Flr5 - Reynold's Number Experiment.docx

DE LA SALLE UNIVERSITY Gokongwei College of Engineering Chemical Engineering Department

CHE LABORATORY 1

AY 2018-2019 2nd Term

(LBYCHEE)

FINAL LABORATORY REPORT Experiment No. 5

REYNOLD’S NUMBER EXPERIMENTS

Group No.

4 NAME

Section SIGNATURE

EA2 Criteria

1.

Acyatan, Alyssa Mae C.

Content (50%)

2.

Bueno, Brian Gerald C.

Presentation (25%)

3.

Dar, Lloyd Ross M.

4.

De Leon, Sean Francis S.

5.

San Pedro, Anna B.

6.

Soriano, Elijah Jeremie D.

Relevance (25%) Total (100%) Percentage Equivalent

4 March 2019 Date of Performance

25 March 2019 Date of Submission Dr. Allan N. Soriano Instructor

Score

1. Introduction and Objectives In the design of the equipment and the actual plant itself, it is necessary to determine the fluid flow of the operation. One such characterization is classifying it as laminar, transitional, or turbulent flow. The rate of production and manufacturing as well the material of construction of a process and equipment are also dictated by the type of flow [1]. Reynolds number is one way to quantitatively identify the type of flow. This is a dimensionless number and its physical significance relates the ratio of the inertial forces to the viscous forces of the fluid [2].

2. Theoretical Background There is a significant effect on the characteristics of fluid flow caused by inertial and viscous forces, in which the latter is dependent on the fluid’s viscosity, a measure of the fluid’s resistance to shear and angular deformation [2]. When fluids move through a closed channel of any cross section, either of two distinct types of flow can be observed. When the velocity of a fluid is quite high, an unstable pattern is observed, in which eddies or small packets of fluid particles are present, moving in all directions and at all angles to the normal line of flow [2]. Taking into consideration the effects of viscosity, the characteristics of fluid flow can be categorized into three flow conditions, laminar, transition, and turbulent flows. What determines the kind of flow are four parameters: (1) the equivalent diameter of the tube, (2) the viscosity, (3) the density of the fluid, and (4) average linear velocity of the liquid [2]. These parameters directly affect the kind of fluid flow and they can be combined together to form the dimensionless Reynolds number (NRe), which tells what kind of flow it is. The formula of Reynold’s Number is given by: (1) Where De = Equivalent diameter of the tube V = Average velocity of the liquid ρ = Density of liquid µ = Viscosity of liquid This dimensionless number is named after Osborne Reynolds, who first demonstrated the difference between laminar and turbulent flows in an 1883 experiment of his. The equipment he used was comprised of a horizontal glass immersed inside a tank filled with water where the flow of water is controlled by a valve [3]. Furthermore, the relationship between the variables considered in the Reynold’s number: as NRe increases, the inertial forces grow relatively larger and the flow gets destabilized into full-blown turbulence. Consequently, as the NRe decreases, the viscous forces increase relatively, and the flow stabilized into a laminar flow [3]. In other words, the Reynold’s number can be used to identify the conditions under which the flow changes from laminar to turbulent. For laminar flow, the adjacent layers of the fluid flow in parallel with each other, therefore encountering no lateral mixing. Laminar flow occurs at low fluid velocities, and it is observed that laminar flow always occurs at Reynolds numbers below 2100 [3][3]. Meanwhile, for turbulent flow, the adjacent layers of the fluid are in contact with one another while they are moving. Turbulent flow consists of eddies at different sizes mixing with the flowing stream [4]. Large eddies are continuously formed along the flow which subsequently break down [2]

into smaller ones. Eddies are formed if there is a fraction of molecules that possesses a cross current component of velocity that could move to regions in which flow velocity is different from the original velocity of the migrant molecules [4]. At ordinary flow conditions, turbulent flow occurs at Reynolds numbers above 4000, although a fully established turbulent flow may not occur until the Reynolds number is around 10,000 [2]. Finally, for a Reynolds number between 2100 and 4000, the fluid may either be laminar or turbulent depending on the condition at the tube entrance, and this type of flow is described as a transition flow. In transition region, NRe value of 2100 – 4000, the flow can be viscous or turbulent depending upon the apparatus details [4]. Generally, the pipe flow of fluids can be identified as laminar, transitional, or turbulent by the behavior of the fluid flow which is characterized by being smooth or erratic. But to precisely identify its type of flow, several variables are determined, and the corresponding Reynold’s number is calculated [4]. 3. Experimental Set-Up 3.1 Actual Set-up

