Pipe Flow - Lab Report 2 PDF

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Pipe Flow LAB REPORT Connor 13295910 Matthew 13295934 Nazmus 12632877 Sam 13356706 Table of Contents Abstract ..................................................................................................................................... 1 Introduction ............................................

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Pipe Flow LAB REPORT

Connor Wowk- 13295910 Matthew Malloy- 13295934 Nazmus Sakib- 12632877 Sam Meisner- 13356706

Table of Contents Abstract ..................................................................................................................................... 1 Introduction .............................................................................................................................. 2 Methodology .............................................................................................................................4 Experimental Procedure ...........................................................................................................0 Reading a Moody Diagram ....................................................................................................... 1 Results ....................................................................................................................................... 3 Discussion .................................................................................................................................9 Conclusion................................................................................................................................ 11 References ................................................................................................................................12 Appendix .................................................................................................................................. 13

Abstract This experiment is designed to analyze the major and minor energy loss of fluid flow through a pipe that is attributed to friction and pipework components. Two different materials were used, galvanized steel and PVC, to test the significance of internal roughness and the frictional coefficients associated with the respective material. Additionally, calculated and measured values from the provided equipment were compared to each other to examine possible discrepancies in the data due to experimental and human error. We found that when studying the energy loss due to friction, it is more practical to simply increase the diameter of the piping and use a cheaper, more durable material rather when selecting materials for applications. Also, when conducting experiments that examine fluid flow through a pipe, it is more reliable to take all readings from properly calibrated equipment such as a venturi meter or digital manometer due to the high number of possible error sources that are present when analyzing any set of pipework.

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Introduction The objective of this experiment is to quantitatively analyze fluid flow through pipes by applying the fluid mechanics theories and principles of energy losses and flow rates. By calculating these values for the test rig that was used, we are able to examine how the material of a pipe and its diameter are related to the major and minor energy losses that occur, as well as their effects on the volumetric flow rate of the fluid. The goal of this experiment is to compare the performance of two pipes, galvanized steel and polyvinyl chloride (PVC), and summarize the advantages and disadvantages of each material for construction. Furthermore, the report aims to examine the differences between calculated and measured values and propose empirical explanations for discrepancies. It is important to consider all factors to accurately analyze the energy loss and flow rate changes that occur in the system. Reynolds Number is a dimensionless quantity that is used to determine if the fluid flow is laminar or turbulent. When Reynolds number is greater than 4000, turbulent flow is present and there is an excess of kinetic energy that produces small vortices or eddy currents. These cause fluid particles to travel in the opposite or perpendicular direction of flow which induces more drag and energy loss within the pipe. The relative direction of the flow is unchanged. During laminar flow all fluid streamlines are parallel and all frictional losses are a result of the shear force as the liquid in contact with the pipe has a velocity of zero. Laminar flow in pipes generally occurs when high density liquids are moving at slow velocities (Munson, ). For Reynolds numbers between 2000 and 4000, the flow is unstable and changes with time as vortices form and subside. In this experiment we will use water flowing at relatively high velocities and expect all Reynolds numbers to indicate turbulent flow.

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After Reynolds Number is calculated for each pipe based on its material and diameter, the value can be used to determine how much energy loss would be experienced due to friction within the pipe. The relationship between Reynolds Number, material roughness, pipe diameter, and frictional loss coefficient is graphically represented in the Moody Diagram. Once the frictional loss coefficient is determined it is used to For this experiment, we were studying fluid flow in an incompressible, steady state condition which allows us to apply Bernoulli’s Energy Equation across each pipe. By doing so, we consider the conservation of energy principle and deduce that the sum of kinetic, potential, and internal energies remains constant across any two points on a streamline. The internal energies include major and minor pressure head loss. Major head loss is due to the surface friction along the interior of the pipe and minor head loss results from the fluid passing through pipework components such as connections, bends, and valves. In order to draw convincing conclusions from our measurements it is important to survey the equipment that was used during the experiment and take note of their purpose, limitations, and potential error. A venturi meter was used to measure the flow rate through a venture tube. The venture tube essentially accelerates fluid through a throat section that has a decreased cross-sectional area. This was utilized to ensure a constant flow rate and accurate data readings while conducting the experiment. Additionally, to control the volumetric flow, an orifice plate was used. The plate can suddenly expand or contract the effective pipe diameter to adjust flow rate, pressure, and velocity accordingly. Furthermore, the pipe fittings that were used in the test apparatus were sudden enlargement pipe fittings. These are important to consider for calculating minor pressure head losses.

