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Fluid flow is relevant to a wide scope of chemical engineering activity.  Pressure differences drive fluid flow; the rate of flow depends on the size of the pressure difference, the physical properties of the fluid, and the geometry of the system.  In chemical engineering applications, fluid flow is frequently in circular pipes.  This laboratory activity introduces students to the measurement of fluid flow and to the relationships between pressure and fluid flow as affected by pipe diameter and flowrate.

The objectives of this lab practical are:

  • to compare fluid flowrates and velocities calculated from measurements of pressure drop over an Orifice Plate, Venturi meter and Pitot tube with measured flowrates;
  • to construct a diagram of friction factor versus Reynolds number for pipes of different diameter and surface roughness.
  • Introduction (including a brief indication of the relevance of the topic to industrial practice and/or the content of a chemical engineering degree programme, a brief indication of new words or concepts the student learned that are relevant to the topic, and a brief overview of the report).
  • Experimental methods (comprising a brief description of what was investigated, referencing the instruction sheet for details of how).
  • Results and discussion (including a comparison with relevant literature).  

Including a reflection on what was learned from doing the practical.

Reports will be marked against intended learning outcomes, as follows:

Obtain a good scope and quality of laboratory results

Present and analyse laboratory results appropriately

Demonstrate understanding of relevant theory

Interpret laboratory results appropriately in the context of chemical engineering and in the light of established knowledge

Demonstrate reflective, thoughtful, insightful learning

Present a professional technical report of a laboratory activity, in terms of structure, content and clarity

Objectives

As significant is blood flow in our bodies so is fluid flow to chemical engineering systems.  Directly, fluid flow is dependent on pressure differences such that the driving force in fluidic system is made possible by the pressure changes along the flow channel which essentially is a closed channel save for the open ends. Now, the rate of flow depends on the size of the pressure difference, the physical properties of the fluid, and the geometry of the system (Engineersedge.com, 2018). Worth noting is the fact in chemical engineering applications, circular pipes are often used in fluidic flow systems.  Therefore, this report is a preliminary investigation and examination of the relationship that exists between pressure gradient and fluid flow in a known pipe diameter by considering different flow rates.

Therefore, the objectives of the laboratory exercise include:

  • To compare fluid flow rates and velocities calculated from measurements of pressure drop over an Orifice Plate, Venturi meter and Pitot tube with measured flow rates;
  • To construct a diagram of friction factor versus Reynolds number for pipes of different diameter and surface roughness.

Before the experiment was done, the set up was established by first setting and resetting the fluid flow apparatus. The pump was turned on while the gate and globe valves were gradually closed to allow pressure build up. The air trappings were then bled by slightly opening the gate valve, this then corrected the system pressure such that it was entirely fluidic. The next thing was to connect the digital manometer which directly reads out the pressure drop (Mechanical Booster, 2018). Meanwhile the gate valve remained closed to allow system pressure to be maintained. The high static pressure and the fact that the valves are closed reduced some systemic error due to disturbances and noise. However, some air leaks were inevitable from affecting the system. The reading was then taken after resetting the zero button meters. At this point system was stabilized and various readings were taken by valve control.

The digital manometer had the pressure drop displayed directly hence could easily be retrieved.  

Now, the readings of pressure meters connected to the Venturi meter and the manometer were taken after every 30 seconds and this was done for a total of 5mins. The results are displayed in tables R1.1, R 1.2 and R1.3.

As for the orifice plates and Venturi meters, to obtain the values of flow characteristics, the valves were regulated manually such that there was gradual reduction in cross section area hence flow rate also decreased by the same factor as fluid velocity through these restrictions increased and thus fluid pressure could drop gradually (Astro.rug, 2018). This is actually Bernoulli’s principle in action.

Further, the flow rate was determined (for both venturi and orifice) by the following formula:

where Q = volumetric flowrate (m3 s–1)

A0 = cross sectional area of orifice or throat (m2) (d0 = 14 mm for the Venturi, 20 mm for the orifice plate; hence A0 = 1.5394×10–4 m2 for the Venturi meter, A0 = 3.1416×10–4 m2 for the orifice plate)

A1 = cross sectional area of pipe upstream (m2) (assume: d1 = 24 mm, hence A1 = 4.5239×10–4 m2)

CD = discharge coefficient (= 0.98 for Venturi meter, 0.62 for orifice plate)

It should be noted that the average velocity of the fluid in the pipe was given by the volumetric flowrate divided by the cross-sectional area:

Experimental methods

As for the average velocity, it was now simple to determine. This was done using equation (3)

However, for a pitot tube the mechanism of operation is quite different (Engineering Toolbox, 2018). The small tube with an L- shaped feature is dipped against a flowing fluid such that the kinetic energy of the fluid gets transformed into static pressure on impact with the tube. However, the governing principle is still Bernoulli’s and therefore equation 4 was used to determine the average velocity (Manshoor, Nicolleau & Beck, 2011).

