This experiment was conducted in order to assess the relationship between the Reynolds number and friction coefficient for two pipe having different cross-sectional areas. The other aim was to investigate the effect of fluid density on the Reynolds number. Different flow rates were set at a laminar flow of water and the pressure determined by a manometer. The same procedure was repeated using Ethylene Glycol. A turbulent flow was also set and data taken. The Reynolds number for each flow was determined using the equation;
Where ힺ is fluid density, v is the mean flow velocity, d is the internal diameter and µ is the dynamic viscosity of the fluid and depends on the temperature of the fluid. The Reynolds number was used to determine the friction coefficient. For the laminar flow,
f = 16/Re
For the turbulent flow,
f = 0.079Re-0.25
Graphs of the friction coefficient against Reynolds number were plotted for each flow and used in the discussion.
Aim
The main objective of this experiment was to determine the relationship between the Reynolds number and friction factor of two pipes with different pipe diameter and conveying different fluids (water and Ethylene Glycol)
Raw Data
Table1: Raw data for Laminar flow rate
Volumetric flow rate (mL/min)
Fluid : H20, Laminar flow , D.O.: 1/4 in
100
Data#
1
2
3
4
5
mL/min
123.9
126.2
126.7
124.4
123.4
mmH20
42
43.9
44.2
43.8
43.8
200
Data#
1
2
3
4
5
ml/min
213.4
211.1
209.91
208.6
208.6
mmH20
74.8
74.0
73.4
73.9
73.4
300
Data#
1
2
3
4
5
ml/min
328.3
326.1
325.2
324.01
324.78
mmH20
117.9
117.3
115.6
116.2
116.4
400
Data#
1
2
3
4
5
ml/min
415.1
411.58
411.60
413.29
412.95
mmH20
150.5
153.2
151.2
150.8
148.9
Table2: Raw data for Turbulent flow rate
Volumetric flow rate (mL/min)
Fluid : H20, Turbulent flow , D.O.: 3/8 in
3000
Data#
1
2
3
4
5
mL/min
2963
3014
2959
2968
2987.6
mmH20
414.1
415.4
414.6
414.6
415.7
2500
Data#
1
2
3
4
5
ml/min
2498
2503
2509
2511
2497
mmH20
299.2
302.1
299.3
300.1
300.9
2000
Data#
1
2
3
4
5
ml/min
2044
2057
2059
2052
2055
mmH20
214.3
215.0
214.4
213.5
212.4
1500
Data#
1
2
3
4
5
ml/min
1516.34
1525
1524
1521
1521
mmH20
129.1
129.3
139.0
130.5
128.0
Results and Calculations
Table 3: Raw data for water, laminar flow O.D. ¼ in
Volumetric flow rate (mL/min)
Volumetric flow rate (m3/s)
Flow velocity (m/s)
Re
f
Inner diameter (m)
Length (m)
density kg/m3
Viscosity
Temperature (0C)
100
1.67E-06
0.107162
476.87
0.0336
0.00445
1.635
1000
0.001
25
200
3.33E-06
0.214323
953.74
0.0168
300
0.000005
0.321485
1430.61
0.0112
400
6.67E-06
0.428646
1907.48
0.00839
Table 4: Raw data for water, turbulent flow O.D. 3/8 in
Volumetric flow rate (mL/min)
Volumetric flow rate (m3/s)
Flow velocity (m/s)
Re
f
Inner diameter (m)
Length (m)
density kg/m3
Viscosity
Temperature (0C)
1000
3.3333E-05
0.72902073
5562.43
0.000915
0.00763
1.635
1000
0.001
25
2000
0.00005
1.0935311
8343.64
0.000827
3000
6.6667E-05
1.45804146
11124.86
0.000769
4000
8.3333E-05
1.82255183
13906.07
0.000727
Table 5: Raw data for Ethylene Glycol, laminar flow O.D. ¼ in
Volumetric flow rate (mL/min)
Volumetric flow rate (m3/s)
Flow velocity (m/s)
Re
f
Inner diameter (m)
Length (m)
density kg/m3
Viscosity
Temperature (0C)
1000
1.6667E-05
0.36451037
192.78
0.00212
0.00763
1.635
1116
0.0161
25
2000
3.3333E-05
0.7290273
385.57
0.00178
3000
0.00005
1.0935311
578.35
0.00161
4000
6.6667E-06
1.45804146
771.14
0.00149
Sample calculations,
Determining the Reynolds number for each volumetric flow rate through each pipe,
For water at laminar flow in the ¼ inch pipe diameter,
Determining the friction coefficient for the laminar flow,
f = 16/Re
f = 16/476 = 0.0336
Determining the friction coefficient for turbulent flow,
f = 0.079*Re-0.25
f = 0.079*5563.43-0.25 = 0.00915
Results Analysis
A graph of the friction against the Reynolds number was plotted for each pipe diameter as shown in graph 1 through 3 below.
Graph 1: A plot of friction coefficient f against Reynolds number for laminar flow of water
Graph 2: A plot of friction coefficient f against Reynolds number for turbulent flow of water
Graph 3: A plot of friction coefficient f against Reynolds number for laminar flow of Ethylene Glycol
Discussion and Conclusion
The experiment was completed successfully with the required components of the practical determined. From the results obtained, the Reynolds number varied depending on the kind of flow and type of fluid. The Reynolds number increased with the increase in the flow rate as supported by the results in table 3 and 4 for the laminar and turbulent flow. The Reynolds number also depends on the type of fluid, despite the type of flow, the values of the Reynolds number shown in table 3 and 5 varied. The Reynolds number for water was much higher than for the Ethylene Glycol. This difference from the Reynolds equation was attributed by the densities of the two fluids. From the graphs plotted for the friction factor versus the Reynolds number, the two parameters were inversely correlated where an increase in the Reynolds number resulted into a decrease in the friction coefficient. Therefore, an increase in the flow velocity increases the Reynolds number and causes a decrease in the friction coefficient. The possible sources of errors for the experiment could be from inaccurate reading and recording of the data obtained and also some analytical errors.
References
Idelchik, I. E. Flow resistance: a design guide for engineers. Routledge, 2017.
Ravi, Ravi Kant, and R. P. Saini. "Nusselt number and friction factor correlations for forced convective type counter flow solar air heater having discrete multi V shaped and staggered rib roughness on both sides of the absorber plate." Applied Thermal Engineering 129 (2018): 735-746.
Maeda, A., et al. "Characterization of exchange flow in vertical pipes of circular and square cross-sections under unstable density gradient." International Communications in Heat and Mass Transfer 82 (2017): 81-88.
