MET 335W Fluid Mechanics Laboratory. Lab 1: Bourdon Tube Calibration. Nick Peak

Transcription

1 MET 335W Fluid Mechanics Laboratory Lab 1: Bourdon Tube Calibration Nick Peak January 15, 2018

2 Purpose The purpose of this experiment is to test the accuracy of a bourdon pressure gauge. This is accomplished by calculating the theoretical pressure in the system and comparing the results to those recorded during the experiment. Error between the calculations and the experimental results can be evaluated and used to calibrate the pressure gauge. Figure 1: Experiment setup with the Bordon apparatus Materials Bordon pressure gauge apparatus Calibrated dead weights (1 kg) Calibrated piston-plunger (1 kg, 315 mm 2 cross-sectional area) Filler bottle with water Procedure 1. Record the cross-sectional area of the piston-plunger and its mass. 2. Using the filler bottle, fill the system with water and attempt to remove any trapped air. 3. If needed, top off the system inlet with water ensuring it is filled to its maximum capacity. 4. Gently insert the cylinder, allowing excess water overflow as the cylinder sinks down. Page 2 of 5

3 5. Visually inspect the piston to ensure it is inserted properly and that it looks vertical 6. Record the reading of the pressure gauge (it should be approximately 31 Pa with the 1 kg piston inserted). 7. Gently add one dead weight onto the piston. Rotate the piston slightly to prevent it from sticking. 8. Record the new reading on the pressure gauge. 9. Repeat steps 7-8, adding one (1 kg) dead weight each time until the total mass reaches 6 kg. 10. Repeat the procedure described in steps 7-9, this time removing the one (1 kg) dead weight at a time. 11. Dry off the piston-plunger with a lint-free cloth. 12. Lightly coat the surfaces of the piston with oil to prevent corrosion. Data The data table (Figure 2) for this experiment is shown below. In addition to the experimental data, the table also compares the test data to the Plunger cross-sectional area: 315 mm 2 Piston-plunger total mass: 1 kg Mass [kg] Increasing Pressure [kpa] Calculated Pressure [kpa] Difference [kpa] Error [%] Mass [kg] Decresing Pressure [kpa] Calculated Pressure [kpa] Difference [kpa] Error [%] Figure 2: Experiment data table with differences and error percentage Page 3 of 5

4 Calculations In order calculate the pressure (seen in Figure 2), the definition of pressure is used. The formula is shown below where p is pressure, f is force in newtons, m is mass in kilograms, A is cross-sectional area of the plunger in square-meters and g is gravitational acceleration in meters per second-squared. The resulting unit of this calculation is one-kilonewton per square-meter (or one kilopascal). Use of this equation is also demonstrated below with appropriate unit conversion factors (Figure 3). p [kpa] = f A = mg A Figure 3: Example calculation Analysis The experimental results are plotted against the calculated values (Figure 4). Although slight, error can be observed when there is distance between the experimental pressure and calculated pressure lines. Error in a wellcalibrated system can be assumed to be somewhat constant throughout an experiment, which would be seen as a generally even offset between the best-fit line and the experimental data. In this test, the best fit line and experimental data line intersect (Figure 5), which can be indicative of an improperly calibrated system. Pressure [kpa] Pressure VS Increasing Mass Experimental Pressure Calculated Pressure Best Fit Line y = x Mass [kg] Figure 4: Pressure VS Mass Page 4 of 5

5 To further highlight the fluctuating degree of error, the percentage is plotted against the mass (Figure 6). The error is significantly higher when no weights are present on the platform, which could indicate problems with the piston inlet such as restricted motion or poor lubrication. The error varies midway through the weight trials, which could be symptomatic of mechanical fatigue. In the case of mechanical fatigue, the Bordon tube would be a possible failing element. This type of failure could be caused by nonlinear elasticity of the tube, in which the tube would have a varying constant of deflection throughout its stroke. Leakage was observed in this experiment near the clamped connection located at the bottom of the piston-cylinder (seen in Figure 1). Because of this leak, the lab participants were forced to remove the piston and refill the fluid inlet midway through the experiment. Additional sources of error that are believed to be negligible are weight calibration, small trapped air bubbles, and contaminants within the fluid system. Figure 5: Intersection of best-fit and test data Percent Error [%] Percent Error VS Mass Increasing Mass Decreasing Mass Mass [kg] Figure 6: Error plotted against mass Conclusion & Recommendations Upon considering the fluctuating degree of error during this experiment, this particular attempt is not a trustworthy method of calibrating the Bordon pressure gauge. To ensure proper calibration, measurement tools must have a reliable system setup that does not introduce sources of error to the device. The pressure gauge could not be accurately calibrated with the apparatus used in this experiment due to several sources of error. These sources include, but are not limited to leakage, poor lubrication, trapped air, mechanical fatigue, poor weight calibration, differential dead weight masses, and general user error. Upon repeating this experiment, a thoroughly sealed piston-cylinder device should be used along with a uniform set of dead-weights. In addition to this, a high-lubricity fluid should be used instead of water to prevent any restricted motion. With these adjustments, the experiment may be repeated and re-evaluated as a reliable calibration method. Page 5 of 5