182 lab 4

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University of British Columbia *

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182

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Mechanical Engineering

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Jan 9, 2024

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Uploaded by ProfessorNeutronGrasshopper35

Introduction Objective Equipment Table Apparatus sketch Procedure Results Discussion Conclusion Appendices VAT o] 4 SR 01 (=1« IR A &NV O AR W WN

Introduction Pneumatics are a type of system that utilizes compressed gas to create work or energy. Air is the most commonly used gas in pneumatic systems. Pneumatic systems captialize on the basic principles of Ideal Gas Law and Boyle’s Law, both of which are in the following equations. PV =nRT equation 1 P,Vv,=P,V, equation 2 Equation 1 is the formula for Ideal Gas Law, where (P) represents pressure, with the units of pascals written as (Pa). (V) represents volume, with the units of (m?). (n) represents the number of moles. (R) represents the Universal Gas Constant. The Universal Gas Constant can be explained as the energy per temperature increase per mole (Admin 2022a), and the value is constant at 8.314459 J/mol*K. (T) represents temperature, with the units of Kelvin written as the variable (K). Equation 2 is the formula for Boyle’s Law, and Boyle’s Law states that a gas’s pressure and volume are inversely proportional as long as temperature is kept constant. As volume increases, pressure falls and vice versa (Admin 2022b). (P) and (V) respectively represent pressure and volume in pascals (Pa) and (m?). In this experiment we will also be exploring how pressure relates to a force applied on the system using the equation: P=F/A equation 3 Equation 3 is the formula that demonstrates how pressure is a product of force per unit area. (P) represents pressure in pascals (Pa), (F) represents force in newtons (N), and (A) represents the area in (m?). There are three parts to this lab, all using the same system consisting of a compressed air tank, containment cylinders with pistons, flexible hose lines, and a pressure gauge. Each part uses a different equation and different parts of the system, and each part has its own hypothesis. Part one tests Boyle’s Law, and the hypothesis is that in the closed system, as one piston is compressed and one is extended, then the pistons will react equally. As one is extended, the other will be compressed. Part two tests equation 2 to hypothesise that it will require quite a lot of force to push the piston in as volume decreases. Part three utilizes Ideal

Gas Law, and the hypothesis is that it will take approximately 60 strokes to bring down the pressure from 100 psig to 70 psig. Objective The objective of this experiment is to observe gas laws, specifically Ideal Gas Law, and its behaviours utilizing a pneumatic system of compressed air tanks, containment cylinders, and gauges. Equipment Table Equipment Uncertainty Digital Caliper +0.01lmm Measuring Tape +0.1cm Pressure Gauge +10psi Pressure Regulator +10psi Compressed Air in Tank n/a Two Pistons n/a Switch n/a Flexible Air Line n/a Table 1: Equipment used and uncertainties in their measurements

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Apparatus sketch fart L - _’ = >51m1(4'i e &ma-.j VRed q}_‘ékm ."frisw_hu_ & ; g lindera. L Digital Caliper ¥ fi > A = L_.VQ\J >C\]]dlfL Q > Mea srin lape n = r N e Lav (1’. D > l’k‘&l‘* D v e m S .- '/l/ / frescuwre I’(quud‘ COMP’\'J&A‘ /1: e Tak Figure 1: Apparatus Sketch and Set-up of the lab. Procedure Initially, before conducting the lab, we ensured our awareness of the safety protocols and practices related to this experiment and also ensured that we had the necessary PPE, as this experiment was considered to be more dangerous to some extent in comparison to the previous experiments. In the first part of the experiment we were required to measure the diameter of the piston,the piston rod, and their stroke length for both of the pistons that were present in our experiment setup. Shortly after, we recorded the volume swept by both pistons by connecting the cap end port to the regulator by pushing and applying force onto the piston rod. The resulting stroke of the piston was also recorded by connecting the road end port of one piston to the cap end port of the other piston. After recording necessary measurements, the hoses were connected to the proper inlets & outlets and double-checked if any leak was present in our system. Once the lab supervisor checked our lab configuration we began the experiment. The switch was toggled to perform one stroke with the pistons. Each stroke was counted until the pressure

