Pipe Friction

Pipe Friction CE 319W - Lab #2

Nathaniel R. Gant

Group Members: Gore, Pickens, Sexton, Wood Date Performed: January 22, 2012 Date Submitted: March 26, 2012 Submitted To: MAJ Dave Johnstone, Ph.D., P.E.

Virginia Military Institute Department of Civil and Environmental Engineering

Help Received: None

INTRODUCTION AND THEORY Water has been a vital resource for humans since the beginning. Humans use water to support their health, hygiene, and amusement. Over time, people have developed methods to transport water from its original source to an accessible area, such as from the ocean to someone’s home. The common method to transport water in today’s society is by a system of pipes, such as the pipe network for a factory shown in Figure 1. The main components of a water

Figure 1: Picture of a pipe network for a factory

system carrying water under pressure are the transmission and the feeder mains from the treatment plant to the distribution system, and the distribution mains consisting of an interconnecting pipe network up to the source point (Gupta 2008). When a valve stops a fluid’s flow in a pipe, pressure waves are created. These waves travel along the pipe until they reach a physical feature of the pipe network, where the wave is partly transmitted and partly reflected back toward the source (Beck 2005). A majority of fluids that flow through pipes create energy losses due to friction. Because of this, determining losses due to friction are extremely important for an engineer to specify the proper pipe size, pump, and fluid combination (Rabinovich 2011).

Pumps manipulate the rate at which volume travels per unit time. This regulates the fluid velocity. It is important to analyze fluid velocity because inaccurate determination of the fluid velocity can lead to high-energy consumption, particle abrasion, pipe erosion, and in some cases, pipe blockage. Sediment conglomeration and pipe erosion cause pipe friction because water particles flowing in a pipe wall collide into these obstructions causing friction. For example, Figure 2 shows a picture of an eroded pipe and it has so much rust built up in the interior that the diameter of pipe that water travels through shrunk. Moreover, the rust causes the water the rub

Figure 2: Picture of an eroded pipe

against a rough surface, which causes energy loss due to friction. The energy loss between two points can measured using the energy balance equation:

In the equation, is the head loss in pressure at a specific point, is the unit weight of water, is the elevation at a specific point, is the velocity at a specific point, is the gravitational constant, and is the loss of head along the pipeline due to friction. The theoretical equation to calculate pipe friction loss is from the Darcy-Weisbach Equation is:

In the Darcy-Weisbach equation, is the headloss along the pipeline due to friction, is the coefficient of friction, L is the length of the pipe, D is the inside diameter of the pipe, is average velocity of the pipe, and is the gravitational constant. Depending on the type of pipe material and pipe features, such as fittings, elbows, valves, expansions, contractions, inlets, and outlets, minor losses of energy are created as well. Minor losses are calculated by

In the equation, is the head loss due to minor losses, is the loss factor, is the velocity at a specific point, and is the gravitational constant.

The purpose of this exercise was to compute the pipe friction and minor losses for a pipe network.

METHODOLOGY For this experiment, a fluid circuit apparatus was put into operation using 0.545-inch diameter copper pipes. This was done by closing all valves and manometer taps, then opening the valves in the line desired. This allowed water to flow through the orifice meter for each line.

Because a submersible pump was attached to the system, air was forced out of all the pipes. Only taps for the desired lines were opened. This emptied air in the pipe. The hydraulic pressure and flow rate were adjusted to achieve the greatest change in height on the orifice meter. Once the flow rate settled, five manometer readings were recorded for the desired flow lines. Valves 10 and valve 11 were manipulated to adjust the flow rate in steps from maximum to minimum and back to maximum. Then the five manometers were read at each step. Ten trials were performed.

The water temperature was considered room temperature for each trail.

RESULTS For the experiment, two collections of results were gathered. One set of results came from the class’s recorded data and the other set of results came from the professor‘s recorded

data. The two collections allowed the experiments to be compared. In Table 1, the properties of the pipes and the water through the pipes are shown. The manufacturer of the pipes noted the diameter of the pipe, which was the only thing needed to calculate the area of the water flow.

Using the average room temperature, the viscosity, and density of the water was determined.

