Flr8 - Unsteady Flow Head.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. 8

UNSTEADY HEAD FLOW

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

11 February 2019 Date of Performance

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

Score

application of Bernoulli equation by solving unsteady state mass balance equation [3]. Considering a tank of varying cross-section with a horizontal pipe connected near the bottom as shown in Figure 2.1 below.

1. Introduction and Objectives In the process industries, various flow operations are all assumed and studied to operate under steady state. These include operations such as mixing, separation operations, and chemical reactions. However, not all industrial processes operate at steady state and some inevitably occur as unsteady state operations. One of the most common is the behavior of filling and emptying a water tank which occur in a large variety of shapes and sizes [1]. This is because the rate of the rise and fall of the amount of water in the tank varies with time. By modelling its behavior, it is possible to be able to predict its efflux time or the time it takes to empty the tank of its contents. Performing an experiment with respect to the efflux time for a tank and doing the needed analyses can provide more knowledge and understanding in the behavior of this unsteady state system. This application is very important in almost all industries because it is part of the startup processes before the processes reach steady state conditions for operation. Also, it is crucial in many emergency situations besides productivity considerations and are of considerable interest in industries like chemical, food, and pharmaceutical [2]. This experiment aims to compare the theoretical efflux times for a rectangular tank with exit pipes of various lengths and sharp edge orifices of various diameters and shapes using water as the fluid. Also, the theoretical and actual instantaneous flow rates of the tank will be compared. This experiment also aims to study the effects of changes of kinetic energies, entrance losses, and friction losses in exit pipes on the flow rates and efflux times as well as to investigate the occurrence of fully developed flow patterns in the exit pipes under unsteady state conditions [1].

Figure 2.1.

Tank with Varying Cross-Sectional Area with a Horizontal Pipe [1]

The change in volume can be expressed as 𝑆𝑑ℎ = 𝑄1 𝑑𝑡 − 𝑄2 𝑑𝑡

(1)

S = area of the surface of the liquid h = vertical depth Q1 = rate of inflow Q2 = rate of outflow If the liquid is discharged through an orifice of area Ao with C, a correction factor, as the discharge coefficient, the rate of outflow, Q2, can be expressed as 𝑄2 = 𝐶𝐴𝑜 √2𝑔𝑐 ℎ

(2)

Rewriting and integrating Eq. 1 gives ℎ2

𝑡 = −∫ ℎ1

𝑆1 𝑑ℎ 𝑄1 − 𝑄2

(3)

When Q1 is equal to zero and Q2 = S2V2 = S2 f(h, L), the time for the water level to change from h1 to h2 is ℎ2

𝑡 = −∫ ℎ1

𝑆1 𝑑ℎ 𝑆2 𝑓(ℎ, 𝐿)

(4)

For laminar flow, the instantaneous average velocity of the liquid in the exit pipe with a constant cross-section is expressed as 𝑉2 =

2. Theoretical Background Efflux time is the time required for draining out the contents of a vessel. It is obtained by the

𝑔𝑐 𝑅22 𝜌ℎ 8𝜇𝐿

(5)

given that the fluid is an incompressible [2]

Newtonian fluid, and there is no acceleration of fluid in the pipe. For turbulent flow, the Blasius formula is used. The fanning friction factor is approximated by 1

𝑓 = 0.0791(𝑁𝑅𝑒 )−4

3.2 Engineering Drawing or Sketch

(6)

Thus, the instantaneous average velocity is expressed by 𝑉2 =

2𝑔𝑐4 𝑅25 𝜌ℎ4 (0.0791)4 𝜇𝐿4

(7)

Using Eq. 5 & 6 to solve Eq. 4, the efflux time for laminar flow is 𝑡=

8𝜇𝐿𝑆1 𝜋𝑅2 4 𝑔𝑐 𝜌

𝑙𝑛

ℎ1 ℎ2

(8)

For turbulent flow, the efflux time is 𝑡=

3

7𝑆1 𝐶 3𝜋𝑅2

3

7 7 2 [ℎ1 − h2 ]

Figure 3.3 Schematic Diagram of Equipment for Unsteady Head Flow

(9)

4. Summary of Procedure

where 𝐶=[

4 1 7 (0.0791)𝐿𝜇 4 1

1

5

]

The pump was turned on to deliver a supply of water in the tank. A pipe was installed in the joint of the test tank and its end was covered with a rubber stopper. Once the level in the depth gauge reached above the 20cm mark, the stopper was removed, and the stopwatch was started when the level reached 20 cm. Time was recorded for every interval of 5cm the level reached the 80cm mark. This procedure was repeated for the different pipes and orifice.

