lab 2 experimental methods

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THE UNIVERSITY OF ILLINOIS AT CHICAGO ME 341-EXPERIMENTAL METHODS IN MECHANICAL ENGINEERING Spring 2024 Centrifugal Pumps Experiment # 2 Submitted by: 2/23/2024 1 Background Centrifugal pumps are mechanical equipment that moves fluid by transferring rotational energy from motor driven impellers. Testing for centrifugal pumps is done experimentally because pump head, hydraulic power, and efficiency are all dependent on flow rate and

rotational speed [1]. One way to increase the pump head of a centrifugal pump is to connect multiple pumps in series. Another way to increase the pump head is to change the impeller diameter. Pump’s with a larger impeller diameter have a high pump head pressure when flow rate and rotational speed are held constant. The theoretical head is linearly negatively correlated with flow rate but due to frictional losses the actual head is less than the theoretical value. Hydraulic power is the power gained by the fluid. A pump’s efficiency is power gained divided by the fluid divided shaft power driving the pump shaft power driving the pump. The purpose of this experiment is to examine the centrifugal pumps of single speed, of a variable speed and two pumps in series in series. As a team and through our experiments with centrifugal pumps, we’ve gained insights of pump performances and operations. We were able to observe flow rate, pressure, and the power consumption. Performing single pump analysis we saw its performance and effectiveness with just one pump. We also looked at the performances of pumps in a series and its efficiency for moving water around. For a single pump we looked at various speeds and the pressure at certain speeds depending on the inflows and outflows of the pump. It just is not that efficient as it also wastes the same amount of energy as the pumps in the series do. Single pumps would not be so practical in an industrial setting that needs a lot of water, it would not be efficient and one would really need a single pump on a smaller scale. It would be effective on an agricultural level, or anywhere where water might not be moved around too much such as a city's sewer system. For a pump in a series we were able to observe the total head produced by the system in pressure delivery. We tested out different speeds and different pressures. We also noticed it needed the same amount of volts as the single pump. It was a lot faster than a single pump at all speeds. Multiple pumps working will produce more pressure. Having pumps in a series can also be beneficial if one pump fails, then there would be another left over to do any work. With the ability to distribute workload on multiple pumps, it improves the systems reliability and performance. Pumps in a series just seem to be more beneficial in an industrial setting where you might need to move a lot of water. It gave us an idea how pumps in a series can also be beneficial to water distribution systems and sewer lines. Any setting that needs higher water pressure will benefit from using pumps in a series. 2 Results Maximum pump efficiency is discovered through experimental testing. These results show the effects of placing pumps in different configurations; isolated, in parallel and in series. The following analysis calculates and compares flow rate, pump head and efficiency of these configurations. Figures 12-14 display curves for the derived theoretical pump heads by

combining pressure heads of the single speed pump and variable speed pump and comparing them to the experimental P1 and P2 in series. The pressure head readings were graphed with respect to flow rate. This was reiterated for 2000, 2200, and 2400 rpm. 2.1 Single Speed Pump Analysis The first trial involves a single pump with varying flow rate. Flow rate is calculated by using the formula . The hydraulic bench outputs values with units of liters which are 𝑄 = ∆? ∆? (1) converted to for calculations with a conversion factor of . The pressure is measured by 𝑚 3 1 1000 a Bourdon tube.Figure one shows how the pump head increases as the flow rate decreases. Figure 1: Pump Head versus flow rate for a single non-variable pump. 2.2 Variable Speed Pump Analysis

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A single pump running at different RPMs shows how flowrate and angular speed of the impeller effect the output pressure of a single pump. Figure 2 shows the performance characteristics of pump head, shaft input power, and pump efficiency for P2 running at 2000 RPM. Shaft power started at 148 watts and remained constant throughout. Efficiency % started at 6% and increased two times to a final efficiency of 8%. Head pressure started at 7m and decreased three times to 4m throughout the flow rate. Figure 2: Pump head, shaft input power, and pump efficiency as a function of flow rate for P2 at 2000 RPM Figure 3 shows the performance characteristics of pump head, shaft input power, and pump efficiency for P2 running at 2200 RPM. Shaft power remained constant at 160 watts. Efficiency started at 7%, increased to 11.5%, and dropped to 9%. The pressure head started at 9m and decreased down to 4m throughout the flow rate.

