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Abstract

To set out a piping system for whatever function needed, it is required to determine the friction factor in order to evaluate the energy losses through the system. Therefore, on this experiment, the intention is to find the friction factor and Reynolds number of several piping systems. The fiction factor was both predicted and found experimentally. When the experimental friction factor was plotted verses Reynolds number, a trend identical to Moody chart was found. Similarly, the predicted friction factor verses Reynolds number plot trend was also comparable to Moody chart. The experimental friction factor values were higher than the predicted ones and its uncertainty was decreasing as the Reynolds number value increases. The reason the experimental friction factor values were higher was the errors in the instruments used, which were air bubbles in manometer, and offset in rotameter.

Introduction

Designing a piping system relies on the assessment of the fluid energy losses due to friction with the pipe walls. The friction reduces the fluids pressure as it maneuver through the piping system. The evaluation of the amount of the energy losses in the piping system depends mostly on experimental evidence, since it is known to be remarkably complicated. The behavior of a fluid in a piping system can be expressed through dimensionless parameters such as the friction factor and the Reynolds number. The objective of this experiment is to determine these parameter for water flowing throw several different pipes with different flow rates. The friction factor can be calculated using the following equation:

f = (2 hL D g) / (L V2) … (1)

Where:

hL is the head loss, hL = ∆P / γwater.

D is the diameter of the pipe.

g is the gravitational acceleration.

L is the length of the pipe.

V is the velocity of water in the pipe.

Additionally, the friction factor can be also predicted since it is a function of Reynolds number and the relative roughness using:

… (2)

Where:

Re is the Reynolds number.

is the relative roughness.

Moreover, the Reynolds number is an important dimensionless parameter that defines the characteristics of a fluid, and can be found using:

Re = VD / ν … (3)

Where ν is the kinematic viscosity of the fluid.

Description of Work

It was instructed to perform the experiment on pipes number 1, 4, 7, & 9 (Figure 1). The pipes were inspected and it was noted that pipes 1 & 4 are made from steel, pipe 7 from copper, and pipe 9 from PVC plastic. The inside diameter and the absolute roughness of the test pipes was determined with the help of Table 1 from the lab manual. The distance between the inlet and outlet taps was determined using a measure tape. On these taps, tubes will be connected to the u-tube manometer (Figure 2) to measure the pressure difference between the two taps of a pipe. Pipe #1 was the first to perform the test on. The upstream and downstream valves were fully opened. The rotameter (Figure 3) and the manometer readings were recorded. The upstream valve was turned clockwise until the rotameter decreased a significant amount (at least 1 GPM). Then, both readings were recorded again. After that, the water flowrate was further decreased by turning the upstream valve. After recording three data points, the previous steps were repeated for each of the four pipes selected.

Figure 1: Test pipes (upstream).

Figure 2: U-tube mercury-water manometer.

Figure 3: Rotameter.

Results and Discussion

First, the water flowrate was converted from GPM to CFS by dividing by a factor of (7.48/60), and the pressure difference was calculated by multiplying the difference between the specific weight of water and mercury by the height difference. The data can be seen in Table 1 down below. To create plot needed, Table 2 was generated where the pressure difference was divided by the length of the pipe. Figure 4 is the visual representation of Table 2, as it clearly shows a linear relation between the water flowrate and the pressure difference over the length. The uncertainty of the flowrate was calculated to be 0.000557 CFS while the pressure uncertainty was 0.0227 psi. The uncertainty is obviously constant for all data points since all of them rely on the ½ of the resolution of the instruments used.

Table 1: Converted water flowrate in CFS and calculated pressure difference in psi.

Table 2: Water flowrate and pressure difference over the length of the pipe.

Figure 4: The pressure difference/length as a function of water flowrate.

Next, the velocity of the water was determined by dividing the flowrate by the cross-sectional area of the pipe. Also the uncertainty of the velocity was calculated by dividing the uncertainty of flowrate by the flowrate and then multiply it by the velocity calculated for each data point. These data points can be seen in Table 3 below. The velocity data were calculated to be used in determining the values of the experimental friction factor using Equation (1). Table 4 shows the different values of calculated experimental friction factors. The uncertainty of the friction factor was calculated using the propagation of error equation where:

uf = f *

The Reynolds number was calculated for each test using Equation (3), and all the data can be seen in Table 4. Similarly, Reynolds number uncertainties were calculated using the propagation of error equation. Figure 5 show a plot of the experimental friction factor as a function of Reynolds number with the error bars noted. A first glance at the plot indicates that it is very familiar, and it looks like a Moody chart. One of the things that was noticed in the plot is that the friction factor uncertainty was decreasing as the Reynolds number increases (i.e. as the flow becomes more turbulent). Another note is that the Reynolds number was always greater than 4000 which means that the flow is turbulent.

Table 3: Water velocity inside the pipe and the uncertainty.

Table 4: Experimental friction factor and the uncertainty.

Table 5: Calculated Reynolds number and the uncertainty.

Figure 5: Experimental friction factor as a function of Reynolds number (Moody chart).

The predicted friction factor was calculated using Equation (2), and all the values can be seen in Table 6 down below. Similar to the plot in Figure 5, another plot was generated, but the predicted friction factor was instead of the experimental friction factor with no error bars, Figure 6. Likewise, the plot trend also follows the trend of a Moody chart. The experimental values of the friction factor are noted to be higher that the predicted ones, and it is believed that it is due to the fact that there are several error factors that can contribute to that.

