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Head Loss in Pipe System

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Submitted By akemasyraf
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Summary
The main principle behind this experiment is the head loss experienced by a moving fluid in a piping system. Head loss is the pressure drop (due to friction) of a flowing fluid. The friction may be caused by many factors, such as friction from the introduction of pipe fittings or friction of the fluid against the pipes inner walls. The objective of this experiment was to determine whether the head loss of fluid in piping of different diameter (d = 0.006m, 0.010m and 0.017m) was obtainable by using the Darcy-Weisbach Equation; h=(4fLu^2)/2gd; OR h=(λLu^2)/2gd. Furthermore, if the head loss was obtainable through the Darcy-Weisbach Equation, we have to compare it with the experimental head loss value and find the percentage error to determine the accuracy of the Darcy-Weisbach Equation. Form the experiment, the test 1 (d =0.006m), the maximum percentage error was 76.8% and the minimum was 72.2%.For test 2 (d =0.010m), the maximum percentage error was 15.6% and the minimum was 4.4%. Lastly for the test 3 (d =0.017m), the maximum was percentage error was 12.9% and the minimum was 4.5%.
Thus, from the obtained results, it can be said that the head loss value of a fluid flowing through a pipe can be calculated by using the Darcy-Weisbach Equation, and its value is fairly accurate. Objectives
The objective of this experiment is to determine whether the Darcy-Weisbach is applicable in obtaining the amount of head loss (due to friction) experienced by a fluid (water) flowing through a smooth pipe. Furthermore, we are to determine the accuracy of the theoretical value of the head loss calculated using the Darcy-Weisbach (if any) by obtaining it’s percentage of error with regards to the experimental value of the head loss.

Data, Observations and Results
Tables:
Table 1: Pipe of Diameter 0.006m

To convert Flowrate,Q: Q=(Q×(〖10〗^(-3)))/T (m³/s)

To calculate Velocity,U: U= 4Q/(πd^2 ) (m/s)

To calculate Reynolds Number,Re: Re= ρUd/μ ; where μ= 1.002x10¯³ kg/m.s and ρ=998 kg/m³ To calculate Friction Factor,f: f= 0.079/〖Re〗^0.25

To calculate λ: λ = f×4

To calculate Theoretical Headloss: h_Th= (λLU^(2 ))/2gd (mH₂O); where L =9.81 m²/s & L = 1m

Volume,V (Liter) Time, T (sec) Flowrate,Q (m³/s)
[x10¯⁴] Velocity,U (m/s) Re f [x10¯³] λ
[x10¯³] Theoretical Headloss (mH₂O) Experimental Headloss
(mmH₂O) Experimental Headloss
(mH₂O) % Error
(%)
5 12.36 4.045 14.300 85457 4.62 18.5 32.108 7290 7.290 77.3
5 12.81 3.903 13.804 82493 4.66 18.6 30.179 6990 6.990 76.8
5 13.38 3.737 13.217 78985 4.71 18.8 27.969 6690 6.690 76.0
5 14.75 3.390 11.990 71652 4.83 19.3 23.589 6390 6.390 72.9
5 15.37 3.253 11.505 68754 4.88 19.5 21.944 6090 6.090 72.2
5 15.62 3.210 11.321 67654 4.90 19.6 21.330 5790 5.790 72.9

Volume,V (Liter) Time, T (sec) Flowrate,Q (m³/s)
[x10¯⁴] Velocity,U (m/s) Re f [x10¯³] λ
[x10¯³] Theoretical Head (mH₂O) Experimental Head
(mmH₂O) Experimental Head
(mH₂O) % Error
(%)
5 8.62 5.800 7.385 73555 4.79 19.2 5.337 5740 5.740 7.6
5 8.82 5.669 7.218 71891 4.83 19.3 5.114 5340 5.340 4.4
5 9.65 5.181 6.597 65706 4.93 19.7 4.370 4940 4.940 13.0
5 9.78 5.112 6.506 64800 4.95 19.8 4.271 4540 4.540 6.3
5 10.57 4.730 6.022 59979 5.05 20.2 3.733 4140 4.140 10.9
5 11.47 4.359 5.550 55278 5.15 20.6 3.234 3740 3.740 15.6

Table 2: Pipe of Diameter 0.010m

To convert Flowrate,Q: Q=(Q×(〖10〗^(-3)))/T (m³/s)

To calculate Velocity,U: U= 4Q/(πd^2 ) (m/s)

To calculate Reynolds Number,Re: Re= ρUd/μ ; where μ= 1.002x10¯³ kg/m.s and ρ=998 kg/m³ To calculate Friction Factor,f: f= 0.079/〖Re〗^0.25

To calculate λ: λ = f×4

To calculate Theoretical Headloss: h_Th= (λLU^(2 ))/2gd (mH₂O); where L =9.81 m²/s & L = 1m

