Essay: Energy losses in pipes and fittings experiment

The energy losses in pipes and fittings experiment was conducted by Rylan Verge, Alice Huang, Erin Agbay, and William Olmsted. The purpose of this experiment was to develop an understanding of pressure losses in pipe flow. According to the memo, the team is part of a large consulting firm that is tasked with predicting the pressure loss along pipeline that is 15m long with a water flow rate of 25 imperial gallons per minute, so that the most cost-effective pumping unit can be installed accordingly. For this to be determined, a system containing copper pipes, pipe elbows, valves, a rotameter, and a pressure reader were used. The experimental procedure consisted of several steps. The first step involved determining the temperature of the water being used in order to find the proper density of the water at that corresponding temperature. Immediately after that, all valves were closed, and valves 14 and 16 were opened first so that the pressure losses between those two sections could be recorded. The water was then turned on and the rotameter was set to 25 initially, and the flowrate in kg/s was determined using a bucket scale. Once this was completed, the difference in pressure was recorded. The next tested flowrates were the rotameter readings of 45, 55, 65, and 75 respectively. The pressure differences were then recorded for each reading. The procedure was then repeated for valves 5 and 6, then 9 and 10, then 10 and 13 in order to analyze values and determine a trend in the pressure losses. The pipe lengths between each pair of valves were recorded so that the Reynolds number could then be calculated. A Moody chart was then constructed to help the group understand the relationship between the Reynolds number and friction factor. 25 gal/min is equivalent to 0.00157 m3/s; this value was converted to make terms simpler for Reynold’s number calculations. This friction factor obtained from the Moody chart was then used to determine the experimental pressure drop, which was found to be about 202.78 kPa. Then by using theoretical data, the pressure loss could be determined using the same method used to determine experimental pressure drop and was found to be about 87.12 kPa. The experimental pressure drop for the proposed pipeline was an overestimate, the result of a higher friction factor. This overestimate could be due to an inconsistent collection of data during the experiment. It is also possible that the best relationship between the Reynolds number and the friction factor could be an exponential relationship, as opposed to a linear one used in the experimental data. For the results obtained, it is recommended that an exponential relationship be used to determine the friction factor and furthermore, the pressure drop in pipes.
Introduction and Valid Equations
In the industry, many chemical processes consist of a network of piping similar to that simulated in this lab. These pipelines can transfer substances or ingredients from one area of the system process to another, usually in sequential order. The pressing issue that needs to be defined and overcome is energy loss in these piping systems, as they may cause major malfunctions in important chemical processes.
The general mechanical energy balance equation obtained from the lab notes can be used to find the pressure losses in the pipes specific to this experiment:
Where P is the static pressure, p is the density of the fluid, g is gravitational acceleration, z is the vertical elevation, V is the mean stream-wise fluid velocity, dW/dm is the amount of work done on/by the system per unit of fluid mass, and F is the energy loss between the two pipe distances due to friction.
F, being the energy loss due to friction, can be calculated by the following equation:
Where f is the “friction factor”, L is the pipe length, and D is the inside pipe diameter. The friction factor obtained from this equation paired with the relationship it shares with the value from equation (1) can be used as a way to check if the experimental findings obtained are accurate or inaccurate. The “friction factor”, f, demonstrates that the loss of friction in the experiment depends on the either turbulent or laminar flow of the fluid, the pipe dimensions, and the properties of the fluid under study.
The Reynold’s Number is an important property of fluids that helps predict flow patterns of different fluids based on its magnitude. It can be calculated using the following equation:
Where μ is the viscosity of the fluid, v is the kinematic viscosity, and Q is the volumetric flow rate of the fluid.
There are a few assumptions associated with this experiment, being that:
• the fluid is incompressible
• no work is being done on or by the system
With these assumptions in mind, the mechanical energy formula can be simplified to the following equation:
Experimental
Experiment Setup & System Diagram
As previously mentioned, a system containing copper piping, pipe elbows, valves, a rotameter, and a pressure reader was used to conduct this experiment. A large drum bucket and scale were also used to determine the volumetric flow rate of water at each rotameter reading. A diagram of the system set up can be seen below.
Figure 1: Experimental diagram of system used to determine the pressure loss in pipe flow.
Safety Considerations
There are several notable safety considerations associated with this lab that every group member had to be informed of and understand before conducting the experiment. First, the laboratory deals with water under high pressures, which may cause bursts in the pipes or in the rotameter if the flow rate was too high. For additional safety purposes not specific to this lab, the rotameter already does not exceed a value of 80. There are electrical outlets nearby to system, which if exposed to water, could induce electrical shocks to their surroundings. In order to avoid accidents in the working space, hard hats, lab coats and adjustable safety goggles were provided. Let it also be noted that water on the floor near the drum bucket and scale could be a potential slipping hazard due to spills while calculating mass flow rate.
