Results and discussion: In the calculation part, we yielded the flow rate of water inside a pipe using two approaches. In the first method we used...
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Results and discussion: In the calculation part, we yielded the flow rate of water inside a pipe using two approaches. In the first method we used the pressure drop, which is caused by orifice or venturi meters, readings to calculate the flow rate. Secondly, we used the volume and time readings to obtain flow rates (Q m ). The values were compared utilizing the error percentage formula. It's noticed that the error range is relatively wide (0.1 % - 32%) for both the venturi and orifice meters and the values are mostly low. This can be referred to the uncertainties associated with measuring the volume, time, and pressure drop. A similar comparison was carried out but this time between flow rate reading s from a flow meter (that gives a direct reading of the flow rate) and the flow rate calculated by measuring volume and time. In this case, the error values were low and consistent. Using the flow rate values, three graphs were plotted. In the first graph, Q m values are plotted against flow rates measured by venturi meter (Q v ) the main observation is that not all data fit linearly, and this can be shown by the R 2 value (0.66) which is not so close to 1. In the second graph (figure 5), Q m values are plotted against flow rates measured by orifice meter (Q o ). In this graph, the R 2 value is closer to 1 (0.93) indicating a better fitting of plotted data. Figure 6 is representing a plot of Q m versus flow rate reading of the flow meter. Just like in figure 5, the R 2 value (0.93) indicates a good fitting of the data; this result is expected due to the low error percent values. The second part of analyzing our results involves plotting flow rate versus (P 1 – P 2 ) 0.5 to calculate the discharge coefficient (C d ) for both venturi and orifice meters (see figure 7 and figure 8). In both cases, linear regression was performed to find C d and after that the value was compared to the theoretical value using error percentage equation. In case of venturi meter, C d is found to be equal 1.12 which is quite away from the true value (0.98). However, the C d value of orifice meter was found to be closer to the true values. The experimental value is equal 0.67, while the true coefficient is equal to 0.60. The reason behind having different coefficients for each meter is related to the amount of pressure lost after passing each meter. Specifically, the orifice meter will cause more pressure loss so the actual flow rate is less than what is indicated by the manometer and a lower C d is considered. On the other hand, the vernturi's shape helps in restoring some of the pressure losses, thus a larger C d is considered. The final part of our data analysis is interpreting our flow rate results in terms of Reynolds number. For each meter, a graph of Re number against C d is plotted (figures 9 and 10). The orifice curve shows almost no change of discharge coefficient when Re number changes. Figure 11 confirms this observation since at the targeted Re range (more than 10 5 ) the values of C d are constant. While from the venturi curve (figure 10) it can be observed that as Re number increase the C d will increase. This relation will hold until reaching a coefficient value of 1. This result is also shown in figure 12, at which a similar behavior of C d values is exhibited at the same Re number range. Also, from figure 12 we can see that the maximum C d value is one this contradicts with our obtained curve at which values above one exist. Having values above one is not logical and resulted from errors involved in taking measurements. A value above one indicates that the actual flow rate is higher than the measured value and no pressure drops occurred at all.
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Conclusion: After measuring the flow rate of water in a pipe using various methods including venturi and orifice meters, the following results are obtained from analyzing these data: As the flow rate increase, the pressure drop will increase for both venturi and orifice meters. Generally, the discharge coefficient for orifice meter is ranging around 0.6 while for venturi it ranges around 0.98. Venturi coefficient is higher since the meter recovers most of pressure losses and the actual flow rates are close to the measured ones. For orifice meter, if the flow is highly turbulent the C d values would remain constant. For venturi meter, C d would increase with Re number but if C d exceeded one it will start to decrease. Having C d values above one shows effect of instruments' uncertainties on calculated data Discussions From Figure 7 we can see the parabolic relaTon between the pressure drop and the volumetric fow rate ±rom the shape o± the graph , ±or both theoreTcal and experimental data, which is expected ±rom the relaTon between them ? ?h?? = h h !"! ! ! . All the graph is in the !! turbulant region with Re >4000. In ²gure 8 by using the data o± the ±ricTon ±actor and Re we were able to obtain the ±ricTon ±actor general equaTon constants, k1= 0.389 and k2= -0.475 , using the power regression in Excel to obtain the equaTon. Finding the literature values wasn't done since that the name o± these constants is unknown. ³he reason ±or doing these pressure drop calculaTons is the importance o± the usage o± pipes in the industry. We need to calculate the ±ricTon ±actor ±or the material, length , diameter and ²´ngs o± pipe to design a pump.       f(exp) Knowing the amount o± energy loss or pressure drop will give us the work that needs to be added by using the pump to maintain the process. Also by knowing the relaTon o± it we can try to minimize whether with a smoother design or any other method that is eµecTve and economic. Conclusion ³here are the results that we got ±rom the experiment. 1- ³he increase o± the fow rate increases the pressure drop in the pipe. 2- Increasing the diameter or decreasing the length decreases the pressure drop in the pipe (pipe 2 h 0) 3- ³he relaTon between the ±ricTon ±actor is inversely proporTonal and the obtained equaTon is ? = 0.389 Re -0.475 with k1= 0.389 and k2= -0.475
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