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Dr. D Stefan Dancila Summer 2021 MAE 1106 Introduction to Aerospace Engineering Fall 2022 Laboratory Report # 2 Barometric Altimetry
Submitted to Paul Hagseth Adjunct Professor paul.hagseth@uta.edu by Juliette Valerio Class Section 003 Email: jav1422@mavs.uta.edu
Dr. D Stefan Dancila Summer 2021 Mr. Paul Hagseth UTA MAE 1106 Fall 2022 2 Summary The collecting the data for the calculated height and information needed to calculate the barometrically calculated heigh, the measured height, absolute atmospheric pressure, air temperature, change in pressure, and air temperature were all given values. In addition, the experiment also gave information about the equipment used and the inaccuracy it may create to the barometrically calculated height. Then, the experiment wants to choose between data between two different equipment readings. With the recorded data provided and selected, the data must be converted to the correct units. The equations would also need to be rewritten to calculate the height barometrically. Once we calculate the height, then we calculate the absolute and relative error with the provided measured height as reference. This would then allow the us to analyze the process of the experiment and how it could affect the error of the barometrically calculated height.
Dr. D Stefan Dancila Summer 2021 Mr. Paul Hagseth UTA MAE 1106 Fall 2022 3 Table of Contents Summary i Table of Contents ii List of Symbols iii 1. Objectives of the Laboratory Experiments 4 2. Experimental Approach 4 3. Experimental Procedure and Results 5 4. Data Analysis, Interpretation, and Discussion 6,7 5. Conclusions 8
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Dr. D Stefan Dancila Summer 2021 Mr. Paul Hagseth UTA MAE 1106 Fall 2022 4 List of Symbols Greek Symbols:
ᵞ reading ρ density of fluid being used
Dr. D Stefan Dancila Summer 2021 Mr. Paul Hagseth UTA MAE 1106 Fall 2022 5 1.
Objectives of the Experiment The Barometric Altimetry lab experiments main goal was to calculate the height at the top of the handrail on the 6th floor balcony off the ERB 670 conference room. The data was gathered using different methods. The option between two readings for the calculations were provided. Using a tape to measure the height was measured to be at h = 83’7”. In addition, readings needed to be taken to obtain the absolute atmospheric pressure on the ground at the entrance of the ERB building. With these calculations, the height of the handrail will be compared to a previous measurement using a tape measure. The time and method put into gathering the data at the handrail is important and can affect the decision to prioritize one method over the other. Lastly, specific instruments do need proper usage to ensure accurate and impactful conclusion for the experiment. 2.
Experimental Approach In order to begin the experiment, the following instruments are needed for a successful test; tape measure, Casio pathfinder wristwatch, a free app named “Barometer”, a thermocouple connected to an electronic multi-meter, and a electronic differential manometer with one port blocked. The absolute atmospheric pressure on the ground at the entrance of the ERB building will be measured by the Casio pathfinder wristwatch and the free app “Barometer.” In addition, the air temperature is then calculated with a electronic multimeter. Another way to calculate the air temperature, is by using the watch censors in the pathfinder watch. Lastly, the electronic differential manometer with one port blocked will then be used to calculate the change in the pressure between the ground level and the handrail level of the 6th floor balcony off the ERB 670 conference room. The data obtained will then be used for the Barometric calculations and then compared to the initial calculation of the tape measure.
Dr. D Stefan Dancila Summer 2021 Mr. Paul Hagseth UTA MAE 1106 Fall 2022 6 3.
Experimental Procedure and Results While conducting the experiment, the pressure at the ground level was recorded with the Casio Pathfinder wristwatch reading PGL= 29.45, which was then converted to 0.74822 meters. This measurement was chosen over the free “Barometer app” since the watch was recording in real time and is easily controlled for accuracy by the individual utilizing it. Then, the temperature at the ground level is calculated with the thermocouple connected to an electronic multi-meter read TGL is 26.1°C converted to 299.2 K. These results of this calculation were chosen due to the other approach creating human error. The instructions specify to wait for a period, so the watch can be exposed to its ambient temperature. This could affect the accuracy as well. The difference between the pressure on the ground level and the 6th floor balcony handrail is then calculated with the electronic manometer with one port blocked and its measurement reading Δp =2.91 hPa converted to -291 pa. Then, the acceleration due to gravity in Arlington, Texas will be then be obtained through the wolframalpha website. The acceleration due to gravity is found to be 9.79471 m/s^2. While, the value of density is found to be pHg = 13500 kg/m^3. The height measured using the tape measure is given to be 83’7” converted to hmeasure=25.4827 meters. We will then use this information to compare the calculated value, which is found in the data analysis. 4.