Table 1: Given values for water properties and pipe properties Diameter 0.545 in -

Area 0.00162 ft2 -

Temp 70°F 20°C

Density 62.3 lbm/ft3 998.23 kg/m3

Absolute Viscosity .000021 lbf-sec/ft2 .001005 Pa-s

Kinematic Viscosity .000021 ft2/sec .000001007 m2/s

Table 2 displays the raw data collected from the class’s manometer readings. These readings were collected each time the flow rate was adjusted. Notice that in line 4 for Table 2 the headloss values are all two-digit. This shows that the flow rate was not adjusted as much as it could have because there were no one digit headloss values.

Table 2: Class’s manometer trial data for each tap Trials # 1 2 3 4 5 6 7 8 9 10

Line 4 H in 46.25 42.75 37.50 31.50 32.75 25.50 36.00 37.25 33.50 38.50

Line 5 H in 40.25 37.00 32.50 26.25 27.00 19.75 28.25 27.25 22.50 26.50

Line 7 H in 59.25 54.75 49.25 42.50 44.25 37.75 52.75 59.50 56.25 64.50

Line 8 H in 57.50 53.00 47.75 41.00 43.00 36.25 50.50 56.50 53.25 61.00

Line 9 H in 50.25 46.25 40.50 34.50 36.25 29.00 41.00 44.00 40.00 46.25

Table 3 displays the raw data collected from the professor’s manometer readings. Notice that in line 4 for Table 3 there was a large range of headloss values. This shows that the flow rate was adjusted enough to give a large variation of values unlike in Table 2. By having a large range of headloss values, the relationship between flow rate and headloss would be more accurate.

Table 3: Professor’s manometer trial data for each tap Trial # 1 2 3 4 5 6 7 8 9 10

Line 4 H in 19.75 46.75 27.00 10.50 39.00 55.75 21.75 48.25 54.50 6.00

Line 5 H in 9.00 42.25 21.50 8.00 37.25 53.25 17.50 40.50 47.25 4.50

Line 7 H in 42.50 56.25 38.50 16.25 43.75 62.50 30.25 65.25 70.00 9.25

Line 8 H in 40.00 55.25 37.00 15.50 43.25 61.50 29.25 62.75 67.75 8.50

Line 9 H in 26.50 49.50 30.50 12.25 40.50 58.25 24.50 53.25 59.00 7.00

Using the equations for experimental headloss, theoretical headloss, flow rate, Reynolds number, minor loss, coefficient of friction, and head loss due to friction, the values from Table 1 and Table 2 were inserted to the equations to compute each value for Table 4.

Table 4: Class’s trial calculations for experimental headloss, theoretical headloss, flow rate, velocity, Reynold’s number, coefficient of friction, minor headloss, and K value (St.Dev= 1.234 and Avg=18.0) Trials

Exp. Hf

Q

V

# 1 2 3 4 5 6 7 8 9 10

in 1.75 1.75 1.50 1.50 1.25 1.50 2.25 3.00 3.00 3.50

gpm 1.047 1.025 0.954 0.978 1.025 1.025 1.193 1.359 1.427 1.492

ft/s 1.441 1.410 1.313 1.346 1.410 1.410 1.642 1.869 1.963 2.052

Re 3191.741 3123.209 2908.340 2981.616 3123.209 3123.209 3636.757 4141.622 4347.912 4545.199

f

Theory hf

Theory hf

hm

K

0.042 0.042 0.043 0.043 0.042 0.042 0.041 0.039 0.039 0.038

ft 0.104 0.101 0.089 0.093 0.101 0.101 0.131 0.165 0.179 0.194

in 1.253 1.206 1.065 1.112 1.206 1.206 1.575 1.977 2.152 2.326

in 6.771 6.271 6.839 6.089 6.408 6.839 8.884 11.679 12.429 13.792

17.507 16.934 21.298 18.042 17.303 18.469 17.693 17.934 17.318 17.585

Likewise, using the equations for experimental headloss, theoretical headloss, flow rate, Reynolds number, minor loss, coefficient of friction, and head loss due to friction, the values from Table 1 and Table 3 were inserted to the equations to compute each value for Table 5.

