PipeFlow_AE341_ESmith

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April 5, 2023 Pipe Flow AE: 341 Fluid Mechanics Laboratory. Section 1004 Author Emilee Smith Instructor Jose Moreto

Pipe Flow Emilee Smith i Contents Abstract ........................................................................................................................................... 1 Introduction ..................................................................................................................................... 1 Theory ............................................................................................................................................. 2 Procedure and Equipment ............................................................................................................... 3 Results and Discussion ................................................................................................................... 6 Conclusion ...................................................................................................................................... 8 Acknowledgements ......................................................................................................................... 8 References. ...................................................................................................................................... 9 Appendices .................................................................................................................................... 10 Questions ................................................................................................................................... 10 Table of Figures Figure 1: H1D Volumetric Hydraulic Bench.. Adapted from ref. (2) \ .......................................... 3 Figure 3: Apparatus with Water and Mercury Manometers [3] ..................................................... 4 Figure 2: What Controls the Flow [3] ............................................................................................. 4 Figure 4: Mercury Manometer [3] .................................................................................................. 4 Figure 5: Water Manometer [3] ...................................................................................................... 4 Figure 6: Thermometer [3] .............................................................................................................. 5 Figure 7: Air Valve Release [3] ...................................................................................................... 5 Figure 8: Graduated Beaker [3] ...................................................................................................... 5 Figure 9: f vs Re on Moody Diagram ............................................................................................. 7 Figure 10: Log(hL) vs log(V) for Laminar and Turbulent Flow .................................................... 7

Pipe Flow Emilee Smith 1 Abstract Using a long pipe apparatus with two different kinds of manometers, water and mercury, this lab provided experimental data for the head loss variation with velocity over Reynolds number regarding both laminar and turbulent flows. With this data, calculated results could be compared to the variation of friction factor and Reynolds number. The experimental data was then plotted on the Moody Chart to analyze the types of flow the occurred and estimate an approximate wall roughness, which was concluded to be 0.0012 mm. Nomenclature : f Friction Factor Re Reynolds Number 𝐿 Length 𝑉 Velocity 𝑔 Gravity 𝑒 Wall Roughness 𝑇 Temperature 𝑣 Kinematic Viscosity 𝐷 Diameter ℎ ௅ Head Loss 𝛾 Specific Weight Introduction This lab report covers the Pipe Flow Lab. The purpose of this lab is to study the flow inside a long and thin pipe in order to observe the variation of head loss with velocity over a range of Reynolds numbers including both laminar and turbulent flows, and to compare the variation of friction factor with Reynolds number with published results [3]. This experiment was performed by Emilee

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Pipe Flow Emilee Smith 2 Smith, Lana Ayyash, and Brenna Gallagher on March 16, 2023, at San Diego State University as a requirement for this course, AE 341, Fluid Mechanics Laboratory. Theory With this experiment we can analyze laminar and turbulent flow which are essential fluid mechanic properties. Laminar flow is steady, comprised only of one component, velocity. Turbulent is unsteady, random flow, with components in all directions. In between laminar and turbulent is transitional. These types of flow relate most importantly to Reynolds number, Re, which is “the ratio of the inertia to viscous effects in the flow” [4]. Depending on the value of the Reynolds number, flow can be described as one of the three types mentioned, although the exact numbers vary. We can find the Reynolds number using fluid velocity, density of our fluid, viscosity, and size of the pipe. According to Fundamentals of Fluid Mechanics, “the flow in a round pipe is laminar if the Reynolds number is less than approximately 2100, turbulent if the Reynolds number if greater than approximately 4000, and transitional (or switching between laminar and turbulent) if the Reynolds number is between these two limits” [4]. With this lab, we can plot our experimental data on the Moody Chart and observe the type of flows that occurred throughout then experiments. 𝑅𝑒 = 𝑉𝐷 𝑣 Equation 1 𝑄 ଵ = 𝑉 ଵ Δ𝑡 ଵ Equation 2 𝑄 ଶ = 𝑉 ଶ Δ𝑡 ଶ Equation 3 𝑄 ̇ ௔௖௧௨௔௟ = (𝑄 1 + 𝑄 2 ) 2 Equation 4 𝑇 ௔௩௚ = 𝑇 ௜ + 𝑇 ௙ 2 Equation 5