Figure 3.1 Actual Setup of the Tubular Heat Exchanger (front view)

Figure 3.2 Actual Setup of the Tubular Heat Exchanger (side view)

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3.2 Engineering Drawing or Sketch

Figure 3.3 Schematic Diagram of Equipment

4. Summary of Procedures 4.1 General Test Procedures Upon setting up the apparatus, the water supply was turned on and the discharge valve at the bottom was partially opened. For each trial, the valve that controlled the water flow was adjusted for laminar, transition, and turbulent flows, and volumetric flow rates were them measured by collecting a specific volume of water from the discharge valve and recording the time it took to reach that volume. This was repeated for three trials and temperature of the water was kept constant. 4.2 Effect of Varying Viscosity In order to measure the effect of varying viscosity, a heater connected to the tank was turned on since temperature control affects the flow rate. Procedures from the first part of the experiment were then repeated for three trials.

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5. Data A. Room Temperature Table 5.1. Increasing Flow 27°C

Observed Flow Laminar Flow Laminar Flow Below Lower Critical Lower Critical Transition Upper Critical Turbulent Highly Turbulent

Trial 1

Trial 2

Trial 3

Vol (mL) 35

Time 30.62

Vol (mL) 33

Time 29.9

Vol (mL) 23

Time 24.71

29

18.56

36

19.14

30

15.75

31

8.3

43

11.04

39

10.33

33

5.56

42

6.7

40

6.53

42 41

5.06 3.35

50 50

5.49 3.74

49 50

5.07 3.79

56 48

2.81 1.49

37 57

7.86 1.84

47 43

2.22 1.46

Table 5.2. Decreasing Flow 27°C

Observed Flow Highly Turbulent Turbulent Upper Critical Lower Critical Transition Below Lower Critical Laminar Laminar

Trial 1

Trial 2

Trial 3

Vol (mL) 44

Time 1.49

Vol (mL) 48

Time 1.44

Vol (mL) 62

Time 2.34

58 48

2.11 1.97

53 50

1.73 2.28

46 45

1.61 1.9

45

2.7

49

2.81

57

3.11

48 31

3.95 3.91

47 44

4.09 5.5

52 45

4.37 5.74

43 39

6.33 9.46

38 38

5.72 9.31

38 38

5.86 9.38

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B. Higher Temperature Table 5.3. Increasing Flow at 52°C

Observed Flow Laminar Flow Laminar Flow Below Lower Critical Lower Critical Transition Upper Critical Turbulent Highly Turbulent

Trial 1

Trial 2

Trial 3

Vol (mL) 25

Time 9.29

Vol (mL) 34

Time 12.56

Vol (mL) 31

Time 11.91

23

11.62

21

10.46

21

9.81

24

6.87

25

7.2

23

6.7

35

4.84

34

4.67

31

4.2

35 40

3.24 2.43

38 43

3.3 3.48

34 44

3.06 2.49

43 43

1.95 3.24

47 53

1.96 2.24

41 53

1.82 1.84

Table 5.4. Decreasing Flow at 52°C

Observed Flow Highly Turbulent Turbulent Upper Critical Lower Critical Transition Below Lower Critical Laminar

Trial 1

Trial 2

Trial 3

Vol (mL) 48

Time 1.9

Vol (mL) 46

Time 1.63

Vol (mL) 54

Time 1.77

47 38

1.93 1.97

44 39

1.61 2.1

52 36

2.27 2.04

45

3.02

43

3.02

42

2.81

35 32

3.1 5.49

32 35

2.94 6.52

36 26

3.53 4.88

19

6.2

19

6.5

26

9.16

6. Results and Analysis To determine the starting and final parameters for a transition flow, the lower and upper critical values are determined. Since only flowrates are determined from the initial data above, the velocities are calculated by dividing the flowrate values to the circular area of the tube, which was calculated to be 1.14 cm 2 given an inner diameter of 12 mm. The Reynold’s number was then calculated using Eq. 1, considering the different densities and viscosities at temperatures 27°C and 52°C. [6]

Commented [AP1]: Palagay ng eqn number from the theories, thanks!

