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Problem Statement

The objective of this experiment was to operate and characterize a hydraulic fluid circuit with different pipe diameters by measuring the flow rate and head loss (pressure drop) of the water flow. The data collected was then plotted and compared with theoretical values in the form of a Moody Chart (using Reynolds Number and Friction factor) and a chart of Head Loss versus Volumetric Flow Rate. The lab studies turbulent flow phenomenon, as well as that of head loss due to internal friction, and the impact flow rate has on these properties.

Experimental System/ Procedure

The system is composed of four pipes of varying diameter (6 mm, 9 mm, 10 mm, and 14 mm) and several valves attached to the board (see Figure 1 in Appendix A for a visual representation of the experimental system). The valves are used to control the flow of the circuit. The pressure meter is attached to the inlet and outlet streams of the pipes via long, plastic tubing, and has two purge valves attached to it. There is a deposit basin, a volumetric tank, and a pump (the hydraulic bench) placed at the back of the board to help manipulate the fluid circuit.

Once the hydraulic fluid circuit and water tank was setup as described in the instruction manual, it is important to ensure that the pipe with the diameter being tested is open. This prevents the pump from getting “deadheaded”, or damaged. Then the water may be allowed to flow through the circuit by opening the red inlet valve at the bottom of the apparatus.

The first stabilized pressure drop between the inlet and the outlet water was measured with a hand-held pressure meter, the setup of which is also described in the instruction manual. To measure the flow rate, the drain in the outflow catch basin must be blocked off via a ball-shaped plug, and the water allowed to accumulate into the volumetric tank. The time it takes for the water level within the tank to reach a predetermined volume was then measured via stopwatch and recorded in an excel file (Table 1 in Appendix B).

When switching out the pipes, the water flow was changed by opening another diameter pipe first and then closing the previous pipe, to avoid deadheading. After all the measurements for all pipe diameters and flow rates were measured, the system was turned off: this was accomplished by hitting the “off switch” on the pump, and making sure a continuous flow path was available (valves between the inlet and outlet were opened) to prevent unanticipated pressure or fluid buildup.

Experimental Methods

To start the experiment, the system had to reach steady state. The system was determined to be in steady state after the data readout on the pressure meter converged to a reasonably consistent range (there was a good deal of fluctuations due to, presumably, the turbulent nature of the water flow).

In finding the flow rates, one person monitored the water level on the volumetric tank while simultaneously operating a stopwatch. For lesser flow rates, the targeted volume (for use in the flow rate calculations) was lowered: the maximum volume measured was 5 L, followed by 2 L, then 1 L.

The varied parameters were pipe diameter (6 mm, 9 mm, 10 mm, and 14 mm) and flow rate. To vary the flow rates, the red inlet valve at the bottom of the apparatus was rotated to varying extents between being nearly closed to fully open, and adjusted according to the corresponding readout on the pressure meter to ensure a sufficient range of data points. As the readout from the pressure meter could be directly added to a graph (see Figure 2 in Appendix B), the pressures that needed to be targeted were able to be determined as the experiment proceeded.

This process was repeated three times for each of five different flow rates, for each of the four different pipes (resulting in sixty measurements). This data was then averaged (see Table 1 of Appendix B).

Results

The relationship between head loss and flow rate, as well as that of friction factor and Reynolds Number, closely match the theoretical trends - see the data curves on Figures 2 and 3 of Appendix B, comparing theoretical data to what was found experimentally. Thus, the data found in the experiment supports the established notions of how these factors vary against each other. In fact, the theoretical values for Reynold’s Number and Friction Factor compared so well with the experimental data, that the points would be indistinguishable on the graph (Figure 3) if not for the different symbiology. This graph also demonstrates that, under the tested conditions, the fluid was entirely within the turbulent regime (having a Reynold’s Number > 2300).

A standard deviation analysis was performed on the flow rate repetitions, with all data falling within two standard deviations - this value, two standard deviations, is represented by the error bars on Figure 2. As can be seen in the figure, the most consistent repeats occurred during the trials with smaller diameter pipes, with the 14 mm pipes having noticeable deviation bars and those of the 6 mm being almost nonexistent.

An error analysis was also performed, comparing the experimental flow rates with the theoretical values. As can be seen in Table 3 of Appendix B, larger errors occurred during larger pipe diameters, faster flow rates, or lesser head losses. Based on this, the data is most trustworthy for smaller diameters and slower flow rates. Before using the data for larger diameters or faster flow rates, additional trials or repetitions should be considered.

However, based on the behavioral consistency of the data with theoretical trends, this experiment appears to be relatively reproducible. Some limitations do arise when considering external environmental pressure: having a greater or lesser pressure acting on the outlets (as would be the case should the experiment be reproduced at different elevations) could substantially impact the head loss. Having fluids of different compositions (for example, water with more or less impurities present) would also have some effect on the physical properties of the flow, as would having fluids at different temperatures.

Conclusions and Recommendations

The trends found in lab have a high level of applicability in industrial processes. Varying the pipe diameter has drastic effects on internal pressure changes, so understanding how the equipment will need to be adjusted (pumps, valves, etc.) for what pipes are being used is essential. Likewise, understanding what effect the flow rate has on the internal pressure of the process is incredibly important, as pipe connections and valves are only operable within certain pressure ranges.

Due to the increasing amount of error between the theoretical and experimental data, some revisions may need to be made on the next run. As the most error occurred at higher flow rates, more volume should be measured per timing (in the lab, the maximum volume used for flow rate calculations was 5 L, and although it may take longer, 10 L may result in more consistent numbers).

Alternatively, more repetitions could be run, which would require more efficient time usage. A large limitation on this efficiency of time usage was the lack of prioritization: rather than having a more in-depth focus on Experiment A (the only one that was run from the prelab), the arranged plan and procedure encompassed all four experiments, in somewhat lesser detail.

Calculating the theoretical values could also be improved. As it stands, at least two values are needed to be estimated - in this lab, Head Loss and the Friction Constant were chosen. Knowing what range of flow rate the Hydraulic Bench is capable of producing would help give a better idea of estimates (or, alternatively, what range of friction factors or head loss is to be expected, or a reasonable value for the friction constant).

The outflow tubes could also benefit from being better secured. For the most intense flow rates, the amount of liquid within the deposit basin (the area acting as a buffer during drainage) occasionally got to such a high quantity that the outflow tubes moved around. This repositioning was noted to have substantial impacts on the head loss, and the tubes had to be readjusted before more repetitions could be performed.