Experiment 4

Friction Factor ABSTRACT Viscous effects generated by the surface of the pipe in pipe flow causes a loss in mechanical energy known as friction loss. Fiction loss has several causes including: conditions of flow, physical properties of the system, movement of fluid molecules against each other and against the pipe’s surface, and the bends and turns along the piping. In order to quantify the amount of frictional losses in the study, the Fanning friction factor, f is used. In the experiment, a fluid flow set-up was used in order to compute an experimental Fanning friction factor from the pressure drop, pipe length and fluid velocity. The value of the theoretical friction factor for the same fluid flow set-up was computed using the Churchill equation. The percentage errors computed between the experimental and theoretical friction factors show that the data obtained from the experiment is not consistent with theory. The errors in both trials are both almost 100% and suggest that there may have been errors in performing the experiment and in the equipment used in the experiment itself. The experiment aims to determine the friction factor of a fluid moving through a straight pipe and to determine the effect of Reynolds number and relative roughness on the friction factor. Keywords: Fluid Flow, Reynolds number, Relative Roughness, Fanning Friction Factor

INTRODUCTION Due to viscous effects generated by the surface of the pipe in pipe flow, there occurs a loss in mechanical energy known as friction loss. Fiction loss has several causes including: conditions of flow, physical properties of the system, movement of fluid molecules against each other and against the pipe’s surface, and the bends and turns along the piping. The determination of friction factor is important in predicting the amount of mechanical energy loss due to friction, thus it is an essential tool in predicting the behavior of fluid flow systems. (Geankoplis, 2003) One of the accepted methods to calculate friction losses resulting from fluid motion in pipes is the use of the friction factor, f. The Fanning friction factor is a dimensionless number used to quantitatively describe the amount of energy loss due to friction. Essentially, it is related to the shear stress at the wall through the equation: (Green & Perry, 2007)

τ =0.5 fρ v

The fanning equation is obtained by performing a form of dimensional analysis on the variables that affect the friction loss, while the friction loss F is obtained through a mechanical balance across the pipe under the assumption that the pressure drop is solely due to the friction:

F=−∆ P/ ρ The objective of this experiment is to determine the friction factor of the fluid moving through a straight pipe using the Churchill equation and the Fanning equation. Consequently, an analysis and a comparison between the two friction factor values are to be performed. Additionally, it is also the purpose of this experiment to determine the effect of Reynolds number and relative roughness on the friction factor of the fluid flow. (Gutierrez & Ngo, 2005)

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As stated earlier, conditions of flow affect the amount of friction loss that occurs across the piping system. In theory for laminar flow, the friction factor is determined using the equation f=16/Re. Whereas for turbulent flow, the friction factor is obtained using the Churchill equation which gives f as a function of Re and the relative roughness, ε /D CITATION Gut05 \l 13321 (Gutierrez & Ngo, 2005) 0.9

1 0.27 ε 7 =−4 log( + ) D ℜ √f For experimental purposes, the friction factor, f, can be computed through an alternative solution using the fanning equation:

F=2 f u2 L/ gc D

Experiment 04│ Group No. 2│

MATERIALS AND METHODS The actual and experimental friction factors are obtained using the equation mention in the introduction and the properties and conditions measured for the flowing fluid in the given fluid flow set-up. The equipment used in the experiment include: a fluid flow setup, steel tape, thermometer, a stop watch and a calliper. The fluid used in the study is water. First, the piping system considered was isolated and primed. In priming, the pump was turned on to allow the water to pass through the pipeline and reach stabilization. The length of the straight pipe and its diameter was then measured and, the amount of water collected for a given time interval of one minute 1 of 3

was measured. The volumetric flow rate and the fluid velocity were then calculated. For the theoretical value, the temperature of the water was first determined thus, allowing for the determination of its properties using the ChE Handbook. The Reynolds number was then computed using these values and the Churchill equation given that the flow is turbulent. For the experimental friction factor, the pressure drop across the pipeline was measured using a manometer, then the friction loss was calculated which, in turn, was used to compute for the experimental friction factor using the Fanning equation. The percentage error among the two friction factor values was computed and, the procedure was repeated for a 2nd trial with different conditions. RESULTS AND DISCUSSION

