Fluid Friction Lab Report

Abstract

This experiment was carried out to investigate the friction factor as well as the major and minor head losses because of friction in three different types of bore pipes, namely elbow pipes, expansion and construction pipes, and long pipes. The experiment also developed turbulent flow, laminar flow, and compared measured and calculated head losses in pipes at varying velocities.

Introduction and Theory

Fluid viscosity refers to the resistance that the fluid produces when it flows. The flow of a liquid depends on the Reynolds number as depicted in the equation below;

……………………………….. (Souchet et al., 2017).

Where,

• is the viscosity of the fluid
• is the Diameter
• is the Velocity
• is the density
• represents Reynold`s Number.

The major head loss is calculated using the equation

Alternatively, the minor head loss is calculated using the equation

Where

• loss coefficient,
• acceleration constant due to gravity
• fluid velocity
• pipe diameter
• pipe length
• coefficient of friction

A laminar flow refers to a flow in which a head loss is directly proportional to the velocity of the flow.

Where k is a constant and v is the velocity

On the other hand, turbulent flow can be defined as a head loss that is directly proportional to the sum of velocity power; that is

Where represents any number. The most important thing to is, head losses due to turbulent flow is more sensitive to velocity (Haddad, 2019).

Figure 1:  Relationship of head loss and velocity (Cerbus et al., 2017)

The transition stage is represented by the section circled, in which there is no proper relationship between V and H.

Apparatus

Caution

The apparatus uses high voltage electricity; hence, it requires a lot of careful handling of electrocution or electric shock. Additionally, the experimenter should also ensure that he or she does not utilize the submersible pump when the tank is empty. Ensure the lab assistant supervises any change made in the experimental procedure or design before undertaking any experiment. 

The experimental system is set up on a hydraulic bench to ensure facilities for volumetric measurements and water supply are on the bench.

The apparatus are:

1. A long pipe for major head loss,
2. An elbow and expansion and a constriction pipe for minor head losses.

• A manometer connected to pipes for reading the pressure difference between the pipes

The apparatus and equipment were as illustrated in Figure 2 and Figure 3. Figure 3 describes various parts of the experimental setup.

Figure 2 Fluid friction Experimental Setup

Figure 3: Experimental Setup Diagrammatic Representation (Buchholz et al., 2019)

Procedure

A centrifugal pump mounted on the inside of the hydraulics bench was used to pump water through the Fluid Friction Apparatus. The water was then allowed to flow via the connector in the channel placed on the desk via the flexible connecting hose, as illustrated in Figure 1. The water was then allowed to flow through selected test pipes. The flow rates via the apparatus were adjusted using the control valve operation on the hydraulics bench. A system of isolating valves was then used to control the flow path via the network of the pipe friction by closing and opening the valves as much appropriate as possible. The dump valve was lowered upon stabilization of the test conditions, retaining the water in the tank. This step was followed by recording the volume and the timings as the level of water rises in the tank.

Further, also recorded was the head loss due to pipe friction through measurements of pressure readings at various patter points on the pipe network. The pressure loss along a pipe was measured by connecting the pressure measurement device. This step first involved expelling any volume of air that could have been trapped in the pressure meter pipes before the readings were taken.

The water of known flow, as used in the experiment was made to flow through both the small and long bore pipes to observe the head losses due to friction. The setup began by first calibrating the apparatus before starting the experiment; the calibration was carried out by removing the trapped air bubbles from the linings of the connecting tubes that connect the pipes and the manometer. This step was followed by connecting the long hose to the manometers, then using the rotameter to set the flow rate to the required values. Subsequently, the changes in the manometer height were observed and recorded. Conversely, the time taken to fill the 10 liters empty tank was noted.  The same procedure was repeated for the other pipes the time taken recorded. The length and diameter of the pipes’ values were provided in the lab manual. The head losses were calculated using the equations presented above.

Results and Discussions

ϒ kinematic viscosity. Note that all units are taken in mm,

Table 1: Results for V1, V2, and V5

Figure 4: Velocity versus measured head loss for V1

Comment

Based on Table 1 above, the values of Reynold’s number in the 7^th row for the V1 pipe for the steady head loss ranges between 3000 and 7500, thereby ascertaining the shape of the graph. The graph illustrates a turbulent flow  in which n is given by the gradient of the figure, which is 2.6735.

