Lab #4 - Pipe Flow - Fluids Lab report 4 PDF

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Lab 4 - Pipe FlowFluid Mechanics Laboratory Section: 3420 - 005 Group: A Monday 2:30 - 3:00 P. March 26, 2018Ahmed Abuaba Feijie Chen Christopher Elliot Matthew GibbonsAbstract In this lab, two experiments were performed in order to determine head losses inpipe systems. In the first experiment, wate...

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Lab 4 - Pipe Flow

Fluid Mechanics Laboratory Section: 3420 - 005 Group: A Monday 2:30 - 3:00 P.M. March 26, 2018

Ahmed Abuaba Feijie Chen Christopher Elliot Matthew Gibbons

Abstract In this lab, two experiments were performed in order to determine head losses in

pipe systems. In the first experiment, water was pumped through two different diameter pipes and an elbow connection. The flow rate was varied for each pipe, and the head losses were recorded for each pipe and the elbow. In the second experiment, water was run through a copper tube into open air. The head loss was measured as the head before the water entered the pipe, and the discharge of the pipe was collected over a period of 30 seconds. Using this data, the friction factors were calculated for both experiments, then compared to the Moody Diagram. Additionally, the data from the first experiment was used to find the minor loss coefficient for the elbow. During the analysis of this data, some large errors were noticed. Despite these errors, the experiment was declared a success.

Introduction The purpose of this experiment is to observe how friction affects a flowing fluid as it travels through conduit and fittings for various flow rates. Whenever a fluid is transported through pipes and fittings, it experiences head losses due to friction with the walls of the pipe and changing flow direction through fitting geometry. It is critical to understand these losses so that the appropriate placement of pumps, pipes, and fitting can be used. Theory When fluids flow through pipes and fittings, they lose energy due to friction between the fluid and the surface of the conduit. This is represented as the head loss in the energy equation. There are two main factors in the determining the head loss: the major head loss due to pipe flow, and the minor head loss due to flow through fittings, valves, bends, and other components. The head loss due to pipe flow can be calculated using the equation below.

In the equation above, L is the length of the pipe, “D” is the diameter of the pipe, “v” is the velocity of the fluid, “g” is the acceleration due to gravity, and “ f ” is the friction factor between the fluid and the pipe. The friction coefficient is a function of the Reynolds number and the relative roughness. The equation for the friction factor can already be derived by solving the above equation for f , but it can be further modified to work with changes in pressure. Theoretically, the major head loss is equivalent to the change in the pressure head over the length of the pipe. By substituting the change in the pressure head into the equation above, the following equation can be used to find the friction factor.

In practice, the friction factor can be estimated by first calculating the Reynolds number and the relative roughness, then by using the Moody diagram. In general, two equations define the friction factor, and pertinent equation depends on the Reynold’s number. If the Reynolds number is less than 2000, then the flow is laminar, and the friction factor is linearly related to the Reynolds number by the following equation.

When the Reynolds number for the flow is greater than 3000, the above equation cannot be used. In this case a different equation must be used. Unlike in laminar flow where the friction factor is only a function of the Reynolds number, the friction factor for turbulent flow depends on the relative roughness of the conduit in addition to the

Reynolds number. The equation below is for friction factor in turbulent flow.

It is important to notice that these equations don’t account for Reynolds numbers that fall between 2000 and 3000. This is because this region is still the subject of great study, and there aren’t any equations to describe this region. As such, this region is referred to as the transition region, and should be avoided for the purposes of this lab. Similar to the major head loss, the minor head loss depends on the velocity head. Unlike the major head loss, the minor head loss does not have a friction factor that is dependent on the Reynolds number. Instead, every component has its own minor head loss coefficient, “K.” For most technical applications, K is assumed to be independent of the Reynolds number. The equation for finding the minor head loss is below.