Table 3: Pipe of Diameter 0.017m

Volume,V (Liter) Time, T (sec) Flowrate,Q (m³/s)
[x10¯⁴] Velocity,U (m/s) Re f [x10¯³] λ
[x10¯³] Theoretical Head (mH₂O) Experimental Head
(mmH₂O) Experimental Head
(mH₂O) % Error
(%)
5 4.47 11.19 4.930 83475 4.65 18.6 1.355 1530 1.530 12.9
5 4.63 10.80 4.758 80563 4.69 18.8 1.273 1330 1.330 4.5
5 5.13 9.747 4.294 72706 4.81 19.2 1.064 1130 1.130 6.2
5 5.34 9.363 4.125 69845 4.86 19.4 0.992 0.93 0.930 6.3
5 6.54 7.645 3.368 57027 5.11 20.4 0.695 0.73 0.730 5.0
5 7.88 6.345 2.795 47325 5.36 21.4 0.502 0.53 0.530 5.6

To convert Flowrate,Q: Q=(Q×(〖10〗^(-3)))/T (m³/s)

To calculate Velocity,U: U= 4Q/(πd^2 ) (m/s)

To calculate Reynolds Number,Re: Re= ρUd/μ ; where μ= 1.002x10¯³ kg/m.s and ρ=998 kg/m³ To calculate Friction Factor,f: f= 0.079/〖Re〗^0.25

To calculate λ: λ = f×4

To calculate Theoretical Headloss: h_Th= (λLU^(2 ))/2gd (mH₂O); where L =9.81 m²/s & L = 1m

Graphs:
Graph 1

Discussion
Head loss in pipe is the pressure drop as a fluid flows through a pipe. Head loss is representing how much pressure will be lost due to the orientation of the pipe system. This is used to determine the efficiency of pipe system. There are many junctions or bends in a typical pipe system. As fluid flow through these bends or junction, the pressure of the fluid flow decreases due to the change of direction of the fluid flow. The pressure of the fluid flow also decrease due to frictional force of the fluid acted on the inner surface of the pipe.
From the table 1, which is for pipe of diameter 6mm, the highest percentage error is 77.3% while the smallest percentage error is 72.2%. The percentage errors indicate the differences between experimental value of head loss and theoretical value of head loss. From table 2, the diameter of the pipe is 10mm. The highest percentage error is 15.6% and the lowest percentage error is 4.4%. Table 3 shows result for the pipe with diameter 17mm. The highest percentage error is 12.9% and the smallest error percentage is 4.5%. From all three tables, we can see that table 1 gives the highest error percentage which is 77.3%. Unalike the error percentage from table 2 and table 3, it only give low error percentage of head loss. So, table 1 is used as a controlled set to be used as a benchmark.
Graph 1 show that friction factor is inversely proportional to Reynolds number. From the equation of the friction factor; f= 0.079/〖Re〗^0.25 we can see that f ∝ 1/Re . Hence, the graph is in compliance with the equation. The general shape and the characteristic of graph 1 and the Moody Diagram is roughly the same, whereby it obeys the equation f ∝ 1/Re.

The possible source of error is that it might be a misalignment in the connection of the pipe system. The reading of the pressure differential device is keep fluctuate. Parallax error when taking the water volume reading. Human error when using the stopwatch.
The safety precaution of the experiment is to make sure there is fluid or water in the pipe system before start the experiment. Other precaution is before undertaking the experiment, which to allow some fluid or water to flow through the whole piping system.

Conclusion
Basically this experiment was conducted to analyse that Darcy-Weisbach equation can be used to predict the head loss due to friction with flow of water through a smooth bore pipe. The general equation of Darcy-Weisbach is h = 4fLu^2 /2gd or h = λLu^2/2gd. Meanwhile head loss is actually defined as the measure of the reduction of the total head of the liquid as it moves through a system. The factors affecting the head loss are length of the pipe between tapping, internal diameter of the pipe, mean velocity of water through the pipe and the pipe friction factor. The results obtained from this experiment showed that as the flow rate is increased, the value of experimental head also increase as shown in Table 1, 2 and 3. However, we can see in Table 1 that the difference between theoretical value and experimental value is quite big which lead high percentage of error. For Table 2 and 3 the difference for theoretical value and experiment is quite small and the error is less than 15 percent. This showed that for the first set of experiment conducted using 0.006m diameter of pipe the experiment is not conducted in a proper manner. Parallax error during to take the readings of water level that is set for 5 liter maybe the main source of error. Another error that can be detected is human error when to stop the stopwatch as 5 liter of water level is reached. Based on the Graph 1, it showed that the Reynolds value is inversely proportional toward the friction factor. Hence, the graph obeyed the condition of the equation of f=0.0075/(Re^0.25). Finally we can conclude that, the head is obtainable by applying the Darcy-Weisbach equation based on the results obtained.

References

B. R. Munson, T. H. Okiishi, W. W. Huebsch, A. P. Rothmayer. 2010. Fluid Mechanics. 7th Edition. Singapore: John Wiley & Sons Pte. Ltd. , pp. 673-682.

Hydraulic Head. 2014. http://en.wikipedia.org/wiki/hydraulic_head

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