The pipe flow probe compared the fluid flow of smooth and unsmooth pipes of changing diameters. The force per unit area bead across the pipes was recorded to happen both the clash factors and Reynolds Numberss. A Moody diagram was plotted comparing the clash factor versus the Reynolds figure. A graph of the experimental clash factor was compared to the theoretical clash factor for the passage of a pipe from smooth to rough.

It is assumed that the fluid used for the pipe flow was incompressible and pipes were wholly horizontal with changeless diameters throughout the tried length. The energy equation is used to compare the steady, unvarying flows at the recess and mercantile establishment.

= force per unit area = denseness

= kinetic energy flux coefficient = mean fluid speed

= gravitation omega = perpendicular tallness of the pipe

=total caput loss = specific work done by the control volume.

The alteration in force per unit area that is found for each pipe is tantamount to the loss of caput across each respective pipe and related by the equation below.

. ( 2 )

It is besides assumed to hold a changeless volumetric flow rate, changeless perpendicular tallness, no work involved in the flow of the fluid, and a changeless flow speed. By utilizing the mean speed we can find whether the fluid is laminal or disruptive. A Reynolds figure below 2300 describes a laminar flow and that above 2300 is disruptive.

, ( 3 )

= Reynolds figure = pipe diameter = viscousness of the fluid.

Below is the Darcy or Moody clash factor, , which is valid for laminar flows. This equation is independent of the raggedness of the pipe.

. ( 4 )

The clash produced by the raggedness in the pipes causes head loss. Unlike Eq. 4, the following equation is valid for turbulent flows with Reynolds values above 2300.

. ( 5 )

The Colebrook equation covers transitionally unsmooth parts which are between smooth and rough walled piping. This equation is inexplicit for.

, ( 6 )

where the comparative raggedness of the pipe is.

Methods

The Pipe Flow Lab equipment included: Four horizontal pipes of changing raggedness and diameters arranged in a pipe flow setup with a self-contained H2O supply, valve to insulate pipe of involvement, inlet flux control valve to command the flow rate, volumetric mensurating armored combat vehicle collects H2O, sight tubing, graduated cylinder, stop watch, callipers, and electronic manometer to mensurate force per unit area.

The alteration in force per unit area of one rough and three smooth pipes of changing diameters were measured. These values helped compare the clash factors to the Reynolds figure of the fluid. Each pipe was separately experimented on by leting the H2O to run through that peculiar pipe until it reached a changeless flow rate. The alteration of force per unit area was read off the electronic manometer and a stop ticker was used to mensurate the clip it took to make full the armored combat vehicle to a peculiar volume. The force per unit area was lowered by a given increase for each test until it reached a given value and repeated for each pipe. The temperature of the H2O was measured at the terminal of the experiment.

Consequences and Discussion

The information for the big smooth pipe, big rough pipe, medium smooth pipe, and little smooth pipe were compiled into Tables 1, 2, 3, and 4, severally. Eq. 3 was used to happen the Reynolds figure and the clash factor was calculated utilizing Eq. 5. These values were so plotted in Fig. 1, which is a Moody diagram comparing the Reynolds figure to friction factor of all the pipes. The Reynolds figure gives the value of a fluids passage from a laminar flow to turbulence. This value is about 2300 harmonizing to Fig. 1. Since all the points on the Moody graph are greater than 2300, we can reason that all the flows in this lab are disruptive.

The diminishing consecutive laminar line was produced by utilizing Eq. 4 which is independent of raggedness. Then above the Reynolds figure of 2300 is the theoretical unsmooth turbulent and smooth disruptive lines. The smooth pipes follow the somewhat downward incline of the smooth disruptive theoretical line. The little and average tubings are for the most portion above the theoretical line which is expected because there is likely construct up in the tubing doing a rebuff raggedness which would increase the clash factor. The big smooth pipe & A ; acirc ; ˆ™s values are below the theoretical line, which is impossible because the tubing can non be smoother than smooth. This mistake could be a cause of human mistake or inaccurate lab equipment. The clash factors of the smooth pipes in increasing order were big, medium, and little. This is what would be expected because the larger diameter pipes should let for easier flow than a smaller diameter pipe.

The big unsmooth tubing follows the theoretical unsmooth disruptive tendency. Since this tubing is rough it should hold more clash than the smooth pipes and an increased clash factor. Fig. 1 exhibits this fact because the big unsmooth tubing values are good above the smooth tubing & A ; acirc ; ˆ™s values. As the Reynolds figure gets really big, it becomes a map of merely comparative raggedness e/D.

Eq. 7 was used to happen the theoretical rough, disruptive flow tendency and a comparative raggedness of e/D, of 0.093 was determined. Table 2 shows the values that were recorded and has lower values for the experimental clash factor than the theoretical values. As with the big smooth pipe, this is non what we would anticipate and it is caused by lab mistakes. Both big pipes were located in the same Reynolds figure part but with different clash factors. This is apprehensible since they have the same diameters but the lone difference is the raggedness inside the pipe doing clash. The fluctuations in clash factor values are due to mistakes that occurred during the probe process.

