CE 331 L Mauriot Report 5

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New Mexico State University *

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331

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Mechanical Engineering

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Apr 3, 2024

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CE 331 – INTRODUCTION TO FLUIDS MECHANICS AND HYDRAULICS LABORATORY Section Number: L-M02 Experiment Number: 5 Experiment: Manometer Pascal Submitted by: Louis Mauriot Submitted to: Zada Tawalbeh Date Experiment Performed: 03/02/23 Date Experiment Report Submitted: 03/09/23 Name of People Who Participated: Louis Mauriot Jarret Lee Dante Salazar John Paul Slape

Table of Contents Introduction ................................................................................................................................................. 2 Objectives .................................................................................................................................................... 3 Experimental Set-Up .................................................................................................................................... 3 Diagram 1: Manometer Apparatus ...................................................................................................... 3 Picture 1: Manometer Apparatus ........................................................................................................ 4 Diagram 2: Pascal’s Apparatus ............................................................................................................. 6 Results ......................................................................................................................................................... 6 Discussion and Conclusion ........................................................................................................................... 8 Appendix ................................................................................................................................................... 10 References ................................................................................................................................................. 12 List of Figures Figure 1: Pressure Figure 2: Difference in Head Figure 3: Force of Liquid Figure 4: Force of Mass Figure 5: Moment by Liquid Figure 6: Moment by Mass Figure 7: Sample Calculations List of Tables Table 1: Final Pressure Results for Manometry Apparatus Table 2: Raw Data from Lab 1

Introduction The normal force exerted by a fluid on a specific area is defined as the pressure of this fluid. There are three distinct sub categories of pressure which can’t be mixed up. Measured relatively to the local atmospheric pressure, we have gage pressure which can be positive or negative depending on whether it Is above or below atmospheric pressure. Measured relatively to a perfect vacuum also known as the absolute zero pressure, we have what is defined as absolute pressure which is strictly positive. A manometer, which is a commonly used instrument in a laboratory experimental setting serves the purpose of measuring pressure under steady state. The pressure reading obtained thanks to the manometer is specifically the gage pressure. Utilizing the pressure produced by a fluid of known density, the manometer allows us to balance it against the unknown pressure to obtain it. Objectives Learning to master and understand the different functionalities and purposes of a manometer such as measuring pressures and differential pressures with a single limb manometer also known as a piezometer tube, a dual limb manometer and an inclined manometer was an initial objective of this experiment. Understanding the principle of Pascal and mastering the knowledge that pressure varies according to depth and not volume or shape of the object such as a container, tank, reservoir containing the fluid was the second objective of this lab. 2

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Experimental Set-Up For this lab we were equipped with the following experimental apparatus: - An F1-29 fluid statics and manometry apparatus - An F1-10 hydraulics bench or source of water for water filling purposes for the F1-29 apparatus - A ruler - Water mixed with food dye for ease of sight when reading levels on experimental apparatus - F1-31 Pascal’s Apparatus Diagram 1: Manometer Apparatus Picture 1: Manometer Apparatus 3

We initially pour colored water into the graduated cylinder until we reach the 130mm mark. We recorded the reading obtained on the single limb manometer. We then very briefly opened the valve to 4

drain some of the water and recorded, thanks to pictures, the head in the first and second limb of the dual limb manometer. We then inclined the last manometer at 60 degrees initially and with the help of the ruler, creating a horizontal plane, we collected the reading. The same process was repeated for the manometer which was then inclined at 30 degrees. Diagram 2: Pascal’s Apparatus For Pascal’s apparatus, we set up an initial vessel on the apparatus, close the drain valve and poured water at the given height h. We then balanced out the whole apparatus with the assistance of the level gage, the lever arm and the counter balance and measured the distances L1 and L2. The remaining data was calculated after the laboratory experiment was done. Results 5

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Figure 1: Pressure P = γ H 2 O@ 4 °C ×h↔P = γ H 2 O@ 4 °C ×∆h Where: P= pressure, (Pa) γ= specific weight of water at 4°C, (N/m 3 ) h= head, (m) Δh= difference in head, (m) Figure 2: Difference in Head ∆ h = h 1 − h 2 Where: h 1 = Head @ 1 st limb, (m) h 2 = Head @ 2 nd limb, (m) Figure 3: Force of Liquid F L = P× A Where: F L = Force of liquid, (N) P= pressure (Pa or kPa) A= area, (m 2 ) Figure 4: Force of Mass F m = m ×g Where: F m = Force of mass, (N) m= mass, (kg) g= gravitational acceleration constant, (9.81m/s 2 ) Figure 5: Moment by Liquid M L = F L × L 1 6

