Expt. 3 - Efflux Time (Prelaboratory)

Labutong, Fidel Ivan Pastores, Janet Stephanie Tagapan, John Paolo Yeung, Angelyn 4ChE-A

1. To determine the efflux time needed to drain a tank with a set of exit pipes with different lengths and diameters 2. To derive mathematical correlation between the efflux time and the pipe size and the tank diameter

Pipe flows may be classified as laminar or turbulent. Re ≤ 2,100

Re ≥ 4,000

In case where any of the two situations are not strictly observed, flow is said to be transitional.

Flow of fluid inside the pipe depends on the length and diameter of the pipe.

The boundary layer is a dynamic phenomenon. Its thickness increases as the fluid moves downstream. Boundary layer from the walls grow to such an extent that they all merge on the centreline of the pipe.

Once this takes place, inviscid core terminates and the flow is all viscous. The flow is now called a Fully Developed Flow. Le=0.06D (𝑅𝑒) 1 Le=4.4D(𝑅𝑒) 6

Laminar flow Turbulent flow

Efflux time apparatus

Pail

Pipe

Viscosity and density of water was measured. Then 3.5 liters of water was prepared in a pail and slowly poured into the tank while covering the orifice. After emptying the pail, water was allowed to flow from the orifice and a second pail was placed to catch the water falling. Time was recorded until the tank was empty.

A pipe was then attached to the orifice of the tank and was filled with water while the exit pipe is being covered. Upon draining, the time it takes for a height interval of 12cm from level view port was recorded until the tank was empty.

First pipe was then removed and replaced with another pipe and the same procedure was used. Formation of vortex was also considered. Three trials were done for each pipe. After using all 10 pipes, 50% glycerol-water mixture was used in place of water, following the same process.

Table 1. Experimental Data for Water Pipe Diameter( Length( No. m) m)

Height Interval(c Velocity m) (m/s)

Reynold Time(s) s No. Le(m) 0.0941 98.95 313.76 3

1

0.005

0.75

1.00

0.0017

2

0.0075

0.77

1.00

0.0045

38.71

830.55

0.37

3

0.011

0.75

2.00

0.0092

14.19

1698.01

1.12

4

0.017

0.74

2.00

0.0228

8.23

4208.12

0.30

5

0.0185

0.74

2.00

0.0304

7.07

5610.83

0.34

6

0.013

0.58

2.00

0.0149

10.27

2750.05

2.15

7

0.0133

0.63

2.00

0.0154

9.78

2842.33

2.27

8

0.0134

0.88

2.00

0.0158

11.01

2916.16

2.34

9

0.0131

1.01

2.00

0.0148

13.49

2731.59

2.15

10

0.01312

1.14

2.00

0.0168

10.07

3100.72

2.44

Table 2. Theoretical Data for Water Pipe No.

D/d

L/D

Velocity (m/s)

Time(s)

Reynolds No.

Le (m)

1

33.74

4.47

0.0069

23.03

1282.24

0.38

2

22.49

4.54

0.0351

4.56

6480.71

2.92

3

15.34

4.46

0.1628

0.98

30041.36

0.27

4

9.92

4.40

1.4878

0.11

171627.02

0.56

5

9.12

4.38

2.0879

0.08

240848.68

0.64

6

12.98

3.46

0.3271

0.49

60372.99

0.36

7

12.68

3.74

0.3548

0.45

65492.45

0.37

8

12.59

5.23

0.3529

0.45

65136.30

0.37

9

12.88

5.98

0.3186

0.50

58811.06

0.36

10

12.86

6.75

0.3176

0.50

58620.53

0.36

Table 3. Experimental Data for Glycerol Solution Pipe No.

Diameter( mm)

Length( m)

Height Interval(cm)

Velocity (m/s)

Reynolds No.

Le(m)

0.0013

Time( s) 120.5 3

1

0.005

0.75

1.00

49.20

0.0147

2

0.0075

0.77

1.00

0.00

35.06

174.08

0.0783

3

0.011

0.75

2.00

0.01

15.15

488.17

0.3221

4

0.017

0.74

2.00

0.02

7.09

851.46

0.8684

5

0.0185

0.74

2.00

0.03

5.56

1067.16

1.1845

6

0.013

0.58

2.00

0.01

11.04

556.28

0.4339

7

0.0133

0.63

2.00

0.02

10.96

590.34

0.4710

8

0.0134

0.88

2.00

0.02

10.89

597.91

0.4807

9

0.0131

1.01

2.00

0.01

11.91

563.85

0.4431

10

0.01312

1.14

2.00

0.02

10.60

639.54

0.5034

Table 4. Theoretical Data for Glycerol Solution Pipe No.

D/d

L/D

Velocity (m/s)

Time(s)

Reynolds No.

