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
Answer:
Introduction
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.
Objectives
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.
Experimental methods
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.
Methodology of Analysis
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 (m^{3} s^{–1})
A_{0} = cross sectional area of orifice or throat (m^{2}) (d_{0} = 14 mm for the Venturi, 20 mm for the orifice plate; hence A_{0} = 1.5394×10^{–4} m^{2} for the Venturi meter, A_{0} = 3.1416×10^{–4} m^{2} for the orifice plate)
A_{1} = cross sectional area of pipe upstream (m^{2}) (assume: d_{1} = 24 mm, hence A_{1} = 4.5239×10^{–4} m^{2})
C_{D} = 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 crosssectional area:
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* (m^{3} 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 (m^{3} s^{–1}) 
1.85E05 
1.66E05 
8.12E06 
2.69E06 
1.24E06 

average velocity 
4.10E02 
3.66E02 
1.80E02 
5.94E03 
2.75E03 








(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 (m^{3} s^{–1}) 
3.08504E05 
2.76E05 
1.29E05 
4.76E06 
1.76E06 

average velocity 
6.82E02 
6.09E02 
2.86E02 
1.05E02 
3.89E03 








(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 
7.42E02 
6.69E02 
1.00E02 
1.10E02 
7.75E03 








(m s^{–1}) 
4.08E04 
3.68E04 
5.50E05 
6.02E05 
4.26E05 

Flowrate (m^{3} 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* (m^{3} 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 
7.8962E05 
0.17454497 
0.75809266 
0.94 
0.02687215 
6.00E+00 
2.640935241 
0.000033 
¼ full 
0.28 
0.52915026 
3.7985E05 
0.08396411 
1.07590633 
0.13 
0.88605665 
3.00E+00 
1.270410523 
0.0000165 
1/10 full 
0.49 
0.7 
5.0249E05 
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 
8.821E05 
0.19498587 
0.70999687 
5.67 
0.75358306 
7.00E+00 
1.865039805 
0.0000385 
¼ full 
0.11 
0.33166248 
2.3808E05 
0.05262729 
1.278789 
2.17 
0.33645973 
2.00E+00 
0.503380021 
0.000011 
1/10 full 
0.07 
0.26457513 
1.8992E05 
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 
9.604E05 
0.21229569 
0.67305883 
57.66 
1.76087464 
8.00E+00 
1.476834952 
0.000032 
½ full 
0.32 
0.56568542 
4.0607E05 
0.08976141 
1.04691035 
20.49 
1.31154196 
3.00E+00 
0.62442522 
0.000012 
¼ full 
0.06 
0.24494897 
1.7583E05 
0.03886783 
1.41040972 
1.64 
0.21484385 
1.00E+00 
0.270384052 
0.000004 
1/10 full 
0.01 
0.1 
7.1784E06 
0.01586772 
1.79948534 
0.4 
0.39794001 
0.00E+00 
0.110383827 
0 
Pipe 4 










Full 
0.12 
0.34641016 
2.4867E05 
0.05496741 
1.25989472 
74.43 
1.87174802 
2.00E+00 
0.23421064 
4.9E06 
¾ full 
0.11 
0.33166248 
2.3808E05 
0.05262729 
1.278789 
75.16 
1.87598677 
2.00E+00 
0.22423962 
4.9E06 
½ full 
0.036 
0.18973666 
1.362E05 
0.03010689 
1.52133409 
54.39 
1.73551906 
1.00E+00 
0.12828245 
2.45E06 
¼ full 
0.03 
0.17320508 
1.2433E05 
0.02748371 
1.56092472 
32.16 
1.50731604 
1.00E+00 
0.11710532 
2.45E06 
1/10 full 
0.03 
0.17320508 
1.2433E05 
0.02748371 
1.56092472 
0.33 
0.48148606 
1.00E+00 
0.11710532 
2.45E06 
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 
XiX' 
(XiX')^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 
3.6E05 
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 


4.56E02 


15.246 








0.213448 





0.07115 




Max 
15.31715 




Min 
15.17485 
Discussion
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/pitottubesd_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), 208214. 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/differencebetweenlaminarandturbulentflow.html
Wolfram. (2018). Experimental Errors and Error Analysis. Retrieved from https://reference.wolfram.com/applications/eda/ExperimentalErrorsAndErrorAnalysis.html
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