(10)

24 𝑔𝑐 𝜌4 𝑅2 4

3. Experimental Set-Up 3.1 Actual Set-up

5. Data Length of Tank = 31.5 cm Width of Tank = 31.5 cm Height of Tank = 91.4 cm A. Pipe and Orifice Dimensions Parameter

Figure 3.1 Actual Set-up for Unsteady Head Flow

Length (cm) Diameter (cm)

Figure 3.2 Pipes of Different Lengths [3]

Orifice 1 -

Orifice 2 -

Pipe 1 80.6

Pipe 2 50.2

Pipe 3 30.5

13.02

9.03

10

9.042

8.084

B. Efflux Time vs. Liquid Length for Orifice Height (cm)

Orifice 1 Efflux Time (sec) Trial 1 0 13.46 15.50 15.88 16.77 18.03 19.09 19.55 23.64 29.67 32.65 46.80 63.09

20 25 30 35 40 45 50 55 60 65 70 75 80

Orifice 2 Efflux Time (sec) Trial 1 0 20.25 21.71 21.83 23.55 24.83 26.40 28.02 31.47 34.60 39.90 47.33 65.13

Height (cm) 20 25 30 35 40 45 50 55

36.85 40.05 46.465 54.23 73.47

The difference in potential and kinetic energy, and the friction losses of the efflux time of the water was determined in this experiment. Each of these factors affect the mechanical energy balance of the equipment system. 100 90 80

Pipe 1

70

Pipe 2

Pipe 2 Efflux Time (sec) Trial Trial Average 1 2 0 0 0 29.78 29.67 29.725 29.61 29.66 29.635 31.45 32.21 31.83 32.67 34.37 33.52 35.11 34.94 35.025 38.31 37.91 38.11 39.65 38.55 39.1 45.39 45.09 45.24 48.95 47.68 48.315 56.30 55.12 55.71 69.11 60.17 64.64 96.49 97.73 97.11

Time (sec)

20 25 30 35 40 45 50 55 60 65 70 75 80

Pipe 1 Efflux Time (sec) Trial Trial Average 1 2 0 0 0 32.21 32.36 32.285 32.29 32.94 32.615 33.82 33.3 33.56 35.85 36.11 35.98 37.40 37.79 37.595 41.07 40.37 40.72 43.32 43.77 43.545 47.68 48.53 48.105 52.65 51.29 51.97 61.04 61.22 61.13 69.88 70.22 70.05 94.75 94.53 94.64

37.87 39.26 46.19 54.24 78.66

6. Results and Analysis

C. Efflux Time vs. Liquid Length for Pipe Height (cm)

35.83 40.84 46.74 54.22 68.28

60 65 70 75 80

60

Pipe 3

50 40 30 20 10 0

-80

-60

-40

-20

Negative Height of Water Level (cm)

Figure 6.1 Experimental Time vs. Water Level Height Using Pipes Varying in Length

Pipe 1 Efflux Time (sec) Trial 1 Trial 2 Average 0 0 0 24.83 25.45 25.14 24.39 24.45 24.42 26.24 26.26 26.25 27.22 27.81 27.515 27.9 28.04 27.97 31.64 31.89 31.765 33.04 32.71 32.875

Three pipes varying in length were used to determine the relationship of the pipes’ length to the time it takes to let the water run out in the tank. Figure 6.1 shows the comparison of the relationship of different lengths of pipes. It can be observed that the pipe 1 with the longest length takes greater time. Therefore, results show that the length is directly proportional to the time of flow.

[4]

7000

0.8

6000

Potential Energy Difference

0.9

0.7

Efflux Time Ratio

0.6 0.5 0.4

Pipe 1 Pipe 2 Pipe 3

0.3

5000 4000 3000 2000 1000 0 0

0.2

0.2

0.4

0.6

0.8

1

Pipe Length

0.1

Figure 6.3 Potential Energy Difference vs. Pipe Length

0 0

0.2

0.4

0.6

0.8

Figure 6.3 shows the relationship of the potential energy difference to the pipe length. The table only shows a horizontal line since the water height is constant at 80 to 20 cm. The length of the pipe was not used and is not related to the formula of the potential energy.

Water Height Figure 6.2 Efflux Time Ratio vs. Water Level Height Using Pipes Varying in Length

The values of the ratio of the experimental and theoretical efflux ratio was calculated and tabulated against water height as seen in Figure 6.2. It can be observed from the table that as the height of the water decreases, the value of the experimental gets closer to the theoretical values. This circumstance can be explained by the amount of potential energy the system exhibits. At lower water levels, the potential energy exhibited is lower which would explain the decrease in the velocity of the flow.