Table 5: Professor’s trial calculations for experimental headloss, theoretical headloss, flow rate, velocity, Reynold’s number, coefficient of friction, minor headloss, and K value (St.Dev= 2.529 and Avg=18.1) Trials # 1 2 3 4 5 6 7 8 9 10

Exp. Hf in 2.50 1.00 1.50 0.75 0.50 1.00 1.00 2.50 2.25 0.75

Q gpm 1.410 0.904 1.002 0.670 0.559 0.670 0.878 1.193 1.154 0.516

V ft/s 1.940 1.244 1.378 0.922 0.769 0.922 1.208 1.642 1.587 0.710

Re

f

4297.232 2756.188 3053.201 2042.301 1702.628 2042.301 2677.003 3636.757 3515.142 1573.899

0.039 0.044 0.043 0.047 0.049 0.047 0.044 0.041 0.041 0.050

Theory hf ft 0.176 0.081 0.097 0.048 0.035 0.048 0.077 0.131 0.124 0.030

Theory hf in 2.109 0.969 1.159 0.574 0.417 0.574 0.921 1.575 1.484 0.364

hm in 12.815 5.476 6.089 3.045 2.613 2.976 4.476 8.815 8.134 1.295

K 18.280 18.988 17.206 19.228 23.743 18.795 16.453 17.557 17.340 13.766

Using Table 4, a scatter plot was produced for flow rates and corresponding headloss for experimental and theoretical values. Figure 3 shows the class’s relationship between pipe friction headloss in inches of water versus the flow rate in gallons per minute on a linear graph. On the Experimental Power (Experimental)

Theoretical Power (Theoretical)

4.0 3.5

y = 1.5156x2.0627 R² = 0.9235

Headloss (in)

3.0 2.5 2.0 1.5

y = 1.1555x1.75 R² = 1

1.0 0.5 0.0 0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

Flow Rate (gpm) Figure 3: Graph of pipe friction headloss versus flow rate from the class’s data

graph, the blue diamonds represent the experiment values and the green squares represent the theoretical values. A trendline was added using excel, it revealed that there was a power correlation for the experimental and theoretical values. The correlation coefficient, or R2 value, for the experimental data was 0.9235. The correlation coefficient for the theoretical data was one. This shows that the experimental data had a very close fit because a R 2 value of one represents a “perfect fit”.

Using Table 5, a scatter plot was produced for flow rates and corresponding headloss for experimental and theoretical values. Figure 4 shows the class’s relationship between pipe friction headloss in inches of water versus the flow rate in gallons per minute on a linear graph. On the Experimental Power (Experimental)

Theoretical Power (Theoretical)

3.0

Head Loss (in)

2.5 y = 1.5298x1.5366 R² = 0.8624

2.0 1.5

y = 1.1555x1.75 R² = 1

1.0 0.5 0.0 0.40

0.60

0.80

1.00

1.20

1.40

1.60

Flow Rate (gpm) Figure 4: Graph of pipe friction head loss versus flow rate from the professor's data

graph, the purple diamonds represent the experiment values and the red squares represent the theoretical values. A trendline was added using excel, it revealed that there was a power correlation for the experimental and theoretical values. The correlation coefficient, or R 2 value, for the experimental data was 0.8624. The correlation coefficient for the theoretical data was one. This shows that the experimental data had a very close fit because a R2 value of one represents a “perfect fit”. Because the class had a higher R2 value, the class’s data had a better power relation than the professor’s data.

Figure 5 displays the class’s relationship of K values versus Reynolds numbers. It is 25

K Values

20 15 10 5 0 2500

3000

3500

4000

4500

5000

Reynolds Number Figure 5: Graph of K values for the valve versus Reynolds numbers from the class’s data

evident that the k values are the same no matter the Reynolds number because a majority of the red dots is in a horizontal line as well as the trendline that was created. However, some error, such as old equipment, may have contributed to the outlier that threw the trendline off.

Figure 6 displays the professor’s relationship of K values versus Reynolds numbers. It is 25

K Values

20 15 10

5 0 1500

2000

2500

3000

3500

4000

4500

Reynold's Number Figure 6: Graph of K values for the valve versus Reynolds numbers from the professor’s data

evident that the k values are the same no matter the Reynolds number because a majority of the yellow dots is in a horizontal line as well as the trendline that was created. However, some error, such as old equipment, may have contributed to the outlier that threw the trendline off.

DISCUSSION Flow in hydraulic channels is always subject to resistance and energy loss (Yoo, D.H. 2005). Not only do pipe walls cause friction, the valves and fittings attaching separate pipes generate energy losses too. This experiment is highly applicable in society because water is transported through pipes every day for sewage control and water usage for homes and offices.