Procedure Experiment 1: In the first experiment, water was pumped through a flow test rig. The rig consisted of a sump tank to collect water, a pump that discharged water from the tank into the pipe system, and a series of valves to control where the fluid travels in the system. By opening and closing valves, the flow could be directed into a specific diameter pipe. Additionally, another valve was used to control how much of the fluid went to the pipes, and how much was directed back into the tank without flowing through the rest of the system. Two pipes, with diameters of 0.595 inches and 0.800 inches, were tested during the experiment, as well as an elbow fitting that came immediately after each pipe. The head difference was measured along the length of both pipes and the elbow. Additionally, the head difference was measured across an orifice meter, and LabView used to calculate the volume flow rate. The following procedure was followed. 1. Start LabView and open the pipe flow monitoring program. Make sure that the data acquisition box and the power source are turned on. 2. Run the program. Follow the on-screen instructions. 3. Make sure that at all times the values allow the flow through at least one pipe. Start the pump. 4. Adjust the trim (bypass) valve to set different flow rates through at least one pipe at a time. Collect data for four flows for each of the two pipes, for a total of 8 flow settings.

5. For the same 8 flow settings, data will also be collected for the head loss over the elbow fitting. 6. When finished, save the data in a file; get a copy of the file. Experiment 2: In the second experiment, water was run through a copper pipe. The head was measured before water entered the pipe, and the pipe discharged into the atmosphere. Because atmospheric pressure can be taken as zero gauge pressure, the major head loss was taken as the head before the fluid entered the pipe. For varying unknown flow rates, the volume of discharged fluid was collected over a period of 30 seconds, then used to find the flow rate. For this experiment the following procedure was used. 1. Weigh the beaker empty and record the reading on the data sheet. 2. Check that the pipe is connected to the water supply and is horizontal; prepare the empty beaker to capture the water discharge when needed and also prepare a stopwatch to measure the discharge time. 3. Open the valve to allow water from the supply to flow through the pipe. 4. Allow the water flow to reach a steady state; this will take a few seconds. 5. Move the beaker to capture the flow discharge, while at the sametime start the stopwatch. 6. While capturing the water discharge into the beaker read and record the piezometric head at the pipe inlet. 7. Move the beaker away from the water stream and at the same time stop the stopwatch; record the time interval. 8. Close the inlet valve to stop the flow. 9. Weigh the beaker with the captured water and record the reading in the table provided on the data sheet. 10. Repeat the steps 2-9 for two more valve settings (you will have a total of three piezometric head values and thus three different flow rates).

Results Water temperature for this lab was T = 20 ℃. All the properties of water shown below that are used in the lab correspond to to the water temperature of T = 20 ℃. kg Density: ρwater =998 3 m N Specific Weight: γ water =9790 3 m −3 N∗s Dynamic Viscosity: μwater =1.00∗10 m2

−6 Kinematic Viscosity: ν water =1.00∗10

m2 s

Plot of Theoretical Moody Diagram The theoretical Moody diagram is of six turbulent curves using different relative roughness values, and one laminar curve because laminar flow does not change with the relative roughness. The relative roughnesses used for the turbulent curves were: Φ = 0, 0.000001, 0.0001, 0.001, 0.01, and 0.05. The turbulent curves were plotted using the Reynolds numbers from 3000 to 10 ⁷ and the turbulent flow used Reynolds numbers from 1000 to 2200. The Moody diagram compares the Reynolds numbers and friction factor of turbulent and laminar flow. The diagram has a logarithmic scale showing the data in log-log coordinates. 0.25 f= ϕ 5.74 2 Turbulent Flow: [ log ( + )] 3.7 ℜ0.9 64 Laminar Flow: f = ℜ

Calculated Velocities, Reynolds Numbers, and Friction Factors

Pipe ID (mm)

Flow Rate (m^3/s)

Head Loss (mm)

Velocity (m/s)