Where: M L = Moment by Liquid, (N.m) F L = Force of liquid, (N) L 1 = Length 1, (m) Figure 6: Moment by Mass M M = F M × L 2 Where: M M = Moment by Mass, (N.m) F L = Force of Mass, (N) L 1 = Length 2, (m) Table 1: Final Pressure Results for Manometry Apparatus Device Pressure (kPa) Single Limb Manometer 0.1275 Dual Limb Manometer 8.83×10 -3 Inclined Manometer 0.112 Discussion and Conclusion The density of the liquid and the geometry of the manometer are the two main factors influencing the head loss between the two manometers. The head loss is the difference between the head levels of two distinct manometers. The reason for head loss is due to the resistance of the liquid flowing through the manometer. 7

Among the various types of purposes this kind of apparatus represents, there are a few that are relevant to mention. From a hydrostatics perspective, the manometer helps understand fluid behavior at rest. For our laboratory experiment, we utilized it to study differential pressure in a fluid (in our case, colored water). The change in air pressure above the surface of a fluid can be studied using this apparatus. The applications of friction on a fluid can also be a concept studied using this manometer set up. Certain medical devices utilize manometers. Inclined manometers can be utilized The dual limb manometer when being utilized can show us a difference in head that is very fast to observe for the naked eye. In our case, we had to use a phone to take pictures and a video to obtain our data for the difference in head for the dual limb manometer. The inclined manometer is very practical in terms of usage. We can easily incline it to a 60-degree angle and a 30-degree angle while locking into both positions. The only inconvenience is when trying to read the actual head measurement and having to use a long ruler lined up with the head of the initial cylinder to collect the data. The more accurate manometer, based on experimental procedures executed on each distinct manometer and the follow up calculations, would be the inclined manometer. The level did approximately remain the same for each glass vessel. This is the basic principle of Pascal’s apparatus that was demonstrated by changing around the vessels. No matter what the shape of the vessel is, the force is dependent on depth of head, not shape or volume of the fluid container. In a perfect, ideal experimental setting, from a static mechanical point of view, utilizing Newton’s third law, the moment of liquid would equal the moment by mass and therefore we would obtain a sum of the moments equal to 0. In most experimental settings, a perfect cancellation of forces or moments is very rare. The obtained sum of moments in our case is close to being equal to 0 (M L -M M = 0.005 N.m). The difference could be due to several sources of error. An initial source of error which was observed during the performance of the experimental procedure is the loss of water at the bottom of 8

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the vessel. The vessel wasn’t properly sealed on the apparatus causing a very slight but potentially significantly contributing source of error consequently into our calculations and creating a gap between the two moments. Another source of error could’ve been a misreading of the two lengths found with the help of the ruler. The latter might not have been positioned quite parallel with the level arm. Also, it is important to take into account among potential sources of error, a misread of the actual lengths on the ruler as well since the apparatus was set up in a way which made it difficult to see clearly the actual length measurement reading. Lastly, when taking the length measurement with the ruler, the level gage might have shifted while trying to read the measurement and record the data. Appendix Figure 7: Sample Calculations ∆ h = h 1 − h 2 = 105 mm − 96 mm = 9 mm P = γ H 2 O@ 4 °C ×h↔P = γ H 2 O@ 4 °C ×∆h = 981 N m 3 × 9 × 10 − 3 = 8.83 Pa P = γ H 2 O@ 4 °C ×h↔P = γ H 2 O@ 4 °C ×L = 145 mm× 10 − 3 m× sin ( 60 ) × 981 N m 3 = 123 Pa F L = P× A = ( 981 N / m 3 × 0.13 m ) × ( π / 4 × ( 0.056 m ) 2 ) = 0.31 N F m = m ×g = 0.1306 kg× 9.81 = 1.28 N M L = F L × L 1 = 0.31 N × 0.16 m = 0.05 N .m 9

M M = F M × L 2 = 1.28 N × 0.035 m = 0.045 N .m Table 2: Raw Data from Lab Single Limb Manometer: Reservoir Head (mm) 130 Single Limb (mm) 130 Pressure (kPa) 0.1275 Pressure (psi) 0.0185 Pressure (mm Hg) 0.957 Dual Limb Manometer: Head @ 1 st Limb (mm) 105 Head @ 2 nd Limb (mm) 96 Difference in Head (H1-H2) (mm) 9 Pressure (kPa) 8.83×10 -3 Inclined Manometer: Reservoir Head (mm) 130 Reading (mm) 155 Offset (mm) 10 Length (mm) 145 Pressure (kPa) 0.123 Reservoir Head (mm) 130 Reading (mm) 334 Offset (mm) 105 Length (mm) 229 Pressure (kPa) 0.112 Pascal’s Apparatus Diameter (cm) 5.6 Mass (g) 130.6 Height (cm) 13 Length L 1 (cm) 16 Length L 2 (cm) 3.5 Force of Liquid F l (N) 0.31 F of Mass F M (N) 1.28 Moment by Liquid M L (N-m) 0.05 10

Moment by Mass M N (N-m) 0.045 References New Mexico State University. Retrieved from class website: CE 331 Lab 5 Basic Manometry and Pascal’s Law) 11

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