In theory, the lower critical value is the value at which laminar flow changes to a transition and upper critical value is the value at which the transition flow ends and changes to a turbulent flow [5]. It is known that while transition flow theoretically occurs if the Reynold’s number approximately ranges from 2100 to 4000, the experimental values may not obey the said range of Reynold’s number in dealing with a real system. For an increasing flow at 27°C, Table 6.1, the experimental lower and upper critical values did not reach the range for the ideal transition state range despite the settings, having only a 5.40 and 11.44 cm/s velocity. Also, for the start of a theoretically turbulent flow, the upper critical state of the system stays laminar. Aside from system inefficiencies due to its not being ideal, friction and human errors during experiment, this may have been due to the reason that this was the initial run of the system after start-up and the system’s engine has not yet adapted to the process conditions, making it a less efficient trial compared to the rest of the trials. In Appendix 1.1 A, it can be seen that a turbulent state has only been visible at the highly turbulent condition while all were in laminar state.

Table 6.1. Increasing Flow at 27°C

Lower Critical Upper Critical

Flowrate (mL/s) 6.11 12.93

Velocity (cm/s) 5.40 11.44

Reynolds Number 759.83 1608.44

Range Laminar Laminar

In Table 6.2, the second trial, a decreasing flow was observed starting from turbulent to laminar. The system followed a transition range for both lower and upper critical values with a velocity of 15.45 and 20.63 cm/s respectively. This suggests that the system had been adjusting to the process conditions despite the upper critical value having only a 2900.95 Reynold’s number.

Table 6.2. Decreasing Flow at 27 °C

Lower Critical Upper Critical

Flowrate (mL/s) 17.48 23.33

Velocity (cm/s) 15.45 20.63

Reynolds Number 2173.54 2900.95

Range Transition Transition

For Table 6.3, it can be seen that a laminar flow was again evident on the lower critical value, which may been caused by the readjustment of temperature to a higher value, 52°C and also the inefficiency of the system. Also, based from the readings and calculated values, the higher temperature, lesser the flowrate and velocity, yet the higher the Reynold’s number. Such is also evident in Table 6.4, with a decreasing flowrate at the same temperature. Results may indicate that the molecules of the fluid exhibit more chaotic changes in motion while travelling along the tube [6]. Table 6.3. Increasing Flow at 52°C

Lower Critical Upper Critical

Flowrate (mL/s) 7.30 15.50

Velocity (cm/s) 6.45 13.70 [7]

Reynolds Number 1443.99 3066.21

Range Laminar Transition

Table 6.4. Decreasing Flow at 52°C

Lower Critical Upper Critical

Flowrate (mL/s) 14.70 18.50

Velocity (cm/s) 12.99 16.36

Reynolds Number 2907.77 3661.14

Range Transition Transition

Figure 6.1. Reynold’s Number vs. Flowrate

Reynold’s number and flowrate were then plotted for all four trials as seen in Figure 6.1. It can be inferred that the Reynold’s number increases not only with flowrate, but also with temperature. It can also be seen that temperature plays a greater difference in a turbulent flow rather than laminar flow also due to the difference in viscosity. Further, the plot indicates a linear relationship for all runs, and no evident fluctuations or changes in trend can be seen to determine the change state. For specifics, energy or pressure difference is the requirement for the motion of a liquid. Liquids do not immediately flow, but first exhibit some resistance. Due to the fluid’s resistance to flow, energy is lost. Resistance to flow is called head loss due to friction [7] and to take friction into account, 16 divided by Reynold’s number is used for Laminar flow and Blasius equation is used for turbulent flow and is given by the equation below:

To take into account the Head loss, Darcy-Weisbach Equation is used and given by:

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Figure 6.2. Head Loss vs. Flowrate

The head loss against flow rate is plotted and exhibited an increasing trend—head loss increases as flowrate increases, despite the minimal deviations in decreasing flows at both temperatures which may have been caused by system inefficiency and/or human errors. Also, the head losses were relatively small and nearly constant at laminar/low flowrates. At turbulent flows, a pike in head loss is observed and thus, more significant and should be considered. 7. Individual Observations Acyatan, Alyssa Mae C.

Bueno, Brian Gerald C.