Traditionally, the condition of pipeline networks in water distribution systems and industrial processes has been monitored by a distributed set of pressure sensors, flow meters, and valve sensors (Beck 2005). Head loss and minor losses reveal the amount of energy needed to pump the water where desired. For example, a pipe that generates 18 ft of headloss would require a pump that could generate 18 ft to balance the energy.

The pipe friction rig used in this experiment was composed of copper pipes. Because the pipes were smooth, the relative roughness ε/d was very small and played an insignificant role in determining the friction factor. Therefore, the friction coefficient, f, could be determined using the formula:

The main lines that were analyzed in this exercise were lines four, five, seven, eight, and nine. Having two collections of data, one from the class and one from the professor, allowed the experiment to be compared in regards to accuracy. For example, if one graph showed a linear trend and the other showed an exponential trend, an error would be present. Both experiments determined that as the flow rate increased, the headloss increased in power-like trend. Although the results were similar, Figure 4, the professor’s headloss versus flow rate graph, had a greater

degree of curvature for its trendline because the manometer readings deviated more. The range of headloss values in line four for the class’s data were 25.50-46.25, but the headloss values in line four for the professor’s data were 6.00-55.75. Because of the length of headloss deviation, the length of variation for the flow rates was different. Because the magnitude of variation for the flow rates was different, the x-values on the graph had a greater variation. Therefore, the data points for the professor’s data points extended out more than the class’s data. The headloss versus flow rate graph shows the significance that the headloss increases as the flow rate increases. This means that as the water moves faster, any obstructions the water runs into takes away more energy. The K values versus Reynolds number graph reveal that the K value is a constant; therefore, it does not change. In the textbook, the minor head loss coefficient, K, for a globe valve is 10.0. The average K value was around 18 for the class’s data and the professor’s data. The percent difference of the K value from the textbook and the experiment was 57.1%.

One explanation why the experimental K value did not match the text value is because the valve may not have been completely open. In Figure 7, the black arrow shows that the water flows through a separation in the center of the valve. The valve plug has to be detached from the valve seat to allow the water to flow through the valve. If the valve plug were not fully detached from the valve seat, the valve would resist more water than it should. As a result, the K value would seem higher than it should.

Figure 7: Globe valve cross section

It is important to know the K value of pipe sections, bends, valves, and fittings because they are vital when determining the total energy loss of water flowing through pipes.

CONCULSION This experiment analyzed the relationship between head loss and flow rate as well as minor loss coefficient, K values, and Reynolds number. As the flow rate increases, the head loss increases in a power correlation. This is important to know because in environmental engineering, pipes are used to transport water from homes and water sources to treatment plants where water can be cleaned and released back into the environment. By knowing that greater flow rates cause greater head losses, engineers can figure out how much energy needs to be created to counteract the friction. Using a pump is a great solution to push water through a pipe system, especially if engineers aim to create a pipe that has a particular flow rate. The minor loss coefficient is a constant value that does not change as the Reynolds number changes. The only thing that causes a K value to change is the type of pipe section, bend, valve, or fitting on a pipe.

Each item has its own original K value. In addition, erosion in a pipe can cause the pipe material not to perform as new. Because the two experiments had similar results, it supports these conclusions. However, there will always be error. For this experiment, there were opportunities

for human error, systematic error, and random error. Since one person read the manometer values aloud, the values were not double-checked. So, a number could have easily been mistaken. Systematic error could have been present because no one checked to confirm that the globe valve was completely open. Random error always exists because no measurement can be taken with exact precision. In addition, the standard deviation was 1.234 for the class’s K value and 2.529 for the professor’s K value; thus, error was present.

REFERENCES Beck, S. B. M., Curren, M. D., Sims, N. D., and Stanway, R. (2005). "Pipeline Network Features and Leak Detection by Cross-Correlation Analysis of Reflected Waves." J.Hydraul.Eng., 131(8), 715-723.

Gupta, R. S. (2008). "Pressue Flow Systems: Pipes and Pumps." Hydrology and Hydraulic Systems, Waveland Press, INC., Long Grove, Illinois, 659.

Rabinovich, E., and Kalman, H. (2011). "Threshold velocities of particle-fluid flows in horizontal pipes and ducts: literature review." Reviews in Chemical Engineering, 27(5), 215239.

Yoo, D. H., and Singh, V. P. (2005). "Two Methods for the Computation of Commercial Pipe Friction Factors." J.Hydraul.Eng., 131(8), 694-704.