Reynolds Number

Friction Factor

1

15.113

0.00020491

167.1242

1.1423

17263.58

0.022484

2

15.113

0.0001823

135.6382

1.0162

15357.83

0.023058

3

15.113

0.00010126

50.34087

0.56448

8530.986

0.027734

4

15.113

0.00007345

30.58257

0.40945

6188.018

0.032023

5

20.32

0.00020576

102.2611

0.63449

12892.84

0.059955

6

20.32

0.00018552

85.85289

0.57208

11624.67

0.061917

7

20.32

0.00012777

45.11431

0.39400

8006.080

0.068594

8

20.32

0.00009633

27.82776

0.29705

6036.056

0.074436

1

2.46

8.2832E-6

241

1.7428

4287.288

0.015318

2

2.46

7.1361E-6

182

1.5014

3693.444

0.015587

3

2.46

5.5077E-6

120

1.1588

2850.648

0.017253

Experiment 1: 1∈¿ 25.4 mm =15.113 mm ¿ ID (mm)= 0.595 ∈¿ ¿

Flow Rate(

m3 )=3.246014 gpm∗( s

6.309∗10−5 1 gpm

m3 s

)=0. 0 0020491

1∈¿=167.1242 mm Head Loss( mm)=5.727701 ∈. H 2

O∗25.4 mm ¿

m3 s

0.015113 ¿ ¿¿2 ¿ ¿ π¿ ¿ Velocity(

Q m = )= s π D2 4

VD = Reynolds Number = ν

Friction Factor=

0.00020491 ¿

m3 s

m ∗0.015113 m s =17263.5799 2 −6 m 1.00∗10 s

1.1423

hL 0.1671242 m =0.022484 = 1.6891 m L 2 2m ∗V ∗(1.1423 ) D s 0.015113 m 2g m 2∗9.81 2 s Experiment 2:

m flow rate =

mwater 0.248 kg kg =0.008267 = s 30 s Δt

m3 m Flow Rate( )= flow rate = s ρ

0.008267 998

kg s

kg m3

=8.2832∗10−6

m3 s

m3 m m s Q =1.7428 Velocity( )= = 2 2 s s π (0.00246) πD 4 4 8.2832∗10−6

VD = Reynolds Number = ν

m ∗0.00246 m s =4287.288 2 −6 m 1.00∗10 s

1.7428

Friction Factor=

hL L ∗V 2 D 2g

=

0.241 m =0.015318 0.25 m 2m ∗( 1.7428 ) s 0.00246 m m 2∗9.81 2 s

Discussion of the Frictional Factors When comparing the measured data with the Moody diagram, the behavior of the collected data seems to generally correlate with the Moody diagram curves. However, none of the data seems to fit any exact curve on the diagram. All of the calculated Reynolds numbers from the data, with the exception of one value from the second experiment, are greater than 3000, meaning that the flow is turbulent for all of the data. Generally speaking, the measured friction factors do slope down, then begin to level off as the data approaches an infinitely large Reynolds number, but the data seems to have shifted to the right on the Moody diagram. On an individual basis, the 0.595 inch pipe most closely models the behavior of the Moody diagram because it fits just below the curve for the smoothest pipe graphed, and it still follows the curve geometry at that location. This is followed by the 0.800 inch pipe. It too follows general geometry of the curves, but its slope down is too steep for its location on the diagram. The data from the second experiment has the friction factor which is most dissimilar to the Moody diagram; the data is far below the curve for the smoothest pipe, and a little to the left too. This suggests that a large error was present in this experiment. Theses issues could result from a number of different factors, especially in relation to the accuracy of the experiment. In the first experiment, all of the pressure drops were recorded by pressure sensors, and the pressure sensors may have been partially uncalibrated. Additionally, the flow rate was measured by an orifice meter, and it could be possible that the recorded flow rate differed from the actual flow rate. Velocity from the flow rate is critical to correctly calculating the Reynolds number, so this too could change the results. In the second experiment, it was easy for human error to enter into the results because the water was collected by human hands, as was the time on the stopwatch. In terms of relative roughness, the 0.595 inch pipe appeared to be a rougher pipe than the smoothest pipe graphed, the 0.800 inch pipe was slightly more smooth, and the copper pipe was far more smooth than the smoothest curve. Because the composition of the copper pipe is known, the theoretical value for the friction factor can be computed. According to the textbook, the roughness of copper is 0.0015 mm. When the roughness is divided by the diameter, the relative roughness is 6.09756E-4. Using this with the calculated Reynolds numbers, the theoretical friction factors are, in the same order as the table above, 0.04040, 0.04404, and 0.04586. Even though the third value is technically in the transition region, a turbulent approximation was used. The