Le

1

33.74

4.47

0.00142443

112.33

53.90

0.02

2

22.49

4.54

0.007199378

22.22

272.44

0.12

3

15.34

4.46

0.033372758

4.79

1262.91

0.83

4

9.92

4.40

0.190659379

0.84

7215.03

7.36

5

9.12

4.38

0.267557279

0.60

10125.03

11.24

6

12.98

3.46

0.067067974

2.39

2538.02

1.98

7

12.68

3.74

0.072755152

2.20

2753.24

2.20

8

12.59

5.23

0.072359501

2.21

2738.26

2.20

9

12.88

5.98

0.06533283

2.45

2472.36

1.94

10

12.86

6.75

0.065121179

2.46

2464.35

1.94

Re = (Dtankvρ)/μ Le = 0.06D(Re) for laminar Le = 4.4D(Re)1/6 for turbulent Efflux Time = 8μLR2ln( 1+ H/L) *

for laminar

Efflux Time = 5μLR2ln( 1+ H/L) * for turbulent

Using pipe 1: Re =

(laminar)

Le = 0.06(0.005)( 313.76) = 0.09413m Efflux Time 8(0.0009155)(0.754)(0.084352)ln(1+ * Efflux Time = 23.03s D/d = (0.08435)(2)/0.005 = 33.74 L/D = 0.75/(0.08435)(2) = 4.47

Using Pipe 4: Re =

(turbulent)

Le = 4.4(0.017)( 4208.12)1/6 = 0.30m Efflux Time = 5(0.0009155)(0.74)(0.084352)ln(1+ Efflux Time = 0.11s

*

Plot of Height Interval (cm) vs Time (s) for water Height Interval (cm) vs Time (s) 16.00 Pipe 1

14.00

Pipe 2 12.00

Pipe 3 Pipe 4

10.00

Pipe 5 8.00

Pipe 6 Pipe 7

6.00

Pipe 8 4.00

Pipe 9 Pipe 10

2.00 0.00

0.00

20.00

40.00

60.00

80.00

100.00

Plot of Height Interval (cm) vs Time (s) for glycerol solution Height Interval (cm) vs Time (s) 16.00

Pipe 1 Pipe 2

14.00

Pipe 3 12.00

Pipe 4 Pipe 5

10.00

Pipe 6 8.00

Pipe 7 Pipe 8

6.00

Pipe 9

4.00

Pipe 10

2.00 0.00 0.00

20.00

40.00

60.00

80.00

100.00

120.00

Plot of entry length vs Ratio of Diameters for Water and Glycerol Solution Le (m) vs D/d

Le vsD/d

1.2

1.2

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0 0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

0 0.00

10.00

20.00

30.00

40.00

Plot of Entry Length vs Ratio of Length of Exit Pipe with Tank Diameter for Water and Glycerol Solution

Le vs L/D

Le vs L/D

2.50

0.51

2.45

0.5

2.40

0.49

2.35

0.48

2.30

0.47

2.25

0.46

2.20

0.45

2.15

0.44

2.10 0.00

2.00

4.00

6.00

8.00

0.43

3.00

4.00

5.00

6.00

7.00

Plot of Efflux Time vs Ratio of Diameters for Water and Glycerol Solution Efflux Time (s) vs D/d

Efflux Time(s) vs D/d 140.00

120.00

120.00 100.00

y = 0.1287x2 - 1.778x + 12.586 R² = 0.9983

80.00

100.00 Experimental

y = 0.199x2 - 4.0194x + 28.716 R² = 0.9966

experimental

80.00

theoretical

60.00

60.00

Theoretical

40.00

40.00 20.00

20.00

0.00 0.00

0.00 0.00

10.00

20.00

30.00

40.00

10.00

20.00

30.00

40.00

Plot of Efflux Time vs Ratio of Length of Exit Pipe with Tank Diameter for Water and Glycerol Solution

Efflux Time(s) vs L/D

Efflux Time (s)vs L/D

120.00

140.00

100.00

120.00 Theoretical

80.00

y = -2.756x + 35.24 R² = 0.009

60.00

100.00

Experimental 80.00

y = -3.6064x + 40.976 R² = 0.0106

experimental theoretical

60.00

40.00

40.00 20.00

20.00

0.00 0.00

0.00 0.00

2.00

4.00

6.00

8.00

2.00

4.00

6.00

8.00

10.00 12.00

1. Give practical applications of the principle of efflux time. What areas of chemical engineering can we apply this concept.

The principle of efflux time can be applied for the pipe connections that we can see everywhere. For the industry, it can be used to measure the time it takes for a fluid to flow out of the pipe or vessels. It is important to know the time it takes to empty a tank because it is the time to process a reactor volume. For reactors, efflux time is a factor used to determine down time.

Fluid mechanics is an area of chemical engineering where we can apply the concept of efflux time.

2. In cases where there is a desired efflux time, what design consideration must be applied? If you are given a desired efflux time, the design of the container should be in a way that diameter and length of the container will be taken into account.

For water at pipe 1: % Difference =

at pipe 5: % Difference =

For glycerol at pipe 1: % Difference = at pipe 5: % Difference =

The efflux time has been determined for a tank with a set of exit pipes with varying lengths and diameters. Efflux time was found to be higher for longer pipes and lower for pipes with larger diameter. However, experimental results were not matched with the theoretical values. This may have resulted from the presence of vortex when draining the tanks, surface roughness, dirt and inaccurate gathering of data for recording the time. From the calculated least and highest % difference, it was observed that it both occurred at pipe 1 and 5 for the two liquids used respectively.

1.Pour the fluid slowly so that the tank will not overflow. 2. Be alert when recording time. 3. Be observant, look for signs of vorticity. 4. Clean the area after the experiment.

5. DON’T PLAY IN YOUR WORKPLACE.