Figure 3: Pump head, shaft input power, and pump efficiency as a function of flow rate for P2 at 2200 RPM

Figure 4 shows the performance characteristics of pump head, shaft input power, and pump efficiency for P2 running at 2200 RPM. Work shaft power was constant from 160 with a slight increase to 163 watts. Efficiency started at 10%, rose to 13%, fell to 12%, and increased 0.5% again. The pump head started at 12m and kept decreasing throughout the flow rate down to 4m. Figure 4: Pump head, shaft input power, and pump efficiency as a function of flow rate for P2 at 2400 RPM Figure 5 shows head coefficient vs flow coefficient at 2000, 2200, and 2400 rpm. 2000 rpm displayed the lowest head pressure throughout except at 0.00035 flow coefficient where it began to increase. 2400 rpm showed highest head coefficient from a 0 to 0.00025 flow coefficient. 2200 rpm showed the highest head coefficient from 0.00025 to 0.004 flow coefficient.

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Figure 5: Head coefficient vs flow coefficient for 2000, 2200 and 2400 RPM Figure 6 shows the hydraulic coefficient vs flow coefficient at 2000, 2200, and 2400 rpm. At 2000 rpm, the hydraulic coefficient remained constant with a miniscule increase around a flow coefficient of 0.0002. At 2200 rpm, hydraulic coefficient remained constant with a miniscule increase at 0.00035 flow coefficient. At 2400 rpm, the hydraulic coefficient also remained constant, however at 0.0002 flow coefficient it showed a steeper increase in hydraulic coefficient compared to 2000 and 2200 rpm.

Figure 6: Hydraulic power coefficient vs. flow coefficient for 2000, 2200 and 2400 RPM

Figure 7 shows the efficiency coefficient vs flow coefficient at 2000 RPM, 2200 RPM, and 2400 rpm. At 2400 rpm, the efficiency coefficient was highest with 13% at 0.00015 m^3/s and maintained higher efficiency overall compared to 2000 and 2200 rpm. 2000 rpm showed the lowest coefficient performance from 6% to 7%. 2200 rpm showed a high peak efficiency of 11% at 0.00033 m^3/s. Figure 7: Efficiency coefficient vs. flow coefficient for 2000, 2200 and 2400 RPM Using pump laws one can theoretically analyze a similar pump with a different impeller speed. Using the equation the values of can be determined. . Figure ? ? = 𝑄 1 ω 1 ? 1 3 = 𝑄 2 ω 2 ? 2 𝑄 2 ℎ 2 = ℎ 1 ? 2 2 ? 1 2 X shows hp vs. Q from P2 (measured values) at 2200 rpm. As Q increases the pump head decreases. Figure 8 shows the theoretical flow rate vs. pump head of a pump similar to P2 with an impeller diameter of 0.1 m at 2200 RPMS. Decreasing the impeller diameter decreases the pump head and the flow rate.

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Figure 8: Flow Rate vs. pump head of P2 running at 2200 RPMS with impeller size 0.15 diameter in blue and impeller size 0.1 diameter in orange. Control Valve Position Description Volume [L] Time [s] Inlet pressure head @ discharge manifold [m H20] 1 Shut-off 0 N/A 24 2 Partially open 10 26.23 18 3 Partially open 10 18.57 12 4 Partially open 10 14.33 6 5 Full open 10 12.21 0 Table 1: Single Speed Pump P1

Valve Position Description Speed [RPM] Volu me [L] Time [s] Inlet pressure head on P2 [m H20] Outlet pressure head on P2 [m H20] Voltage [V] Curre nt [A] 1 Shut-off 2000 0 N/A 0 9 159 1.19 2 Partially open 2000 5 40.74 0 7 159 1.19 3 Partially open 2000 5 30.47 0 5 159 1.19 4 Partially open 2000 5 21.98 -2 2 159 1.2 5 Full open 2000 10 33.29 -4 0 159 1.21 1 Shut-off 2200 0 N/A 0 11 173 1.18 2 Partially open 2200 5 41.22 0 9 173 1.2 3 Partially open 2200 5 25.1 0 7 173 1.21 4 Partially open 2200 5 19.33 -2 5 173 1.21 5 Full open 2200 5 13.68 -4 0 173 1.23 1 Shut-off 2400 0 N/A 0 13 187 1.23 2 Partially open 2400 5 30.75 -1 10 187 1.23 3 Partially open 2400 5 19.83 -2 7 187 1.25 4 Partially open 2400 5 14.81 -3 3 187 1.26 5 Full open 2400 5 11.93 -5 0 187 1.28 Table 2: Variable Speed Pump P2