gauge was decreased to a pressure of 70 psi. The calculations were completed after gathering all the data that was needed. Results In this lab, we worked with cylinders, air tanks and pressure gauges to better our understanding of ideal gas law and pressure. We are able to calculate the force we applied with the formula F=PA, where force equals pressure times the area. We calculated the pressure by adding the measured pressure to the pressure of the atmosphere. The cylinder displacement in part one could be calculated with the equation P, V,=P,V, as the volume and the pressure of the system should equal before and after the experiment, meaning the displacement of one cylinder should equal the displacement of the other. Finally, we are able to calculate the number of strokes needed by calculating the number of moles needed for 30 psi of air and calculating the amount of air required for 1 full stroke of the cylinder using the equation PV=nRT. By dividing the moles needed by the moles used for 1 stroke, we are able to get the number of strokes needed. Discussion Part 1: In part 1 of the experiment, we compressed a cylinder as one of the cylinders was fully compressed and the other was fully retracted. We expected the compressed cylinder to retract as the other one was pushed to about half its length as the lengths of the cylinders are almost equal. Part 2: In part 2 of the experiment, we compressed cylinder 1 to % of its length, by applying force to it. We measure the pressure of the cylinder to be about 12 psi or 82.737 kPa when it is compressed, we could then calculate the absolute pressure of the system as the atmospheric pressure is 101.3kPa, giving us about 202.6kPa. The area of the cylinder’s surface could be calculated with the formula, A=n(r)? giving us 8.98 x10™ m?2 The error in this part could come from technical errors such as wrong reading from the equipment used, or human errors such as not connecting the gauge properly, allowing for a leak, not pushing the cylinder to exactly half of its length, etc. Part 3: For part 3, we reduced the tank pressure from 100 to 70 psi in a measured 43 strokes of the cylinders. We calculated how many strokes are needed by calculating the moles of air required for reducing 30 psi, giving us 1.6 mol, and calculating the moles of air one stroke of the cylinder uses, giving us 0.0372mol. Finding the quotient of the 2 gives us about 43 strokes. This is surprising, as this is the exact amount of strokes experimentally taken. Although numbers were rounded, the answer remains the same throughout the calculations.

Conclusion In this lab, 3 different separate experiments were conducted to come to a solid conclusion. Using the principles of Ideal Gas Law, and Boyle’s Law, we were able to prove that in a closed system, these laws do come into effect, and behave as hypothesised. As volume decreases, pressure increases, and this was proven in part two of the experiment. As more force was applied to the system, decreasing the volume of the cylinder, the pressure gradually increased. As one piston displaces gas in a certain volume in a closed system, the pressure remains constant and is moved, as demonstrated in part one of the experiment, proving Boyle’s Law. In part three of the experiment, using Ideal Gas Law, we saw the relationship between the pressure and volume in aspects of mols. Utilizing the switch and pressure regulator, we can see how the relationship occurs between the release of the gas and equalisation of pressure. The answer to the number of strokes calculated being the same as the measured number of strokes further proves the validity of Ideal Gas Law. Appendices % APSC 182 Matter and Energy I - Lab Sep-Dec 2023 University of British Columbia Okanagan - Engineering OKANAGAN DATA SHEET: Name: Se/'pe/l\r & AJriaV\ Group#: gk Date:2023/12/07 Include errors and units in all your values. Pneumatic Systems and Ideal Gas Law Behavior Part 1 Determining the volume displacement of cylinders. Cylinder 1: Piston diameter = 250 Bimrn Ho0/5 Rod diameter = (0473 rm Measured stroke= 257 \54 om Cylinder 2: Piston diameter = 3% .83 mm Rod diameter = (0,92 vam Measured stroke = 5 dem 1 2% o Calculated volume swept by cylinder 1 = Calculated volume swept by cylinder 2 = VoY w0t m? Step 4: Cylinder 1: Measured full stroke = 15 4w Cylinder 2: Measured resulting stroke = 2 bem Step 5: Cylinder 1: Measured full stroke = IS4 am Cylinder 2: Measured resulting stroke = |4 Fem Part 2 Determining the force related to the pressure in a cylinder/piston system Measured: What is the resulting pressure? ‘IL Q’S‘\ / 82,737k Pa Calculate: What is the resulting pressure? JiOINE Kk P a Part 3 Cycling of Air Cylinders during Tank drawdown | | Number of strokes needed (measured) = N % steo \"<-5 Number of strokes needed (calculated) = 4'3 Stokes What is the initial mass of the air in the tank? (at 100 psig) S VR R What is the final mass of the air in the tank? (at 70 psig) ;7753 k3 What mass of air is used from the air tank? Ois3a k“\ How many moles of air have been used from the tank? L 6 MoleS ¥ My Dy TA name & Signature: Appendix 1: data result sheet

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Lgample Calculehions: ch(* T PV RS P, : admosphere pressure = 101, 3 kpa Vaz 2V, _SRV=R.0% > R 2P >F=G)i0.3 R=202.6 kea ] E&_L—‘-ig |]>75;=6~89475 kPQ / (jalloh: 375541 | PV:Y\'RVT :>n':§P$V_ 7 = (Iooxé.fi‘ﬂ/?&kpq)-(sx 3, 78541) . Sl =2 22 moles ne= (70x6,8947¢ kR)(5¢ 3. 78541) (8 3149 (22 + 273) An=35.232-3 79 = = 3, 72 Mu\b& L / =1 ~" 32 (z 14 24X10 424X ) c=(| XE 847000 ) 124 X0 24Xio " mi)— 0,0 886 moles (%.3145) (22+273) . 4 | #54(°ke$=o.0156 szL-:L43 S+ eokes s Appendix 2: sample calculations

Works Cited Admin. (2022a, May 18). What is the value of R in ATM? - value of gas constant, formula. BYJUS. https://byjus.com/physics/value-of-r-in-atm/#:~:text=The%20gas%20constant%20value%20is, 1%E2%8B%85K%5E%E2%88%921. Admin. (2022b, July 5). Boyle s law - definition, equation, & facts with examples. BY JUS. https://byjus.com/chemistry/boyles-law/#:~:text=Boyle’s%20law%20is%20a%20gas%20law% 20that%?20states%20that%20a,pressure%20falls%20and%20vice%20versa.