percent error for each experiment is, in order, 62.08%, 64.61%, and 62.38%. In addition to all the previously mentioned errors, there is one additional factor that may have produced these errors. In general, the equipment in the lab has been used for many years, and has thus experienced wear over time. As such, it is quite possible that wear in the system may have decreased the accuracy of the data. Calculated Minor Loss Coefficient and Reynolds Number The table below shows the calculated Reynolds Number and Factor K values. The calculations can be found under the table. Fitting ID (mm)

Flow Rate (m^3/s)

Head Loss (mm)

Velocity (m/s)

Reynolds Number

1

29.21

0.00020491

12.0842786

0.3057808 8931.8560 2.5357090

2

29.21

0.0001823

11.669903

0.2720406 7946.3050 3.0938475

3

29.21

0.00010126

5.6646318

0.1511071 4413.8390 4.8674425

4

29.21

0.00007345

3.947795

0.1096071 3201.6243 6.4472719

5

29.21

0.00020576

18.834862

0.3070492 8968.9068 3.9196342

6

29.21

0.00018552

15.6380434

0.2768457 8086.6621 4.0031875

7

29.21

0.00012777

8.2259424

0.1906672 5569.3878 4.4394878

8

29.21

0.00009633

5.9949588

0.1437502 4198.9444 5.6920417

1∈¿ 25.4 mm =29.21 mm ¿ Elbow ID(mm)=1.15 ∈¿ ¿

Flow Rate(

m3 )=3.246014 gpm∗( s

6.309∗10

−5

1 gpm

m3 s

)=0.00020491

m3 s

1∈¿=12.0842786 mm Head Loss( mm )= Elbow ∈. H 2 O=0.475759∈. H 2

O∗25.4 mm ¿

Measured K Factor

m3 Q s m m = =0.3057808 Velocity( )= 2 2 s s π (0.02921) πD 4 4 8.2832∗10−6

VD = Reynolds Number = ν

K Factor =

hL 2

V 2g

=

m 0.3057808 ∗0.02921 m s =8931.8560 2 −6 m 1.00∗10 s 0.0120842786 m =2.5357090 2m (0.3057808) s m 2∗9.81 2 s

Plot of Minor Loss Coefficient with Reynolds Number

Comparison of Theoretical and Measured Minor Loss Coefficient The measured K values in the lab change a great deal based on the variables in the lab. The average experimental K value calculated in the lab was 4.375 and the textbook’s calculated K value for a 90 degree elbow was 0.9. These values have a percent difference of 386.11%. The textbook’s value does not take into consideration

the diameter of the pipe, the flow rate going through the elbow, and the roughness of the pipe. One of the many variables that causes change is the diameter of the pipe. There were two different diameters of pipe used during this part of the lab. The first diameter was 0.595 inches and the second was 0.80 inches. From the diameters being different the flow rate will be changing too because of the diameters. The most important part of this lab to remember is that the book value is a generic value for the 90 degree elbow and is not taking any of the lab variables into consideration. %Difference=

0.9− 4.375 Theoretical Value− ExperimentalValue ∗100=386.11 % ∗100= 0.9 Theoretical Value

Conclusion This lab showed us that fluids traveling through pipe systems result in pressure losses because of friction. In the lab we observed the effects of pipe friction and minor losses due to different flow rates through different pipe sizes. The friction factor, f, and Reynolds number, Re, for the different cases were plotted on a Moody diagram to help show the similarity of the experimental data to the theoretical data. Additionally, the minor loss coefficient for the elbow in the first experiment was plotted with respect to the Reynolds number in order to see any correlation between the two characteristics of the system. Some errors did appear when the data was analyzed and plotted. For more information on the presence of errors, please refer to the preceding section. Despite these errors, the data was collected easily and as accurately it could have been obtained. Overall, the experiment successfully completed its objective in spite of its errors....