Valve Position Description Speed [RPM] Volu me [L] Time [s] Inlet pressure head on P2 [m H20] Outlet pressure head on P2 [m H20] Voltage [V] Curre nt [A] 1 Shut-off 2000 0 N/A 25 34 159 1.17 2 Partially open 2000 5 18.38 21 26 159 1.19 3 Partially open 2000 5 10.78 17 18 159 1.21 4 Partially open 2000 5 8.21 13 10 159 1.22 5 Full open 2000 5 7.56 8 0 159 1.23 1 Shut-off 2200 0 N/A 25 36 173 1.18 2 Partially open 2200 5 15.95 20 27 173 1.22 3 Partially open 2200 5 10.81 16 18 173 1.24 4 Partially open 2200 5 8.53 11 9 173 1.25 5 Full open 2200 5 6.9 7 0 173 1.26 1 Shut-off 2400 0 N/A 25 38 187 1.2 2 Partially open 2400 5 18.32 21 30 187 1.28 3 Partially open 2400 5 11.11 16 20 187 1.3 4 Partially open 2400 5 8.56 11 10 187 1.32 5 Full open 2400 5 6.81 6 0 187 1.35 Table 3: Trials of Pumps in Series P1+P2.

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2.3 Pumps in Series Analysis After running experiments that isolated P1 and P2 they were placed in series to show how that configuration increases the pressure. Figure 9 shows pump head (m) vs flow rate (m^3/s) for single speed pump p1, variable speed pump p2, and P1 + P2 series pump. The series pump showed higher pressure readings up until a flow rate of 0.0005 m^3/s where the readings matched P1 pressure head then fell lower than P1 pressure head afterwards. P2 showed the lowest pressure head readings overall. Figure 9: Pump Head, Hp (m) vs flow rate, Q (m^3/s) at 2000 rpm with curves of P1, P2, and P1 and P2 in series.

Figure 10 displays how variable speed pump 1, variable speed pump 2, and P1 + P2 series pumps’ pressure head readings (m) change with respect to flow rate (m^3/s). P2 readings displayed lowest pressure head readings, P1 displayed moderate pressure readings, and P1 + P2 displayed the highest pressure readings. However, around 0.0005 m^3/s, P1 showed higher pressure readings. Figure 10: Pump Head, Hp (m) vs flow rate, Q (m^3/s) at 2200 rpm with curves of P1, P2, and P1 and P2 in series. Figure 11 displays how variable speed pump 1, variable speed pump 2, and P1 + P2 series pumps’ pressure head readings (m) change with respect to flow rate (m^3/s). The behavior of the three curves was similar to Fig. 10. However, the pressure head readings were lower by 1m to 3m in contrast to fig. 10 data.. P2 readings displayed lowest pressure head readings, P1 displayed moderate pressure readings, and P1 + P2 displayed the highest pressure readings. However, around 0.0005 m^3/s, P1 showed higher pressure readings.

Figure 11: Pump Head, Hp (m) vs flow rate, Q (m^3/s) at 2400 rpm with curves of P1, P2, and P1 and P2 in series.

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In figure 12 for 2000 rpm, the experimental curve from 0 m^3/s to 0.000175 shows higher pressure head values relative to theoretical head pressure. At 0.0002 m^3/s, theoretical and experimental pressure head values match. After 0.000275 m^3/s, experimental pressure head value significantly differed from theoretical. Figure 12: Pump Head, Hp (m) vs Flow Rate, Q (m^3/s) with curves of the pump heads for derived theoretical and experimentally obtained at 2000 rpm. At 2200 rpm, figure 13 shows similar behavior to fig. 12 at 2000 rpm in terms of behavior. From 0 m^3/s to 0.0001 m^3/s, experimental pressure head was higher, 0.0013 m^3/s shows a matching pressure head value, and experimental deviates from theoretical after. Additionally, the experimental curve deviates apart earlier at 0.0002 m^3/s in comparison to fig. 12.