Pipe Flow Emilee Smith 3 ℎ ௅ = 𝑓 𝐿 𝐷 𝑉 ଶ 2𝑔 Equation 6 Procedure and Equipment For this experiment, we used the provided Volumetric Hydraulic Bench shown in Figure 1. In addition to the Hydraulic Bench, we used the apparatus seen in Figure 2 which includes both mercury and water manometers. This system has a 524mm long pipe with a diameter of 3mm. Figure 1: H1D Volumetric Hydraulic Bench.. Adapted from ref. (2) \ Volumetric Hydraulic Bench Manufacturer. TecEquipment Model. H1D Sump Tank capacity. 160 Liters. Collecting Tank capacity 35 Liters. Pump capacity 0 to 60 liters/minute at 1.5 m head Adapted from ref. (2).

Pipe Flow Emilee Smith 4 Figure 3: Apparatus with Water and Mercury Manometers [3] Figure 5: Water Manometer [3] Figure 4: Mercury Manometer [3] Figure 2: What Controls the Flow [3]

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Pipe Flow Emilee Smith 5 Step by Step Procedure: 1. Measure the temperature of the water for the experiment using the thermometer seen in figure 6. 2. Next, turn on the pump and fully open the bench valve and pipe valve a clear all air bubbles from the manometers. a. Then close pipe valve and Turn OFF pump. b. Push air valve release (seen in Figure 7) so decrease the level inside manometer to below zero. 3. Turn the pump back on. 4. Slowly open the pipe valve until head loss (water) is approximately 50mm. Using the smaller graduated beaker (seen in Figure 8), measure the volume flow rate at volumes of 200mL and 250mL. a. Calculate volume flow rate: 𝑄 = ( ௏௢௟௨௠௘ ௧ప௠௘ ) തതതതതതതതതതത 5. Then, multiply previous head loss by a factor of 1.25 and measure the volume as done in step 4. a. Continue doing this for seven runs total (giving us a head loss of 190.73mm). b. For the eighth run, multiply by 1.5 (286.1mm). 6. After this we are out of capacity range of the water manometer and need to move to the mercury manometer. Figure 6: Thermometer [3] Figure 7: Air Valve Release [3] Figure 8: Graduated Beaker [3]

Pipe Flow Emilee Smith 6 a. Conduct four runs using mercury with an increment factor of 1.5. 7. Fill out the table provided. 8. Finally, turn off pump. Results and discussion After conducting the experiment, we used the data collected to calculate the volume flow rate, Q. Using the volume flow rate, we could then calculate the velocity of the water through the pipe for every run. Once we had all our variables, head loss, length of the pipe, diameter, velocity, and gravity, the friction factor for each run was calculated and recorded. Reynolds number was also calculated using velocity, diameter, and kinematic viscosity. The experimental results were plotted on the Moody Diagram as shown in Figure 9. As you can see, our flow begins laminar and proceeds to become turbulent. Using this graph, we can analyze and approximate a wall roughness for the pipe. Our data concluded a roughness of 0.0012 mm. Secondly, Figure 10 shows a graph of log(ℎ ௅ ) 𝑣𝑠 log(𝑉) in both cases, laminar and turbulent flows. The first seven runs proved to be laminar, all with Reynolds number below 2100, and the final 6 runs were turbulent, with Reynolds numbers above (or near) 4000. The expected slopes for laminar and turbulent flows on the log(ℎ ௅ ) 𝑣𝑠 log(𝑉) graph were one and two, respectively. The experimental results, also depicted on Figure 10, gave us slopes of 1.1845 and 1.9831. For laminar flow, our percent error was 18.5% and for turbulent, 0.8%. The results for turbulent are understandably similar because turbulent flow is so random and irregular, with a much wider range to obtain. Laminar is linear and consistent and it is more difficult to keep a flow laminar.