Barometrically Determined Height To start of the data analysis and calculations with the given data performed in the experimental procedure the value of pressure at ground level must be found. Where ᵞ = reading use the equation below to find that 𝑃𝐺𝐿 = 9.89362 ∗ 10^4 Pa. 𝑃𝐺𝐿 = ρ ∗ g ∗ ᵞ 𝑃𝐺𝐿 = (13500 𝑘𝑔/ 𝑚2 ) (9.79471 𝑚/ 𝑠 2 ) (7.48221 ∗ 10^−1 ) = 9.89362 ∗ 10^4𝑃𝑎 The value of density can be found using the equation below. It is found that 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 = 1.5176 𝑘𝑔/ 𝑚3 . ρ = P RT ρ = 9.8362 ∗ 10^4𝑃𝑎 /(287.05 𝐽 /𝑘𝑔𝐾) (299.2 𝐾) = 1.15176 𝑘𝑔/ 𝑚3
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Dr. D Stefan Dancila Summer 2021 Mr. Paul Hagseth UTA MAE 1106 Fall 2022 7 Using the hypsometric law 𝑑𝑝/ 𝑑ℎ = -pg the rewritten equation is written below to find the calculated/barometrically determined height. Using the rewritten equation to find the calculated height from pgl to the 6th floor balcony the height is found to result in ℎ𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 = 25.795 𝑚. ℎ𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 = −Δp ρg ℎ𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 = −(−291𝑃𝑎) /(1.5176 𝑘𝑔/ 𝑚3 ) (9.79471 𝑚/ 𝑠 2 ) = 25.795 5.
Difference in Results The difference in result for this experiment is 0.3123 meters. 6.
Source of Error The absolute error can be calculated using the equation below to find that the difference is 0.3123m. 𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒𝐸𝑟𝑟𝑜𝑟 = ℎ𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 − ℎ𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒𝐸𝑟𝑟𝑜𝑟 = 25.795𝑚 − 25.4827𝑚 = 0.3123𝑚 The relative error is found to be 1.226% using the equation below. 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒𝐸𝑟𝑟𝑜𝑟 = 𝐴𝑏𝑠𝑜𝑙𝑢𝑡𝑒𝐸𝑟𝑟𝑜𝑟 ℎ𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 ∗ 100 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒𝐸𝑟𝑟𝑜𝑟 = 0.3123𝑚 25.4827𝑚 ∗ 100 = 1.226% The interpretation of the error observed coincides with human error and the equipment used. With the height using the tape measure used as reference it is easy to conclude that the equipment and human error have impacted the measurement and therefore the calculations. With better equipment, we did not have to consider uncertainties. The Lab Guidance manual ensures to single out any uncertainties measured using the equipment provided with a ± symbol. These display characteristics will hinder the accuracy of the barometrically determined height.
Dr. D Stefan Dancila Summer 2021 Mr. Paul Hagseth UTA MAE 1106 Fall 2022 8 There are also other methods of measurement that can be heavily affected by human error. The usage of the Casio Pathfinder watch’s sensors to measure the temperature and the steps to do so prove this. Therefore, the source of the error when using the measured height as reference comes from human error and the display characteristics of the equipment used. 7.
Conclusions The main goal of this lab was to measure the height at the top of the handrail on the 6th floor balcony off the ERB 670 conference room and comparing the measured and calculated heights. The relative and absolute errors are used to compare the measured and calculated heights and to show how human error can distort the data. Throughout the experiment, it explained how through ± symbols that the equipment would not give 100% accuracy. Furthermore, its asked to provide the accurate measurements between two sets of equipment and to explain the preferred option for conducting the experiment. While trying to find the height at the top of the handrail on the 6th floor balcony, the experiment required these obstacles to find out how they could affect the absolute and relative errors when calculating the barometrically determined height. To conclude this lab, the equipment used human error and the interpretation of ± ranges on the displayed data so an increase in the absolute and relative error of the experiment would be displayed.