0

Kinetic Energy Difference

0

0.2

0.4

0.6

0.8

1

-5

-10

-15

-20

-25

Pipe Length

Figure 6.4 Kinetic Energy Difference vs. Pipe Length

In Figure 6.4, it can be seen that the longer the pipe, the lower the kinetic energy difference applied. When comparing the longest pipe to the shortest pipe, a huge difference in kinetic energy can be observed. This can be explained due to the contact of water with [5]

the surface of the pipes. This trend supports the prior observations concerning the efflux time ratio and pipe length. That a higher pipe length will lead to a higher efflux ratio.

70 60 50

18

Time

16

Friction Loss

14 12

y = -0.7368x + 61.003

40

R² = 0.7938

30

20

10

10

8 6

0

4

0

20

2

40

60

80

100

Height of Water

0 0

0.2

0.4

0.6

0.8

1

Pipe Length

Fig 6.6 Experimental Time against the Water Level for the First Orifice

The same procedure was done to analyze the water level of emptying the tank. However, this part of the experiment, the exiting of the water flow was changed from the various pipe now to different opening or the circumferential exit through orifices. As the height of the water inside the tank decreases as seen in Figure 6.6, the average time that it reached that certain point increases. It would take a longer time for the water to exit the tank when the water level is minimal

Figure 6.5 Friction Loss vs. Pipe Length

The contact of water within the pipe causes friction loss. Figure 6.5 shows the trend between the friction loss and the length of the pipe. It can be observed that a greater friction loss is present within the longest pipe A longer pipe would account for a longer friction loss as water is continuously in contact with the surface of the pipe.

70 60

Time

50 40

y = -0.7212x + 65.676 R² = 0.8247

30 20 10 0 0

20

40

60

Height of Water

[6]

80

100

Fig 6.7 Experimental Time against the water level for the first orifice

San Pedro

Table 6.1 Reynolds Number and Total Time for each Pipe Pipe NRe Flow Time 80.6

27842.79891

Turbulent

1301.473

50.3

39941.38097

Turbulent

994.089

30.2

59211.70729

Turbulent

742.7095

Elijah Soriano

Table 6.1 shows the Reynolds Number and time calculated in different length of pipes. It can be observed that this data supports the trends created in the table earlier that the total time decreases as the length of the pipe also decreases.

8. Conclusion and Recommendation In this experiment, the varying pipe length and orifice circumferential area were used, to determine the time it took for the water in the tank to be drained. As expected, the pipe with longer length resulted in increased time, due to slower flow caused by fluid contact within the pipe. Frictional forces tend to lessen the fluid flow; thus, taking longer time for longer pipes to drain the water. Consequently, the efflux time ratio approached unity at lower water heights, indicating that the experimental time slowly becomes equal to the theoretical time. This trend is due to the lower potential energy exhibited by having lower water levels. On the other hand, the circumferential area for the orifice also affected the draining time the water. Having smaller area indicated faster fluid flow, which decreased the time for the water to be drained.

Table 6.2 Potential and Kinetic Energy Difference, and Friction Loss for each Pipe Pip Friction PE Diff KE Diff f e Loss 5871.28 0.00612347 80.6 -3.1414 6.201774122 5 9 5871.28 0.00559526 50.3 9.844602941 5 7.90704 6 5871.28 0.00507077 30.2 16.69512422 5 21.9349 8

7. Individual Observations Name Alyssa Acyatan

Brian Bueno

Lloyd Dar

Sean De Leon Anna

rate of drain. Also, as the water’s height goes down, the time to reach the mark increases. There were leaks observed while the experiment was performed. This may contribute to the errors in the flow. The flow was relatively longer for longer pipes as compared to shorter ones.

Observation As the pipe length decreased, the time duration for each trial also decreased. This was even more evident when only the two orifices were used which cut down the time duration by half compared to the pipes. In this experiment, the time that it takes for the certain water level to reach every interval increases. I have also observed that it took longer to drain the tank when using the longer pipe. The pipe length and orifice area greatly affected the amount of time needed for the water to drain off the tank. Increasing pipe length and decreasing orifice opening resulted to faster draining time.