Error analysis

Now, the experiment was designed to ensure errors were limited at minimum levels; however, as is often the case with experiments, reliability of results varies and would depend on a range of factors such as operator misreading values; repeatability, the systemic error which are often carried forward and the fact in any random data, variations must be expected regardless of experimental conditions (Engineersedge.com, 2018). This was analyzed in the results section..

Calculation

In determining the statistical variation, firstly, the mean value of pressure difference of Venturi meter was calculated using the following equations:

where  is the average or mean value; , is the standard deviation of , is the standard error.

The final value of the variation measurement was determined using equation 13:

Results and discussion

In this case, there were three sets of results obtainable in tables R 1.1, R1.2 and R1.3. In the first table, the volumetric flow rate for the three constrictions were calculated from the experimental values obtained. In the second table, fanning frictional factor f and Reynold’s number were calculated as illustrated in the table R 1.2 and the resulting graphs plotted, that is, F against Re.

Table R 1.1: Fluid flow, flowrate measurement using Orifice, Venturi and Pitot meters

Trial 1

Trial 2

Trial 3

Trial 4

Trial 5

Valve opening

Full

~¾ full

~½ full

~¼ full

~1/10 Full

Manual measurement

Volume V (litres)

10

10

10

10

10

Time (s)

12.09

13.72

31.28

37.82

25.06

Volumetric flowrate Q* (m3 s–1)

0.000827

0.0007288

0.0003197

0.0002644

0.000399

Average velocity *        (m s–1)

1.828289745

1.610999

0.706691

0.584451

0.881982

Orifice meter

ΔP raw data

-6.67

-5.32

-1.28

-0.14

-0.03

(Unit:           )

ΔP (Pa)

6.67

5.32

1.28

0.14

0.03

('P)^0.5

2.582634314

2.306513

1.131371

0.374166

0.173205

Flowrate (m3 s–1)

1.85E-05

1.66E-05

8.12E-06

2.69E-06

1.24E-06

average velocity

4.10E-02

3.66E-02

1.80E-02

5.94E-03

2.75E-03

(m s–1)

Venturi meter

ΔP raw data

-18.47

-14.74

-3.25

-0.44

0.06

(Unit:            )

ΔP (Pa)

18.47

14.74

3.25

0.44

0.06

('P)^0.5

4.297673789

3.8392708

1.8027756

0.663325

0.244949

Flowrate (m3 s–1)

3.08504E-05

2.76E-05

1.29E-05

4.76E-06

1.76E-06

average velocity

6.82E-02

6.09E-02

2.86E-02

1.05E-02

3.89E-03

(m s–1)

Pitot tube

ΔP raw data

2.75

2.24

0.05

0.06

0.03

(Unit:              )

ΔP (Pa)

2.75

2.24

0.05

0.06

0.03

2x'P

5.5

4.480

0.100

0.120

0.060

2p/'rho'

0.0055

0.00448

0.0001

0.00012

0.00006

Local velocity

7.42E-02

6.69E-02

1.00E-02

1.10E-02

7.75E-03

(m s–1)

4.08E-04

3.68E-04

5.50E-05

6.02E-05

4.26E-05

Flowrate (m3 s–1)

Table R 1.3: Fluid flow, Fluid friction in smooth pipes

Valve opening

Δ P for Venturi meter

[p]^0.5

Volumetric flowrate Q* (m3 s–1)

Average velocity

log u

Δ P per unit pipe length

log Δp/L

P/U

Reynolds number ®

Fanning Friction factor (f)

(Pa)

(m s–1)

(Pa m–1)

