For the main experiment, a set of values were recorded per assembly - namely, the manometer height difference and the flow rates from each of the flowmeters. 

Figure 4: Purging Air bubbles

Assembly 2, with a theoretical and experimental pressure drop of 782.692 Pa and 372.780 Pa respectively, started off a trend of large discrepancies between the experimental and theoretical values - these values had a percent error of 52.372%. This trend continued with Assembly 3 (13262.810 Pa compared to 2746.800 Pa) and Assembly 4 (22473.420 Pa compared to 4414.500 Pa) - the former had a percent error of 79.290%, and the latter had a slightly larger percent error of 80.357%. It should be noted that, despite these large differences, both the theoretical and experimental pressure drops tended to increase with the complexity of the assemblies. Furthermore, though the large difference in complexity between Assembly 2 and Assembly 3 easily explained the much larger experimental and theoretical pressure drop of the latter, it was surprising to see that Assembly 4 also had a similarly large increase in pressure drop despite only receiving a relatively small alteration on only one subassembly. 

Saying that, with correlations being weak and inconclusive throughout the experiment, a number of sources of error may have resulted in these discrepancies. 

Perhaps most significantly, theoretical pressure values were calculated using the K-value for when the valve was closed ⅓ of the way - in this experiment, however, the pressure valve may not have been precisely ⅓ closed. Considering that a ⅔ closed valve was only about a 20 degree turn away, and its K-value was 210 (as opposed to the much smaller 5.5 of a ⅓ closed valve), even a small fault in the estimation of ⅓ may have resulted in a much higher or lower K-value than assumed. Future experimentation should incorporate ball valves with markings indicating what amount they are closed to.

Figure 9: Measuring height difference

The validity of this relationship was tested with a similar procedure as in the first experiment; the relationship applied reasonably to each assembly, and it was used to find the flow rate of each flow meter. The velocity (v) of the fluid through the flow meter was then found using the flow rate and the cross-sectional area (A) of the pipes (which in turn is found using the radius R) : 

Using this velocity, along with density, diameter (D) and viscosity (μ), the Reynolds number (Re) for each assembly and subassembly was found:

At the same time, the total loss coefficients (K_L)of each assembly and subassembly were found by summing the loss coefficients of each pipe component - these were sourced from Experiment 5 - Pressure Drop in Piping Systems’ Table 1. From the same source, it is shown that the minor head loss (Pm = γhm) due to these components can be found using the total loss coefficient:

Furthermore, for Assembly 3 and 4, the minor head losses found by summing the minor losses of their respective top/bottom subassemblies and their left/right subassemblies for a total minor head loss throughout.

The total piping length (L) of each assembly and subassembly was found by summing the lengths of the inidividual straight pipes used (lengths of pipe components were assumed to be negligible compared to the straight pipes). 

Using the Reynolds number derived earlier, along with  a roughness value of ε = 0.0015, the friction factors (f) of each subassembly were found through the Haaland equation:

It should be noted that this equation only applies to turbulent flow (Re > 2600); all previously derived Reynolds numbers proved turbulent flow throughout the experiment. 

These, in turn, were used to find the major head loss (Pf = γhf) using another equation derived from Experiment 5:

Note that for for Assembly 3 and 4, as was done for the minor head losses, the major head losses throughout their subassemblies were again summed.

The sum of the total major and minor pressure drops in each subassembly led to a theoretical total pressure drop across the system:

Eq. 9

This was compared to the experimental pressure drop found earlier.

It should also be mentioned that due to the complexity of the experiment, time constraints prevented more trials from being executed - a larger sample size may have resulted in more valid results. Future experimentation would call for samples done at various flow rates, and thus various velocities - data collected with laminar or transitional flow would be valuable, as well as data with turbulent flow simply for comparison.

Figure 10: Evident leakage in the apparatus

Figure 2: Constant Head tank