Pipe Flow Emilee Smith 7 Figure 9: f vs Re on Moody Diagram Figure 10: Log(hL) vs log(V) for Laminar and Turbulent Flow

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Pipe Flow Emilee Smith 8 Conclusion This experiment provided a comprehensive understanding of the different flows, turbulent and laminar. We were able to easily estimate a wall roughness for the pipe to be 0.0012 by plotting our experimental data on the Moody Diagram. The results of the log vs log graph, although with percent errors of 18% and 0.8% for laminar and turbulent flow respectively, the numbers were still close to expected slopes of 1 and 2. Our results confirmed the relationship between Reynolds number and both laminar and turbulent flow, laminar remaining under 2100 and turbulent over 4000. Acknowledgements All experimental data were collected with the assistance of Emilee Smith, Lana Ayyash, and Breanna Gallagher. We thank San Diego State University for providing the necessary facilities, and Jose Moreto for the insightful instructions.

Pipe Flow Emilee Smith 9 References. 1. Liu X. Guidance for Writing Reports, AE 341 Lab. 2017. p. 2. 2. H1D Volumetric Hydraulic Bench Data Sheet [Internet]. p. 1–3. Available from: www.tecquipment.com 3. Pipe Flow Lab Instructions from Jose Moreto 4. Munson, B. R. (2009). Fundamentals of Fluid Mechanics . John Wiley.

Pipe Flow Emilee Smith 10 Appendices Sample Calculations: 𝑄 ଵ = 𝑉 ଵ Δ𝑡 ଵ = 100𝑚𝐿 ∗ 10 ି଺ 𝑚 ଷ 1𝑚𝐿 59𝑠 = 1.695 ∗ 10 ି଺ 𝑚 ଷ /𝑠 𝑄 ଶ = 𝑉 ଶ Δ𝑡 ଶ = 150𝑚𝐿 ∗ 10 ି଺ 𝑚 ଷ 1𝑚𝐿 90.85𝑠 = 1.651 ∗ 10 ି଺ 𝑚 ଷ /𝑠 𝑄 ̇ ௔௖௧௨௔௟ = (𝑄 1 + 𝑄 2 ) 2 = (1.695 ∗ 10 −6 𝑚 3 /𝑠 + 1.651 ∗ 10 −6 𝑚 3 /𝑠) 2 = 1.673 ∗ 10 −6 𝑚 3 /𝑠 𝑉 = 𝑄 𝐴 = 1.673 ∗ 10 ି଺ 𝑚 ଷ /𝑠 7.069 ∗ 10 ି଺ 𝑚 ଶ = 0.23668 𝑚/𝑠 𝑓 = ℎ ௅ 𝐷 𝐿 2𝑔 𝑉 ଶ = 50 ∗ 10 ଷ 𝑚 0.003𝑚 0.524𝑚 2 ∗ 9.795𝑚 𝑠 ଶ ቀ 0.23668𝑚 𝑠 ଶ ቁ ଶ = 0.10011 𝑅𝑒 = 𝑉𝐷 𝑣 = 0.23668 𝑚 𝑠 ∗ 0.003𝑚 1 ∗ 10 ିଷ 𝑚 ଶ /𝑠 = 710.041 𝑇 ௔௩௚ = 20 + 21 2 = 20.5°𝐶 Questions Question 1: Can you explain why in the Moody Diagram, in the laminar portion, 𝑓 𝑣𝑠 𝑅𝑒 ஽ follows a straight line? Solution: The laminar portion of the Moody Chart follows a straight like because the 𝑓 𝑣𝑠 𝑅𝑒 ஽ for laminar flow is linear: 𝑓 = ଺ସ ோ௘ .

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Pipe Flow Emilee Smith 11 Question 2: Do you expect to have the same slopes when you plot log(ℎ ௅ ) 𝑣𝑠 log(𝑉) in both cases, laminar and turbulent flows? Solution: I do not expect the have the same slopes when I plot log(ℎ ௅ ) 𝑣𝑠 log(𝑉) in both cases because the expected values that are provided show a slope of 1 for Laminar flow and a slope of 2 for Turbulent. Therefore, I expect the slopes of my experimental data and calculations to be like the expected values with deviation.