Pipe 1

Full

15.41

3.92555729

0.00028179

0.62289662

-0.20558402

8.15

0.91115761

2.40E+01

9.424675068

0.000132

¾ full

9.38

3.06267857

0.00021985

0.4859774

-0.31338392

4.94

0.69372695

1.90E+01

7.353032506

0.0001045

½ full

1.21

1.1

7.8962E-05

0.17454497

-0.75809266

0.94

-0.02687215

6.00E+00

2.640935241

0.000033

¼ full

0.28

0.52915026

3.7985E-05

0.08396411

-1.07590633

0.13

-0.88605665

3.00E+00

1.270410523

0.0000165

1/10 full

0.49

0.7

5.0249E-05

0.11107407

-0.9543873

-0.07

0

4.00E+00

1.680595153

0.000022

Pipe 2

Full

7.43

2.72580263

0.00019567

0.43252286

-0.36399094

37.34

1.57217431

1.70E+01

4.137081137

0.0000935

¾ full

3.43

1.85202592

0.00013295

0.29387437

-0.53183828

19.76

1.29578694

1.10E+01

2.810908388

0.0000605

½ full

1.51

1.22882057

8.821E-05

0.19498587

-0.70999687

5.67

0.75358306

7.00E+00

1.865039805

0.0000385

¼ full

0.11

0.33166248

2.3808E-05

0.05262729

-1.278789

2.17

0.33645973

2.00E+00

0.503380021

0.000011

1/10 full

0.07

0.26457513

1.8992E-05

0.04198205

-1.37693632

0.06

-1.22184875

1.00E+00

0.401558341

0.0000055

Pipe 3

Full

2.91

1.70587221

0.00012245

0.27068311

-0.56753885

91.29

1.96042321

1.00E+01

1.883007029

0.00004

¾ full

1.79

1.33790882

9.604E-05

0.21229569

-0.67305883

57.66

1.76087464

8.00E+00

1.476834952

0.000032

½ full

0.32

0.56568542

4.0607E-05

0.08976141

-1.04691035

20.49

1.31154196

3.00E+00

0.62442522

0.000012

¼ full

0.06

0.24494897

1.7583E-05

0.03886783

-1.41040972

1.64

0.21484385

1.00E+00

0.270384052

0.000004

1/10 full

0.01

0.1

7.1784E-06

0.01586772

-1.79948534

0.4

-0.39794001

0.00E+00

0.110383827

0

Pipe 4

Full

0.12

0.34641016

2.4867E-05

0.05496741

-1.25989472

74.43

1.87174802

2.00E+00

0.23421064

4.9E-06

¾ full

0.11

0.33166248

2.3808E-05

0.05262729

-1.278789

75.16

1.87598677

2.00E+00

0.22423962

4.9E-06

½ full

0.036

0.18973666

1.362E-05

0.03010689

-1.52133409

54.39

1.73551906

1.00E+00

0.12828245

2.45E-06

¼ full

0.03

0.17320508

1.2433E-05

0.02748371

-1.56092472

32.16

1.50731604

1.00E+00

0.11710532

2.45E-06

1/10 full

0.03

0.17320508

1.2433E-05

0.02748371

-1.56092472

0.33

-0.48148606

1.00E+00

0.11710532

2.45E-06

Table 1.4: Error analysis for Flow fluid experiment

Time (min)

Pressure difference of Venturi meter (Pa)

Pressure difference of unit pipe length (Pa m–1)

L=1m

Xi-X'

(Xi-X')^2

0.5

15.1

15.1

-0.146

0.021316

1

15.12

15.12

-0.126

0.015876

1.5

15.36

15.36

0.114

0.012996

2

15.24

15.24

-0.006

3.6E-05

2.5

14.82

14.82

-0.426

0.181476

3

15.31

15.31

0.064

0.004096

3.5

15.33

15.33

0.084

0.007056

4

15.37

15.37

0.124

0.015376

4.5

15.18

15.18

-0.066

0.004356

5

15.63

15.63

0.384

0.147456

TOTAL

152.46

0.41004

10

4.56E-02

15.246

0.213448

0.07115

Max

15.31715

Min

15.17485

Flow behaviour in venture and orifice are closely similar as far as manual flow is concerned. Flow in pitot tube exhibited higher flow characteristics. For example, at a manual flow of 0.000827m3/s, the flow magnitude in pitot tube is 10 times greater. This indicates that flow is most rapid in the pitot tube.

The pressure drop is occurring most rapidly in the pitot tube since it has the steepest slope. As log of velocity is increasing, the pressure drops in all of the three steadily decreases.

The steepest slope was registered in the manual flow followed by the orifice. In the pitot tube, the slope is almost zero. This indicates that as the Reynolds’s number is increasing, the friction factor reduces steadily in all except pitot tube. This is true since for rapid flow to be realised, the pressure drops must be greater such that the friction factor is overcome. Normally, in turbulent flow, Reynold’s number is greater and this translates to greater pressure drops; in part to overcome the friction in flow.

Conclusions

Therefore, from the results and discussion, it is actually realized that pressure drops in fluidic system greatly determine the type of flow likely to be exhibited by the fluid (at constant conditions of temperature).

References

Astro.rug. (2018). Bernoulli Applications. Retrieved from https://www.astro.rug.nl/~weygaert/tim1publication/astrohydro2014/astrohydro2014.III.2.pdf

Engineering Toolbox. (2018).Pitot Tubes. Retrieved from https://www.engineeringtoolbox.com/pitot-tubes-d_612.html

Engineersedge.com. (2018). Pressure Drop along Pipe Length - Fluid Flow Hydraulic and Pneumatic, Engineers Edge. Retrieved from https://www.engineersedge.com/fluid_flow/pressure_drop/pressure_drop.htm

Manshoor, B., Nicolleau, F., & Beck, S. (2011). The fractal flow conditioner for orifice plate flow meters. Flow Measurement And Instrumentation, 22(3), 208-214. doi: 10.1016/j.flowmeasinst.2011.02.003

Mechanical Booster. (2018). Difference Between Laminar and Turbulent Flow - Mechanical Booster. Retrieved from https://www.mechanicalbooster.com/2016/08/difference-between-laminar-and-turbulent-flow.html

Wolfram. (2018). Experimental Errors and Error Analysis. Retrieved from https://reference.wolfram.com/applications/eda/ExperimentalErrorsAndErrorAnalysis.html

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