9. Industrial Applications Every chemical process industry relies on the flow of the system, to possibly identify products that are manufactured. The knowledge on these flow types enable the correct and accurate calculation of various reactions, especially when simulated. Two flows are present for chemical industries, the steady-state and unsteady-state flows. The previous is independent of time, in which its properties do not change with time, while the latter is time dependent. Most processes involved in the industry are known to perform at steady-state. Some of which are mixing and separating reactions, which are typically conducted in continuous systems. However, to achieve steady-state, the process first experiences unsteady-state behavior, particularly during start-up processes. Similarly, downtime processes also incur unsteady-state flow, since inlet flow is stopped,

An increase in pipe diameter increases the [7]

causing the system to have varying flow rates.

causing for water to travel longer when compared to that of orifices. Furthermore, as the tube length increases, the efflux ratio decreases. This can be explained by the transition of the laminar flow to its turbulent counterpart. When the liquid exits the orifice, it produces a laminar flow; however, when it exits the pipe, it transitions, and becomes turbulent causing the deviation.

10. Guide Questions 10.1 Does the experiment efflux time deviate more from the theoretical efflux time as the exit pipe becomes shorter? Explain. There is a deviation of the actual efflux time as the exit pipe becomes shorter. This is attributed to the friction factor. In addition, to that, the fouling in the pipe may increase the friction. This effect is increased as the length increases, increasing the efflux time.

10.5 Discuss briefly the development of flow patterns for circular tubes. In general, there are two types of flow: laminar and turbulent. As the name implies, laminar flow is characterized by a low fluid velocity. As such, eddy does not occur when the fluid flows this way. Basically, eddy is the swirling of the fluid and the formation of reverse currents. On the other hand, turbulent flow is characterized by a high fluid velocity which results to the occurrence of eddy. The type of flow can be determined by determining the Reynold’s number. Reynold’s number is a dimensionless number which is defined as the ratio of the fluid density, fluid velocity, and pipe diameter to the fluid velocity. For laminar flow, the value ranges from 0 to 2100 while for turbulent flow, the value is greater than 4000

10.2 How does the experimental efflux time obtained with very short tubes compare with the theoretical efflux time predicted for the drainage of the tank through an orifice? As the used pipe got shorter, the efflux time was near that of the orifice. However, it still took a longer efflux time when a pipe was used rather than an orifice. 10.3 How does the magnitude of the neglected terms in the mechanical energy balance compare with that which were not neglected? Tabulate and give percentage errors. With the simplifications made in the mechanical energy balance, the calculated values for this experiment are lesser compared to the actual values. However, the calculation in the mechanical energy balance still considers some assumptions which makes the values lesser compared to the actual or experimental data

REFERENCES [1] Olaño Jr., S. Performance of a Tubular

Condenser Experiments in Chemical Engineering, 2nd ed., pp. B-15 – B-20. [2] Geankoplis, C. (1993). Transport processes and separation process principles. 3rd ed. Upper Saddle River, NJ: Prentice Hall Professional Technical Reference, pp.803-805. [3] Uma Devi, A., Gopal Singh, P.V., Reddy, G.V.S.K., Dharwal, S.J., and Subbarao, C.H.V. (2011). A Review on Efflux Time. MiddleEast Journal of Scientific Research, 9(1), 5763. Retrieved from http://www.idosi.org/mejsr/mejsr9(1)11/9.pdf [4] Subbu, M. (2014). Efflux Time. Retrieved from http://www.msubbu.in/ln/fm/UnitII/EffluxTime.htm

10.4 Explain the deviation obtained and the effect of the tube length on the actual and theoretical efflux rates as prepared in Analysis #9. Generally, as the length of the tube is increased, the efflux time is also increased. This can be explained by the extended surface the length of the pipe possesses, [8]

[5] Available

online at http://www.brighthubengineering.com/hydrau lics-civil-engineering/55543-pipe-flowcalculations-1-the-entrance-length-for-fullydeveloped-flow/

4. For Potential Energy:

5. For Kinetic Energy: APPENDICES Pipe

Area

L

D

V

80.6

0.09

0.806

10

2.50655

50.3

0.09

0.503

9.042

3.976692

30.2

0.09

0.302

8.048

6.623431

Pipe

Viscosity

Gc

Density

R

C

80.6

0.000898

1

997.5

0.0049

1.148304376

50.3

0.000898

1

997.5

0.0049

0.877096288

30.2

0.000898

1

997.5

0.0049

0.6553012

Sample Calculations: 1. For C:

2. For V:

3. For NRe: 𝑁𝑅𝑒 =

ρVD µ

=

997.5(2.5)(0.010) = 27770.044 0.000898 [9]