An mistake that could hold affected the consequences of this probe would be the existent smoothness of the pipes. The smooth pipes could hold build up from the old ages of usage that would do some raggedness. The raggedness would in bend interfere with the fluid flow. Another signifier of mistake was with the halt ticker and volume reading to happen the flow rate. There is a per centum of human mistake in these measurings and the electronic manometer was besides fluctuating during the experiment. These mistakes can account for the fact that the experimental clash factors were lower than the theoretical values for the big pipes seen in Table 1 and 2. The equations used were estimates and could besides account for a little beginning of mistake.

Decisions and Recommendations

The values obtained in this probe led to the computation of the clash factors and Reynolds Numberss for four different pipes. These values were so plotted in a Moody diagram to compare how the raggedness and diameter of each person pipe affected the flow rate of each. The little, medium, and big smooth pipes followed the smooth disruptive theoretical tendency. The big pipe had values below the theoretical values. The experimental values should ever hold been above the theoretical since a pipe can & amp ; acirc ; ˆ™t be any smoother than smooth. These consequences could be caused by the lab mistakes that were listed supra. The clash factors of the smooth pipes in increasing order were big, medium, and little. This is what would be expected because the larger diameter pipes should let for easier flow than a smaller diameter pipe. The big, unsmooth pipe followed the unsmooth disruptive tendency. As the Reynolds figure became big the comparative raggedness became the relationship, e/D. This pipe besides had experimental clash factor values below the theoretical values which is impossible and caused by mistakes in the probe. The clash factor of the unsmooth pipe was much greater than the smooth pipes, which means that there is more clash in unsmooth pipes.

For future probes, it would be good to take more informations points in order to more accurately stand for the findings. This could besides assist maintain the border of mistake smaller since one or two inaccurate points could be disregarded with a larger information sample. More precise measuring tools would besides be really good since there was much uncertainness with the current setup.

Table 1: Large smooth pipe with interior diameter of 1.766 centimeter

Volume ( L )

Time ( sec )

DP ( kPa )

Rhenium

degree Fahrenheit exp

degree Fahrenheit Thursday

10

10.31

8.2

77458.04

0.0185

0.0190

10

10.25

7.0

77911.45

0.0156

0.0192

10

12.13

5.9

65836.14

0.0184

0.0195

10

13.22

5.0

60407.90

0.0186

0.0199

10

15.50

3.9

51522.09

0.0199

0.0203

10

18.19

2.8

43902.83

0.0197

0.0211

10

23.06

1.8

34631.07

0.0203

0.0218

10

33.19

0.8

24061.24

0.0187

0.0256

Table 2: Large rough pipe with interior diameter of 1.668 centimeter

Volume ( L )

Time ( sec )

DP ( kPa )

Rhenium

degree Fahrenheit exp

degree Fahrenheit Thursday

10

13.69

25.2

61761.29

0.0754

0.0980

10

15.31

20.3

55226.13

0.0759

0.0980

10

17.85

14.6

47367.62

0.0742

0.0980

10

22.00

9.5

38432.37

0.0734

0.0980

10

31.35

4.9

26970.08

0.0769

0.0981

Table 3: Medium smooth pipe with interior diameter of 0.748 centimeter

Volume ( L )

Time ( sec )

DP ( kPa )

Rhenium

degree Fahrenheit exp

degree Fahrenheit Thursday

5

23.19

38.0

40652.15

0.0237

0.0213

5

25.42

33.0

37085.89

0.0247

0.0216

5

26.59

28.0

35454.06

0.0229

0.0218

5

30.04

23.4

31382.27

0.0244

0.0223

4

28.12

17.5

26820.01

0.0250

0.0227

4

33.15

13.2

22750.49

0.0262

0.0233

3

35.06

7.9

16133.32

0.0312

0.0239

Table 4: Small smooth pipe with interior diameter of 0.386 centimeter

Volume ( L )

Time ( sec )

DP ( kPa )

Rhenium

degree Fahrenheit exp

degree Fahrenheit Thursday

1

27.00

36.0

13532.09

0.0278

0.0279

1

28.62

31.6

12766.12

0.0274

0.0284

1

32.50

27.2

11242.04

0.0304

0.0290

1

40.22

21.5

9084.20

0.0368

0.0296

1

45.60

16.5

8012.42

0.0363

0.0303

1

53.78

12.4

6793.72

0.0380

0.0306

1

65.50

5.4

5578.11

0.0245

0.0336

Fig. 1. Friction factor vs. Reynolds figure for selected pipes plotted against theoretical curves.

Fig. 2 Experimental clash factor vs. theoretical clash factor for selected pipes plotted with a 1:1 tantrum.