Experimental Procedure
To begin the experiment, the water was turned on and allowed to run with all valves open to flush the system of water from precious experiments/use. After some time, an accurate reading of the water’s temperature could be recorded which then allowed for a corresponding density to be determined. It was outline in the lab files to begin analyzing pressure losses in the copper pipe between valves 14 and 16 first. The flow rate on the rotameter was then set to 25 and the pressure between the two valves was displayed by the screen. After, the system was purged and repeated with 3 separate pairs of valves (9-10, 5-6, and 10-13). Once the pressures had been documented in the lab book tables, the flow rate was then increased to read 45, 55, 65, and 75 respectively on the rotameter, where the procedure would be repeated for the list of valve pairs. The length of the pipe was measured using a retractable measuring tape; this value is a key component for calculating the Reynold’s Number. In order to validate the flow rate given by the rotameter, a drum bucket was filled in 10 second intervals at each rotameter reading in order to calculate the mass flow rate of the water in kilograms per minute.
Results and Discussion
The temperature of the water measured at the start of the experiment after flushing the system was found to be 3.8°C. The pipe diameter and length were measured to be 0.0254m and 2.134m respectively. The experimental data and overview of trials performed throughout the experiment can be seen in Table 4 of Appendix A. Several properties of the water were obtained from external resources and online files associated with the lab. Using the temperature of water from the experiment, the water density, dynamic viscosity, and kinematic viscosity were found and can be seen in Table 1 below, along with the summary of properties calculated in the lab. The summary of constants used for the calculation in this experiment can be found in Table 5 of Appendix A.
Table 1: Summary of the data collected during the experiment.
Using the appropriate values outlined in Table 1, a Moody chart was constructed to aid in studying the relationship between the two properties. This chart can be seen below:
Figure 2: Moody chart constructed for the experimental data obtained.
After plotting the values, a linear relationship between them can be seen. After converting the 25 gal/min to 0.00157 m3/s, the Reynolds number for the proposed pipeline was calculated using the properties for the water obtained in the experiment. The trendline from Figure 2 was then used to estimate the friction factor for the proposed pipeline using the Reynolds number found for the proposed flowrate. The friction factor was further used to calculate the pressure drop in the proposed pipeline. The calculated values for the proposed pipeline using the Figure 2 trendline are summarized in Table 2.
Table 2: Calculated properties for the proposed pipeline.
A second moody chart was then created using the theoretical data provided in the lab files for turbulent fluid in a smooth copper pipe specifically at 25 gal/min. This moody chart can be seen below:
Figure 3: Moody chart constructed for the theoretical 25 gal/min turbulent flow in a smooth copper pipe.
The friction factor associated with the appropriate Reynold’s number was calculated using the equation for the linear line of best fit seen in Figure 2. The friction factor was calculated to be 0.0052. A summary of the calculated data can be seen in the table below:
Table 3: Summary of properties from the Figure 3 trend line.
The two frictional factors calculated using the Reynolds number for the proposed pipeline are 0.0169 and 0.0052. The frictional factor calculated from the lab data is an overestimate compared to the theoretical friction factor calculated. This discrepancy could be due to the lack of a linear relationship between the Reynolds numbers and friction factors from the experimental data which also caused the estimated friction factor for the proposed pipeline to also be an overestimate. The pressure drop found in the experiment for the proposed pipeline was also an overestimate because the friction factor calculated was too large. The difference between these two values could be a result of inconsistent data collection. Although it seemed that the most suitable relationship between the Reynolds number and the friction factor was linear, the theoretical data demonstrated an exponential relationship. When testing the exponential relationship on the experimental data, it produced a smaller R2 value than the linear relationship, meaning it would be a worse fit than the linear relationship. It can be concluded that the linear relationship was then a better fit for the data, although this may not have been the case given a better sequence of data collection.
Concluding Statements and Recommendations
After conducting this experiment, the experimental friction factor determined for the proposed 25 gal/min flowrate pipeline was 0.0174. The experimental pressure drop calculated using this friction factor was about 202.78 kPa. Comparing this to the theoretical friction factor of 0.0052, the friction factor calculated in the experiment was vastly larger than the theoretical value. This resulted in a lower theoretical pressure drop of 87.12 kPa. These discrepancies are likely the result of inconsistent data collection and human error during the laboratory. However, it is possible that the relationship between the Reynold’s number and the friction factor from the experimental data does not have a linear relationship. Since a linear relationship was used to determine friction factor from the Reynolds number, this could account for the overestimation of the friction factor. This could have led to a higher pressure drop then expected. When testing the power law relationship with the experimental data, a lower R2 value was found then when using a linear relationship, leading to the assumption that a linear relationship best fit the collected data.
Other parameters worth investigating for this experiment could be the effect of temperature on the pressure drop, as this would affect the density of the fluid flowing in the pipes. Another parameter that worth studying could include the effect different materials have on the flow of liquids. Since the material of the pipes are in contact with the fluid, a change in material could have a drastic effect on the friction factor. In addition, wall roughness has a direct effect on friction factor, which comes from the chosen material. As a result, this would influence the pressure drop.
Since the theoretical data used a power law relationship when comparing the Reynold’s number to the friction factor, it is recommended that a power law relationship should also be used for the experimental data to obtain a more accurate pressure drop for the proposed pipe. Therefore, when installing the proposed pipeline, a power law relationship should be used to determine the most accurate friction factor and pressure drop. The company should use a pressure drop of 59.117 kPa so that the most cost-effective pump can be installed for their process.