Measurement Of Fluid Flow In Chemical Engineering – Lab Report

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)

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 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