Dar, Lloyd Ross M.

De Leon, Sean Francis S.

It is observed that there is certainly a transition from laminar to turbulent flow with the appearance of the ink injected into the water. The characteristic of the dye which easily combines with water helps one to observe the significant flow changes. I have observed that the visual appearance of the fluid flow changes as the pipe valves were adjusted to meet the desired behavior of the flow. Various flow rates were gathered by timing the collected amount of volume. The ink exhibited more uniform flow at was expected to be laminar flow. The observed use of the dye in determining the type of flow present was comparable to the one we see in literature. [9]

San Pedro, Anna B.

Soriano, Elijah Jeremie D.

It helps in understanding the principles we learn in the classroom as we see it here. With increasing temperature, the Reynold’s number also increases – more significantly with a turbulent flow. Also, at turbulent flows, head loss is more significant. The transition from laminar to turbulent becomes visually apparent as the flow rate increases. In addition, the time taken to collect the water took longer in the laminar flow than in the turbulent flow.

8. Conclusion and Recommendation The determination of the Reynolds number was made possible by knowing the flow rates of the fluid at different temperature levels. As expected, Reynolds number exhibited higher values at higher flow rates. This is because flow rate directly affects the fluid velocity, which in turn is directly proportional with the Reynolds number. Similarly, increasing flow rate resulted in increasing head loss, primarily because of the increased fluid friction present. Although successful, the experiment still has some variations from the theoretical concepts. This is evident for the calculation of the upper and lower critical limits, since some values weren’t within the transition flow range. This deviation is caused by the process startup and process change. During these times, fluctuations from the steady-state values are obtained, causing variations in gathered data. Hence, the experimenters recommend that data shall be collected at adequate time after the startup processes. 9. Industrial Applications Reynolds number is computed to be the ratio of inertial and viscous forces, which determines whether the flow is either laminar or turbulent. At laminar flow, the viscous forces are greater, causing the fluid particles to be more streamline, whereas turbulent flow has irregular fluid motion [8]. Determination of Reynolds number is important to analyze the type of flow a fluid is undergoing. Analysis of aerodynamic properties of different surfaces can be conducted by applying specific wind flows. Computation of the Reynolds number is also applied when the aircraft wind lift is tested, especially when high aircraft speed causes the increase of the surrounding air’s density [9]. REFERENCES [1] Olaño Jr., S. Reynold’s Number Experiments in Chemical Engineering, 2nd ed. [2] Geankoplis, C.J.2003.Principles of Transport Processes and Separation Processes. Pearson Education

South Asia Pte Ltd. [3] Available online at https://www.academia.edu/31580118/Experiment_4_REYNOLDS_NUMBER [10]

[4] Available online at https://studylib.net/doc/8239671/experiment-11-reynolds-number-and-transitional-

flow [5] NPTEL. (n.d.). Application of fluid mechanics in mines. Retrieved March 24, 2019 from

https://nptel.ac.in/courses/123106002/MODULE%20-%20IV/Lecture%201.pdf [6] Meridian International Research. (2003). Observation of the application of chaos theory to fluid

mechanics. Retrieved March 24, 2019 from http://www.meridian-int-res.com/Aeronautics/Chaos.pdf [7] Pentair plc. (2019). Retrieved from https://www.pentair.com/pentair-hydromatic.html [8] Nuclear Power. (n.d.). Reynolds number. Retrieved from https://www.nuclear-power.net/nuclear-

engineering/fluid-dynamics/reynolds-number/ [9] Vispute, S. (2019). What is Reynolds number and what are its applications? Retrieved from

https://sciencestruck.com/what-is-reynolds-number-what-are-its-applications APPENDICES Appendix 1.1 A. Increasing Flow: 27 C

B. Decreasing Flow: 27 C

Appendix 1.2 A. Increasing Flow: 52 C

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B. Decreasing Flow: 52 C

Sample Calculations Refer to Appendix 1.1 A 1. Friction Loss Laminar Flow: f= 16/Re = 16 / 131.721703 = 0.12147 Turbulent Flow (Highly):

= (0.079) / (3840.5322)0.25 = 0.01003 2.

Head Loss

Laminar Flow: h= 0.012147 (100cm2)(0.93652cm2/s2) / [2(981cm/s 2)(1.2cm)] = 0.00452

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