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Methodology The pump used to push water through the pipe system is a Lowara CEAM 70/3/A-V. It is capable of inducing a volumetric flow rate of 30 to 80 liters per minute, which is more than adequate for the testing done in this experiment with 15 and 25 mm pipes. The pump is attached to one end of the pipes and all valves are closed except for the pipe being tested. A flowmeter is attached after the pump which measures the flow rate through the entire apparatus. The unit used in the experiment is a Dwyer UV-4112 flowmeter with a max pressure or 150 psi or 1034 kPa. This flowmeter is accurate to +/- 2 percent (Dwyer, 1). Digital manometers on both sides of the pipe being tested allow the pressure drop over the pipe to be measured. The digital manometer used is a Dwyer 4902-NIST. It is capable of measuring pressures from 0 to 30 psi or 0 to 206.84 kPa and has a maximum pressure of 60 psi or 413.69 kPa. The pressure drop readings collected for the experiment are calculated automatically by the computer in the unit by subtracting the for pressure from the manometers from each end and . It is important that none of the instruments are damaged by exceeding the maximum pressures given by manufacturers. To ensure this does not occur, the pump is relatively small and cannot exceed these limits while moving water through 15 and 25 mm pipes.

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Figure 1: Diagram of Dwyer flowmeter (UTS online)

Figure 2. Diagram of the Venturi Meter that was used in the testing apparatus

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(UTS Online)

Figure 3. Diagrams showing the orifice plate and and cross section of the connection fittings that were used in the testing apparatus (UTS Online)

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Experimental Procedure 1. Turn on the water pump and wait for steady flow to be established. 2. Record pressure drop reading from the digital manometer. 3. Record water flow rate from the flowmeter. 4. Repeat steps two and three for each pipe (2 PVC pipes and 2 galvanized steel pipes).

Figure 4. Picture showing the setup of the testing apparatus that was used for this experiment (UTS Online)

5. Calculate average velocity in for each pipe using v = (volumetric flow rate) / (pipe cross sectional area)

6. Calculate Reynolds number using

, where μ = Dynamic

Viscosity = 1x10-3 for water at 20 degrees C, D = internal diameter, ⍴ = density, and v = average velocity. 7. Find Frictional Coefficient using Moody Diagram (see specific procedure for this below).

8. Determine frictional head loss using the formula

, where g

is acceleration due to gravity. 9. Calculate Friction Pressure Drop using (Pressure drop = ρg*FHL). 10. Propagate error from instrument readings through calculations. 11. Compare friction pressure drop calculated to friction pressure drop measured in (2). Note: all calculations done using Microsoft Excel, sample calculations available in Appendix.

Reading a Moody Diagram The process to identify the frictional coefficient for each pipe is: 1. Calculate the relative pipe roughness, which is the roughness coefficient (𝝐) divided by the diameter. 2. Plot a vertical line on the graph from the Reynolds number. 3. Follow the curve of the Relative Pipe Roughness for the given pipe until it touches the Reynolds number line and mark this point. 4. Plot a horizontal line from this point to the y-axis of the graph and record the frictional coefficient. 5. Repeat for each pipe and both flow rates.

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Note: error for calculating Friction Factor estimated to be +/- 0.001 based on human error while graphing.

Figure 5. Moody Diagram showing how the frictional coefficient was determined for the first flow rate in each of the four pipes

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Figure 6. Moody Diagram showing how the frictional coefficient was determined for the second flow rate in each of the four pipe

Results

1st flow rate Calculate Flow Rate

d Friction Flow

Pipe (L/min Rate (m3/s)

Type )

15m

67

0.001116

Pressure Flow

Reynolds Friction

Drop

Velocity

Number

Coefficie Head-

(kPa)

(m/s)

(Re)

nt (f)

28

4.487

79875.51

0.028

Friction

Pressure Drop

loss (HL) (kPa) 4.116

40.386

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m

666667

4

Galva

0.000933

73810.98

nized

56 3333333

PVC

15m m

60

4.58

8

0.038

6.447

63.249

0.02

0.471

4.624

0.034

0.860

8.446

25m m PVC

63435.42 84

0.0014

5.4

2.257

2

25m m Galva nized

62962.39 81 0.00135

7.5

2.306

5

Table 1. Presents initial given data as well as relevant calculated values for each pipe for the first flow rate

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Figure 7. Bar graph comparing the measured pressure drop with the calculated pressure drop for the first flow rate. Note that error bars are included and are based on propagated error for calculated values and the manometer manufacturer’s manual for measured values

2nd Flow Rate

Calculate d Friction Flow Rate

Friction Flow

Pipe (L/min Rate Type )

(m3/s)

Friction

Pressure

Pressure Flow

Reynolds Coefficie Head-

Drop

Velocity

Number

nt (f) (+/- loss (HL) (kPa, +/-

(kPa)

(m/s)

(Re)

3%)

Drop

(+/-5%)

5%)

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15m m PVC

1.875326 33380.81 28 0.000467

6.7

519

2

0.022

0.565

5.542

0.049

2.078

20.389

0.028

0.0841

0.826

0.032

0.111

1.090

15m m 2.292266 36905.49

Galva nized

28 0.000467

15.1

711

4

25m m PVC

0.806245 22655.50 30

0.0005

1.2

8332

7

25m m 0.854190 23319.40

Galva nized

30

0.0005

1.7

6806

5

Table 2. Presents initial given data as well as relevant calculated values for each pipe for the second flow rate

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Figure 8. Bar graph comparing the measured pressure drop with the calculated pressure drop for the second flow rate. Note that error bars are included and are based on propagated error for calculated values and the manometer manufacturer’s manual for measured values