Figure 5: Velocity versus calculated head loss for V

Comment

Similarly, based on Table 1 above, the values of Reynold’s number for the V1 pipe for the calculated head loss ranges between 3000 and 7500, thereby ascertaining the shape of the graph. The graph illustrates a turbulent flow  in which n is given by the gradient of the graph, which is 0.4833.

Figure 6: Velocity versus measured head loss for V2

The Reynold’s number from Table 1 for V2 of the measured head loss ranges between 18,000 and 33,000, which ascertains the relationship in the above graph (shape) (Haddad, 2019). The graph illustrates a turbulent flow  in which n is given by the gradient of the graph, which is 1.78433.

Figure 7: Velocity versus Calculated head loss for V2

Comment

The graph illustrates a turbulent flow  in which n is given by the gradient 1.78433.

Figure 8: Velocity versus measured head loss for V5

Comment

From the shape of the graph and Reynolds number, it can be concluded that the flow is turbulent, with the value of n as 0.7577. According to the graph, the value of V increases with a decrease in measured head losses.

Figure 9: Velocity versus calculated head loss for V5

Comment

From the shape of the graph and Reynolds number, it can be concluded that the flow is turbulent, with the value of n as 0.2609. According to the graph, the value of V increases with increase in calculated head losses.

 Calculations

We convert the flow rate   to m³/s by multiplying it by 2.7778 ×10^-7

Where ∆h represents a change in height, g is the acceleration due to gravity, and ρ is the density of water that is 1000kg/m³

Reynold`s number

,

D is the diameter (0.017m),   is 1×10^-3kg·m⁻¹·s⁻¹.

Experiment friction coefficient,

L is the length of the pipe (0.8m)

f <sub>Moody`s</sub> is the value of the friction coefficient that is read from the Moody`s chart at the particular values of the Re No.

Table 4: Expansion and Contraction Pipes Calculations

Flow rate in   is converted to m³/s by multiplying by 2.7778 ×10^-7

Change in pressure =

Where ∆h is the change in height, g is the acceleration due to gravity constant and ρ is the density of water that is 1000kg/m³.

Reynolds number,

Where, the diameter D is given as (D is 0.0284,   is 1×10^-3kg·m⁻¹·s⁻¹).

;

Where the outlet area is 6.33 ×10^-4 m² while the inlet area is 2.27×10^-4 m²,

Where the pipe length, L, is 0.125m

F _blasius = 0.3164/Re^1/4

Where D₂ is greater than D₁

Flow rate in  is multiplying by 2.7778 ×10^-7 to convert to m³/s

Change in pressure = ρg(∆h)

Where ∆h is the change in height, g is the acceleration due to gravity, and ρ density of water, which is 1000kg/m³

Reynolds Number ,

Where the diameter, D is given as 0.017m,   is 1×10^-3kg·m⁻¹·s⁻¹.

Where the outlet area is 6.33 ×10^-4 m² while the inlet area is 2.27×10^-4 m²

Experimental friction coefficient,

Where pipe length, L, is given as 0.125m

The loss coefficient,

Table 6: ELBOW PIPE (readings)

The readings for the elbow pipe were taken by connected the manometer tubes to the elbow and setting the rotameter as we had set for other pipes.

Figure 10: Moody`s Chart

Figure 11: Showing the general decrease in friction in the long pipe as the Reynolds number increases.

Conclusion

Based on Moody’s Chart, the frictional values obtained were nearly consistent with those of the long pipe values displayed in the literature. As such, the objective of this experiment was achieved since there was every pipe had head loss caused by internal friction of the pipes.

References

Buchholz, T., BorgWarner Ludwigsburg GmbH, 2019. Fluid friction clutch. U.S. Patent Application 16/135,565.

Cerbus, R.T., Liu, C.C., Gioia, G., and Chakraborty, P., 2017. Kolmogorovian turbulence in transitional pipe flows. arXiv preprint arXiv:1701.04048.

Díaz‐Damacillo, L., and Plascencia, G., 2019. A new six parameter model to estimate the friction factor. AIChE Journal, 65(4), pp.1144-1148.

Haddad, A., 2019. Evaluation and Correlation of Friction Head Losses in Smooth and Rough Pipes. The Eurasia Proceedings of Science Technology Engineering and Mathematics, 7, pp.357-362.

Souchet, D., Jarry, M., and Fatu, A., 2017. Performance characteristics of viscoseals in laminar and turbulent flow regimes. Tribology International, 114, pp.152-160.