Table 6: Predicted friction factor.

Figure 6: Predicted friction factor as a function of Reynolds number (Moody chart).

Conclusion

The purpose of the experiment is to figure the friction factor and Reynolds number of several piping systems. The friction factor was to be calculated in two ways, the experimental and the predicted. Both, the experimental and predicted showed similar trend when plotted vs the Reynolds number, even though the experimental values were much higher. It is believed that human error could have contributed to the huge sums of experimental friction factor calculated. One of these errors is that air bubbles were found on the top of the manometer and they can manipulate the data for pressure. Another human error can be the reading of the rotameter values and the determination of the offset of it. All in all, the experiment can be somehow found to be successful since both the experimental and the predicted friction factor follow the same trend even though the experimental were a bit shifted upward due to error.

Appendix

Table 7: Raw data.

Sample Calculation

· To convert water flowrate from GPM to CFS:

Q = (6.75 – 2.5) GPM * (1 ft3 / 7.48 Gal) * (1 min / 60 sec)

Q = 0.0095 ft3/sec (CFS)

· To calculate the velocity, V = 4 * Q / (π * D2) :

V = 4 * 0.0095 (CFS) / [π * (0.662/12 (ft))2].

V = 4.49 ft/sec.

· To calculate the experimental friction factor, f = (2 hL D g) / (L V2):

hL = ∆P / γwater

f = (2 ∆P D g) / (L V2 γwater)

f = (2 * (9.46 * 144) * (0.622/12) * 32.2) / (13.0.125 * (4.49)2 * 62.4)

f = 0.2829

To calculate the friction factor uncertainty uf = f * :

uf = 0.2829 *

uf = 0.034

Pressure Difference / Length vs. Flow rate

Pipe #1 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 2.2731944444444444E-2 2.2731944444444444 E-2 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 9.4696969696969682E-3 7.7985739750445629E-3 5.5704099821746881E-3 0.73963314681588055 0.65590109245936579 0.56519136690647476 Pipe #4 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 1.5597147950089126E-2 1.4483065953654188E-2 1.1140819964349376E-2 0.64892342126298974 0.62101273647748478 0.55123602451372233 Pipe #7 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 2.1167557932263815E-2 1.7825311942958999E-2 1.3368983957219251E-2 0.49541465494271247 0.46750397015720757 0.43959328537170261 Pipe #9 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 5.5704099821746872E-4 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 2.2731944444444444E-2 2.2281639928698752E-2 2.0053475935828877E-2 1.6711229946524065E-2 0.48843698374633626 0.46750397015720757 0.44657095656807883

Q, Flow rate, (CFS)

Pressure Diff./Length (psi/ft)

Experimental friction factor vs Reynolds number

Pipe #1 1485.0460894526443 1485.0460894526443 1485.0460894526443 1485.0460894526443 1485.0460894526443 1485.0460894526443 3.3295989238142941E-2 5.2861022123582312E-2 0.12497505513361 3.3295989238142941E-2 5.2861022123582312E-2 0.12497505513361 25245.783520694957 20790.645252337021 14850.460894526446 0.28290031305183133 0.36991095034491961 0.62475598379531316 Pipe #4 1120.993528688768 1120.993528688768 1120.993528688768 1120.993528688768 1120.993528688768 1120.993528688768 2.6699307949637711E-2 3.1908730534760579E-2 6.2204056657528158E-2 2.6699307949637711E-2 3.1908730534760579E-2 6.2204056657528158E-2 31387.818803285507 29145.83174590797 22419.870573775363 0.3733158475269715 0.41433617384 109511 0.62155081538791657 Pipe #7 1176.6862008147066 1176.6862008147068 1176.686200814707 1176.6862008147066 1176.6862008147068 1176.686200814707 6.4117619943137834E-3 1.0124359089925036E-2 2.25439372840 12744E-2 6.4117619943137834E-3 1.0124359089925036E-2 2.2543937284012744E-2 44714.075630958861 37653.958426070618 28240.468819552971 0.12142634460249392 0.16158335150200928 0.27010948310783633 Pipe #9 1140.3687254809192 1140.3687254809195 1140.3687254809195 1140.3687254809192 1140.3687254809195 1140.3687254809195 6.3423195534861067E-3 8.3229184242103044E-3 1.3726785660641118E-2 6.3423195534861067E-3 8.3229184242103044E-3 1.3726785660641118E-2 45614.749019236784 41053.274117313107 34211.061764427592 0.12637950029462106 0.14933732839046931 0.20541683857411411

Re, Reynolds number

f, Friction factor

Predicted friction factor vs Reynolds number

Pipe #1 25245.783520694957 20790.645252337021 14850.460894526446 3.0099660611241981E-2 3.0839725724298033E-2 3.2390392068517945E-2 Pipe #4 31387.818803285507 29145.83174590797 22419.870573775363 2.8009472687256211E-2 2.8264821991480994E-2 2.9283627731874061E-2 Pipe #7 44714.075630958861 37653.958426070618 28240.468819552971 2.1229588756817856E-2 2.2086040194221251E-2 2.3640363369580447E-2 Pipe #9 45614.749019236784 41053.274117313107 34211.061764427592 2.1133437231301917E-2 2.1648935888170222E-2 2.2586638858399406E-2

Re, Reynolds number

f, Friction factor

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