Table 4.1 Measured and Computed Values

Trial 1 2.50x10-4 m3/s

Trial 2 2.50x10-4 m3/s

35.3678 m/s

35.3678 m/s

3x10-3 m

3x10-3 m

23.7 ℃

23.7 ℃

Experiment 04│ Group No. 2│

997.379 kg/m3

997.379 kg/m3

0.920775 cP

0.920775 cP

114930.57

114933.1231

1.7 cmHg

2.3 cmHg

2.1051 J/kg

2.8481 J/kg

1.0 m

1.0 m

4.57 x10-5 m

4.57 x10-5 m

0.01523

0.01523

ε /D

In this experiment, we’ve considered the mechanical energy lost due to friction, which is brought about by the type of fluid as well as the specifications of the pipe. And as followed in the procedure, the volumetric flow rate of the water, its velocity, and the manometer reading were recorded; the length, roughness, and inside diameter of pipe were measured; and the temperature of the water were obtained. Then the temperature-dependent properties of water were acquired, such as viscosity and density. The properties of the water are evaluated at the temperature of 23.7 degrees Celsius as was measured during the experiment proper. After which, the Reynolds number, mechanical energy loss due to friction, and relative roughness were calculated using the formulas provided. These values all together were utilized to compute for the theoretical Fanning friction factor using the Churchill equation since the fluid flow was found to be turbulent. Then, mechanical energy lost due to friction would later be used under the fanning equation to compute for the experimental fanning friction factor. All gathered data, for trials 1 and 2, are listed on Table 4.1. As seen on the table, the data from the first and second trial are almost the same.

Volumetric flow rate of the water, V Velocity of the water, u Inside diameter of the pipe, D Temperature of the water,

Density of the water, ρ Viscosity of the water, μ Reynold’s number, NRe Manometer reading, Rm Mechanical energy lost due to friction, F Length of the straight pipe, L Roughness of the pipe, ε Relative roughness of the pipe,

The results shown in Table 2 tell that there’s friction present especially near the walls of the pipe than that of the center. From this observation, we may also deduce that the velocity of the fluid would be faster in the middle part than that near the walls of the pipe. As seen on table 4.1, it is a turbulent flow and the friction factor is a function of both the Reynolds Number and the relative roughness of the pipe. It was observed that when Reynolds Number increases, the fanning friction factor also increases. Table 4.2 Experimental and Theoretical Friction Factor

Experimental Fanning friction factor, fexperimental Theoretical Fanning friction factor, ftheoretical % error

Trial 1 2.524x10-6

Trial 2 3.915 x10-6

0.011135

0.011135

99.98%

99.97%

Further, the percentage errors were computed as well, which gave a very high value, almost a 100%. This implies that the experiment proper is not a very good approximate. Or more realistically, the assumption that the pipe used is commercial steel pipe is in fact unsuitable since the one used is some kind of a plastic. Another cause of error is due to number of factors which include both human and equipment errors, on how the students read the change in pressure and volume in the experiment. Also, it may be the damaged equipment itself due to age and wearing. CONCLUSIONS AND RECOMMENDATIONS 2 of 3

The experiment aimed to determine the friction factor of a fluid moving through a straight pipe and to determine the effect of Reynolds number and relative roughness on the friction factor.

measurement of the required parameters such as volume, pipe diameter and manometer reading. REFERENCES

The 1st objective of the experiment was not fully accomplished since the percentage error obtained was very high. The high discrepancy between the experimental and theoretical fanning friction factor implies that there were some errors made during the performance of the experiment or there may have been some problems with the fluid flow set-up used.

1. Geankoplis, C. J. (2003). Transport Processes and Separation Process Principles (4th ed.). Pearson Education, Inc. 2. Gutierrez, C. L., & Ngo, R. L. (2005). Chemical Engineering Laboratory Manual Part 1 3. Green, D., & Perry, R. (2007). Handbook, Perry's Chemical Engineers' (8th ed.). McGraw-Hill Professional.

The 2nd objective of the experiment was also not fully accomplished. Since the conditions used for the 1st and 2nd trials were the same, the Reynolds number and relative roughness were also the same. Thus the effect of changing the Reynolds number and the relative roughness could not be observed in the experimental data. A useful modification that can be done on the methods of the experiment is to use two different pipes in the 1st and 2nd trial. This will enable the students to see the effects of the Reynolds number and relative roughness on the friction factor through experimental data.

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It is also highly recommended to carefully follow the procedures stated in the laboratory manual and also to do a proper

Experiment 04│ Group No. 2│

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