Figure 13: Pump Head, Hp (m) vs Flow Rate, Q (m^3/s) with curves of the pump heads for derived theoretical and experimentally obtained at 2200 rpm. At 2400 rpm in fig. 14, the behavior of the curves were similar again. Experimental curve starts with higher pressure head values from 0 m^3/s to 0.0002 m^3/s, matches the pressure head at 0.0002 m^3/s, and then departs from the theoretical curve afterwards.

Figure 14: Pump Head, Hp (m) vs Flow Rate, Q (m^3/s) with curves of the pump heads for derived theoretical and experimentally obtained at 2400 rpm. 3 Discussion For a centrifugal pump the pump head ( decreases as the flow rate increases. This ℎ ? ) occurs because frictional losses within the pump increase which reduces the head pressure produced by the pump. The shaft input power ( ) initially increases with an increase in flow ? ? rate, it reaches a maximum power, and then decreases. This occurs because the shaft input power is related to the product of flow rate, pump head, and fluid density, considering pump efficiency. Pump efficiency ( η ) has a bell-shaped curve as a function of flow rate. There is an optimum flow rate at which the pump operates at maximum efficiency. This is because at very low or high flow rates, the pump operates inefficiently due to factors like hydraulic and mechanical losses. Increasing the pump speed results in increases in flow rate, head, and power. The head coefficient relates the ratio of the head produced by the pump to the kinetic energy per unit weight imparted to the fluid by the impeller. The flow coefficient relates the flow rate of the pump relative to its size and speed. The hydraulic power coefficient describes how efficiently the pump converts the kinetic energy in the fluid flow into mechanical power. Figure 6 shows a relatively flat hydraulic power coefficient vs. flow coefficient graph. That means that the system operates with stable efficiency across different flow conditions. The pump is capable of handling variations in flow without significant losses in hydraulic power

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efficiency. Figure 7 shows that the pump is most efficient at each rpm at different flow rates which is what the theory for the experiment predicts. The pump scaling laws show that decreasing the impeller diameter results in a decrease in the flow rate. This makes sense because a smaller impeller moves less fluid through the pump for each rotation. The pump head is proportional to the square of the impeller diameter. Reducing the impeller diameter therefore decreases the head. A smaller impeller transfers less mechanical energy to the fluid which leads to a lower elevation that the fluid can be pumped. However, a reason to decrease the impeller speed is that the power required to operate a pump is proportional to the cube of the impeller diameter. Therefore in applications where a smaller impeller can achieve acceptable levels of flowrate and pressure the smaller impeller can save operational power costs. 4. For pumps in series, plot the theoretical pump head vs. flow rate curve derived from the individual pump head vs. Q of the two pumps. Compare this theoretical plot with the one that is experimentally obtained. In all three RPM settings tested, a distinct trend arises. For lower flow rates, the observed experimental curve is higher than predicted theoretically. This discrepancy could stem from measurement error in the bourdon gauge or the exclusion of the measurement of inlet pressure of the single speed pump. As flow rate increases, the experimental curve falls beneath the theoretical, with an increasingly steep negative slope. This is anticipated given the relationship that losses escalate due to the square of velocity. Author Contribution and Teamwork 4 References [1] Department of Mechanical and Industrial Engineering. “Experiment #2: Performance of Centrifugal Pumps.” Chicago, IL: University of Illinois at Chicago, Fall 2022. [2] Figliola, R., and D. Beasley. “Theory and Design for Mechanical Measurements, 6th Ed.,” Hoboken: Wiley, 2015. 5 Appendix: Sample Calculations Flow Rate 𝑄 = ∆? ∆? 1𝑚 3 = 1𝐿 1000

18 26.23*1000 = 0. 00068624 Hydraulic Power ? 𝑓 = 𝑄γℎ ? = ? 𝑓 0. 000123 · 9800 · 7 = 8 Pump Shaft Power ? ? = η 𝑚???? 𝐼? ? ? = 0. 75 · 159 · 1. 19 = 142 Pump Efficiency η ??𝑚? = ? 𝑓 ? ? η ??𝑚? = 8 142 = 0. 0593 = 5. 93% Pump Scaling Laws ? ? = 𝑄 1 ω 1 ? 1 3 = 𝑄 2 ω 2 ? 2 3 𝑄 2 = 𝑄 1 ? 2 3 ? 1 3 𝑄 2 = 0.000124*.1 3 .15 3 = 3. 59 * 10 −5