

Hence, there will be change pressure due to this height.

For example, P = ρgh

Here h = 0.2m , ρ = 1000 kg/ m³ , g = 9.807 m/s²

P = 0.2 x 1000 x 9.807

P = 1.961 Kpa

The pressure is the correction needed.

iii. What alterations to the dimensions of the piston of the dead weight tester would you suggest if it were desired to calibrate a gauge having a full reading of 3500 kPa using the same weights? Calculate the required diameter of the piston to obtain the full-scale reading of 3500 kPa.

Given: – P=3500 kpa

 g =9.807 m/s²

To find :-  Required diameter = ?

Formula:-

Weight (W) = mass x acceleration due to gravity (g)

Pressure (P) = W/ Area of piston (A)

Area (A) = π/4 x d²

If we use same weight of 1 kg, then the area of piston will be 2.802 x 10^-3 m².

Therefore the diameter is 0.05977m.

CONCLUSION

From the data presented above, it is possible to conclude that pressure in the cylinder and gauge pressure recorded do not vary based on whether the weight intervals are increasing or decreasing.  Since the weight being added or taken off the cylinder were the same every trial, it makes sense how the graphs should be similar.  The reason behind the graphs of increasing and decreasing reading was not exactly alike was because of a mix between the calibration of the Bourdon Gauge being slightly inaccurate, and human error.    The percent relative error and absolute error both the increasing and decreasing intervals were not similar even though they were both measurements of error.  This had to be because of the differences between the formulas of percent relative error and absolute error.  Absolute error was found by taking the absolute value of the pressure in the cylinder minus the gauge reading.  When the values being inputted were small, the absolute error would be small.  Likewise, when the values being inputted were large, the absolute value was going to be large because of the way the formula is set up.  Percent relative error on the other hand does not increase with larger numbers, rather it remains relatively constant.  This was because the formula for percent relative pressure was absolute error divided by pressure in the cylinder, then that value multiplied by 100.  Both absolute error and percent relative error were important to know in order to draw better understand the Bourdon Gauge by showing different ways it could be compared to the theoretical value.  Finding the standard deviation on the graph helped determine whether the calibration of the Bourdon Gauge was accurate or not.  With that, and the data from the other tables, graphs, and calculations, the calibration of the Bourdon Gauge seemed to be fairly accurate.  Human error was, and always will be a factor when determining the measurements in a study, but with proper calibration of instruments, the accuracy of the readings can be trusted with confidence.  

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