ΔP Venturi

ΔP Orifice

ΔP Sudden

(kPa)

(kPa)

Expansion (kPa)

178.5

10

Water flow rate (m3/s)

1.4

0.000333

Table 3. Presents the given pressure changes for each piece of equipment used in the experiment

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Venturi meter (m3/s)

Qmeasured

0.00033

Qcalculated

0.000283

Table 4. Presents measured and calculated volumetric flow rate for the venturi meter. Error ≅14.2%

kL= 0.3 2𝛥𝑃

V1 = √⍴𝑘𝐿

Qexpansion= V1A1 Sudden Expansion (m3/s)

Qmeasured

0.00033

Qcalculated

0.00024

Table 5. Presents measured and calculated volumetric flow rate through the

expansion fittings in the pipework. .Error ≅27.2%, attributed to experimental error and discrepancy in kL

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V2 =

𝑄𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑

Re =

𝑉𝑑⍴

𝐴

𝜇

Qorifice = 𝐶𝐴√

2𝛥𝑃 ⍴

Orifice Plate (m3/s) Qmeasured

0.00033

Qcalculated

0.000378

Table 6. Presents measured and calculated volumetric flow rate through the Orifice Plate. Error≅14.5%

Discussion The data regarding the pressure change reflects significant differences between frictional properties of the Galvanized and PVC piping materials. Due to the PVC pipes having roughness of approximately zero, they produced a smaller head loss in the flow. As expected, there were greater pressure differences in the first flow rate compared to the second because of the greater fluid velocities. However, there was greater variation between the calculated and measured pressure drops in the second flow. The original flow rate measurement included a two percent error. After the sets of calculations velocity has been squared and another variable with error is introduced, the friction coefficient from the moody diagram. Total variance possible is estimated to be +/- 5 % for the final values of calculated pressure drop. The calculated values and measured values are do not have error bars that intersect and therefore error could not have come from the instruments themselves. The error is most likely due to many factors but the largest possible contributions include the assumption that the water is at 20 degrees or irregularities in the pipe that cause the measured to be fundamentally

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different from calculations based on theoretical values. The second flow has volumetric flow rates that are about half the magnitude of the first, which objectively would seem to yield less discrepancies in calculation, since the turbulence of the flow was not as severe. The calculated flow rate values via the orifice plate, sudden expansion, and venturi meter all had significant error, deviating them from the measured flow rate. Averaging the three calculated flow rates yields Q = 0.00031. This value is within 9% of the measured flow rate. The difference is presumed to be caused by experimental error. This experiment is useful for analyzing and comparing materials used in pipework based on their internal roughness and diameter. The testing apparatus and equipment allows us to quantitatively determine what kind of material would be the most efficient in terms of required power for moving fluid for applications such as household plumbing. Numerous experiments could be conducted with the current testing apparatus. For example, the flow rate could be slowed and data could be recorded from a laminar flow or a fluid other than water could be tested to examine the significant changes in energy loss caused by an increase or decrease in viscosity. Modifications to this experiment have nearly unlimited potential. Bends, elbows, and valves could be introduced to the apparatus to measure a wider range of minor head loss. Any number of materials could be tested such as riveted steel, concrete, and cast iron, rather than just galvanized steel and PVC. Piping that changes height as it passes through the apparatus could be used to test if there is more head loss from gravity or from friction caused by internal roughness. Additionally, any combination of components could be introduced such as a pump, fan, or turbine to analyze all aspects of the expanded energy equation that is derived from Bernoulli’s principle.

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Conclusion Comparing the PVC pipes to the galvanized steel pipes, it is obvious that PVC experiences far less head loss due to the frictional effects of the fluids. However, the data also reveals that increasing the diameter of the flow has a more significant effect in changing the magnitude of head loss than using a different material of the same diameter. This is due to the reduction of turbulent and sequential frictional effects in the flow. Accordingly, when selecting a material for piping applications, it is apparent that increasing the internal diameter of the pipework and using a cheaper, more durable material will be more beneficial in terms of cost effectiveness and efficiency. Regarding the measured quantities and the calculated quantities, it would be more reliable to record measured data rather than computing it with limited known values due to the meters being able to acquire accurate data at specific points in the pipe. The calculations do not fully account for deviations in the flow of the fluid, which is reflected in the differences between the measured and calculated values.

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References

http://www.dwyer-inst.com/PDF_files/Priced/uv_cat.pdf

Munson, B.R. (2006). Fundamentals of Fluid Mechanics (5 ed.). Hoboken, NJ: Wiley & Sons.

https://www.johnmorrisgroup.com/AU/Product/91454/Dwyer-490-2-WetWetHandheld-Digital-Manometer-0-to-30-psi

https://www.sensorsmag.com/components/manometer-basics https://www.astro.rug.nl/~weygaert/tim1publication/astrohydro2014/astrohydro20 14.III.2.pdf

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Appendix

Sample calculation of Q measured for the Orifice Plate that was used in the test rig

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Sample calculations of the Q measured for the ex...