LAB_2

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516

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Mechanical Engineering

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Oct 30, 2023

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Department of Mechanical and Industrial Engineering Please select your current program below: ● Mechanical Engineering Industrial Engineering Course Number 516 Course Title MEC Semester/Year 5 th SEM 3 rd YEAR Section Number 06 Group Number 1 Assignment No. 2 Assignment Title Reynolds Apparatus and Pipe Friction Submission Date October 1st 2023 Due Date October 1st 2023 Student Name Student ID (xxxx1234) Signature * James Mohrhardt Xxxx97151 (Note: Remove the first 4 digits from your student ID) *By signing above you attest that you have contributed to this submission and confirm that all work you have contributed to this submission is your own work. Any suspicion of copying or plagiarism in this work will result in an investigation of Academic Misconduct and may result in a “0” on the work, an “F” in the course, or possibly more severe penalties, as well as a Disciplinary Notice on your academic record under the Student Code of Academic Conduct, which can be found online at: http://www.ryerson.ca/senate/policies/pol60.pdf .

Lab Questions: 1) For the flow visualization experiment (Part I), calculate the Reynolds number (Re) for each flow rate, based on the sample data provided on the following page. Note that the inside diameter of the glass tube is Di=12.7mm. Be sure to use the density and dynamic viscosity of water at the tank temperature. Include a sample calculation of the Reynolds number in your report. Check these Re values against the established ranges in your textbook for laminar and turbulent flow in a pipe. For example, consult Chapter 6 of the textbook by White [2]. Q(Lit/s) Re Flow Appearance 0 0 N/A 0.02 2246.27 Laminar 0.04 4492.55 Turbulent 0.06 6738.83 Turbulent 0.08 8985.11 Turbulent 0.1 11231.38 Turbulent 0.12 13477.66 Turbulent 0.14 15723.94 Turbulent 0.16 17970.21 Turbulent 0.18 20216.49 Turbulent 0.2 22462.77 Turbulent Table 1 : inclination at 45-degree calculations of Reynolds number.

Q(Lit/s) Re Flow Appearance 0 0 N/A 0.8 1497.51 Laminar 1 1871.89 Laminar 1.2 2246.27 Laminar 1.4 2620.65 Transition 1.6 2995.03 Transition 1.8 3369.41 Transition 2 3743.79 Transition 2.2 4118.17 Transition 2.4 4492.55 Turbulent 2.6 4866.93 Turbulent 2.8 5241.31 Turbulent Table 2 : Inclination of 15-degree calculation of Reynolds number. 2) Convert the manometer readings to differential pressure data. Note that the pressure loss (∆ ? ), as indicated by the inclined U-tube manometer is: Δ ? = 𝛾 ∆ℎ = 𝛾 ∆ 𝐿 sin ( 𝜃) (2) where ∆h is the head loss, 𝛾 is the specific weight of the manometer fluid (water), Δ 𝐿 is the difference in the upper and lower manometer reading (measured along the incline) and 𝜃 is the angle of the manometer with respect to horizontal.

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3) Plot the pressure loss 𝛥? (in Pascals) as function of the flow rate ? . Graph 1 : Pressure Loss vs Flow Rate at 45-degree incline. Graph 2 : Pressure Loss vs Flow Rate at 15-degree incline. 4 ) In the laminar flows, does the dye streak increase in diameter as it flows downstream due to diffusion? How do you expect the mixing rate due to diffusion in laminar flow to compare to the mixing rate in turbulent flow? What are some of the implications of this? In the context of laminar flow, the dye streak maintains a constant diameter as it travels downstream, primarily due to minimal diffusion effects. Instead, the dye adheres closely to the smooth, curved velocity profile characteristic of laminar flow. This flow profile remains remarkably uniform and steadily

progresses downstream. This stands in sharp contrast to turbulent flow, where the dye streak's diameter tends to expand, partly influenced by diffusion, owing to the erratic and chaotic velocities exhibited by individual particles. Theoretical expectations regarding pressure loss align with these observations. In laminar flow, the pressure loss maintains a linear relationship with the flow rate, while in turbulent flow, this loss becomes proportional to the square of the flow rate. These findings are corroborated by the data, illustrating a quadratic trend in turbulent flow and a linear trend in the laminar flow region. As we transition from laminar to turbulent flow, the relationship shifts from linear to quadratic, providing further evidence for the distinct linear and quadratic dependencies in the context of a 45-degree incline. Subsequently, the data demonstrates a linear relationship when plotting turbulent flow against the square of the flow rate, consistent with the expected inverse proportionality between pressure loss (P) and the square of flow rate. 5) According to theory, the pressure loss in pipes is directly proportional to the flow rate for laminar flow. For turbulent flow, the pressure loss is approximately proportional to the square of the flow rate. Do your data confirm this result? From the first graph it is clear that pressure loss is defiantly proportional to flow rate. But square of the flow rate is confused from equation of pressure loss is proportional to the square of the flow rate. It is not exactly proportional due to square of flow rates unaccounted factors link loss in manometer tube. Then the second graph it clearly shows that there is also pressure loss and its proportional to the square flow rate. But there is a decrease of angle of inclination of 45 to 15. 6) Based on your data, estimate the values of Recr, upper and Recr, lower. How do your values compare with the values given in your Fluid Mechanics textbook? This lab measured the flow rate and manometer deflection at two different angles. Using these measurements, the Reynolds number was calculated for each flow ( ?? = 𝜌𝑉𝐷 𝜇 ) and the pressure loss across the manometer was also calculated ( 𝛥? = 𝜌𝐿 ?𝑖? 𝜃 ). The flows were then characterised using the Reynolds numbers and respective ranges taken ( ?? ?𝑟,??𝑤𝑒𝑟 = 2000 and ?? ?𝑟,???𝑒𝑟 = 4000 ). The pressure loss was then plotted against the flow rate to verify 𝛥? ???𝑖??𝑟 ∝ ?𝑙?𝑤 ?𝑎?? and 𝛥? ??𝑟???𝑒?? ∝ (?𝑙?𝑤 ?𝑎??) 2 . The figures did follow these relationships for laminar and turbulent flows respectively. Following this, the critical ?? values were estimated using the data collected, and they were extrapolated to be ?? ?𝑟,??𝑤𝑒𝑟 ≈ 2000 and ?? ?𝑟,???𝑒𝑟 ≈ 4000 . These values agreed with the values. Overall, this lab verified the pressure loss characteristics and Reynolds number classification of laminar and turbulent flows.