Head Loss in Piping Systems and Centrifugal Pumps - Final Report ChE 0301, Tuesday A-5 Matthew Ball, Michael Hensler, Reinis Bergholcs, Will Humble, Krishna Gnanavel November 29, 2016 1 Table of Contents Page 1.0 Introduction and Background…………………………………………………………………4 2.0 Experimental Methodology 2.1.1 Equipment and Apparatus for Piping System……………………………………….8 2.1.2 Equipment and Apparatus for Centrifugal Pumps.………………………………….9 2.2.1 Experimental Procedure for Piping System………………………………………..11 2.2.2 Experimental and Procedure for Centrifugal Pumps………………………………12 3.0 Results 3.1 Piping System Results…..…………………………………………………………...14 3.2 Centrifugal Pump Results……………………………………………………………17 4.0 Analysis and Discussion 4.1 Piping System Analysis..…………………………………………………………….22 4.2 Centrifugal Pump Analysis…………………………………………………………..24 5.0 Summary and Conclusion………………………………….………………………………...26 6.0 References………………………………………………..…………………………………..29 Appendix A-1: Experimental Data………………………………………………………………30 Appendix A-2: Example Calculations…………………………………………………………...33 2 Nomenclature Head Loss Piping System Symbol Term t V Q u Re H H/L Ff e/D D k g 𝜌 Time Tank Volume Volumetric Flow Rate Flow Velocity Reynolds Number Head Loss Head Loss per Length Friction Factor Relative Roughness Pipe Diameter Overall Loss Coefficient Gravity Kinematic Viscosity Length of pipe Fluid Density Centrifugal Pump Symbol Term 𝜈 L H Q u A z P I V N T F Pf 𝜂𝑠ℎ𝑎𝑓𝑡 𝜂𝑡ℎ𝑒𝑟𝑚𝑜 𝜂𝑜𝑣𝑒𝑟𝑎𝑙𝑙 Pressure Head Volumetric Flow Rate Linear Velocity Throat Area Fluid Height Power Input (Mechanical) Input Amperes Input Voltage Rotations per Minute Torque Torque gauge reading Power Output (Fluid) Efficiency (Shaft) Efficiency (Thermo) Efficiency (Overall) Units and Value (if applicable) s m3 m3/s m/s dimensionless m m/m dimensionless dimensionless mm dimensionless 9.81 m/s2 m2/s m kg/m3 Units and Value (if applicable) m H2O m3/s m/s m2 m W amps V 1/min Nm N W dimensionless dimensionless dimensionless 3 1.0 Introduction and Background Pumps and piping systems are, and have been, widely used in the engineering field. Perhaps the earliest known use of a pump was in 2000 BC when the Egyptians invented the shadoof to raise water from large reservoirs, such as rivers [1]. About 800 years later, Archimedes developed the Archimedean screw pump, which is considered one of the greatest inventions of all time [1]. This invention was, and still is, used in irrigation systems and some sewage treatment plants. The centrifugal pump, which was used in this experiment, was invented by Denis Papin in 1687 and used for drainage [1]. Since then, centrifugal pumps have been further innovated to include more features to make them beneficial for practical and industrial applications. Some of the advantages of centrifugal pumps include their operating reliability, safety, long service life, versatility, and overall efficiency. In industry, pumps are implemented in many ways, from small laboratory-scale devices to large industrial units. Their main purpose is to transport fluids through piping systems. The energy industry primarily uses centrifugal pumps to transport fluids through piping systems and into reactors to produce power. Another common use for centrifugal pumps is in the watertreatment industry. They pump specific amounts of raw wastewater into and out of treatment plants. Although these examples are just a few applications of centrifugal pump technology, they are very useful in chemical processing industries. Concepts relevant to this process help draw conclusions to the technical objectives of this experiment. Figure 1 shows a diagram representing how a centrifugal pump works. Figure 1: Inside a Centrifugal Pump [2] 4 As pictured in Figure 1, fluid is suctioned into the inlet duct (D). An electrical motor (not pictured in Figure 1) rotates the shaft (A), which turns the impeller (B). The blades of the impeller project the fluid outward. The circular motion of the fluid, represented on the left-hand side of Figure 1, gives the fluid a high velocity. This high-velocity fluid then flows through the pump case (C) and into the volute (E), where the fluid is discharged. The pump case has a gradually increasing area, which converts the fluid’s velocity energy into pressure energy. Once the fluid has been discharged from the volute, it flows through a network of pipes. In the circuit, the pipes have a variety of straights, bends, elbows, or tees. Figure 2 is a generalized illustration of head loss in straight pipes. Figure 2: Head Loss in Straight Pipes As shown in Figure 2, fluid flows with a specified fluid velocity (u) along a pipe of length L and diameter D. At Point 1 in the pipe, the pressure head is given by h1, whereas the pressure head is given by h2 at Point 2. The difference in head pressure between these two points is denoted by hf. The source for this head loss through the straight length of pipe is due to the friction between the fluid and walls of the pipe. In addition to straight lengths of pipes in the pipe network, there also exists bends, corners, and elbows. The purpose for pipe fittings is to change the direction of the fluid flow. Figure 3 shows a generalized image of a pipe bend and the head losses attributed to it. 5 Figure 3: Head Losses in Pipe Bends In addition to the frictional losses between the fluid and pipe walls within the straight length of pipe, there also exists head loss due to the pipe fitting, which is known as “form friction” or “minor losses.” Table 10 in Appendix A-1 gives values of minor losses for various pipe fittings. As fluid flows through the bend, there is a force acting radially inwards on the fluid to provide the inward acceleration needed to change directions. This radial force results in an increase in pressure near the outer wall of the bend, starting at Point A and rising to a maximum at Point B. Additionally, a reduction of pressure near the inner wall gives a minimum pressure at Point C and a gradual rise in pressure from Points C to D. Thus, the fluid experiences a pressure gradient between A and B and between C and D. The fluid particles closest to the wall between these points have low velocities and cannot overcome the pressure gradient. This leads to a loss of fluid energy along the bend known as “bend loss.” The first technical objective for piping systems was to determine the head loss across a series of straight pipe sections of varying diameters and surface roughness at varying volumetric flow rates. The second technical objective was to determine the head loss across a series of bends and elbows of varying geometry at varying volumetric flow rates. To achieve each of these objectives, calculations of the energy dissipation due to head loss were performed. In both technical objectives, the head loss is quantified by, HL = Hupstream - Hdownstream, (1) 6 where Hupstream is the head loss from the upstream port and Hdownstream is the head loss from the downstream port. After the head loss is known, a graph can be created with the head loss per unit length versus the Reynolds number, which is calculated by, Re = 𝑢𝐷 𝑣 (2) In Equation 2, u represents the linear velocity, D is the diameter of the pipe, and v is the kinematic viscosity of the fluid. By graphing the head loss per unit length against the Reynolds number, numerous trends can be analyzed. These trends are shown and discussed later in the report. The first technical objective for the centrifugal pumps was to create performance curves to determine the respective best efficiency points (BEP) for single pump operation at speeds of 2000 and 3000 RPM. The second technical objective was to determine characteristic curves at 3000 RPM for the operation of Pump A and Pump B in parallel and in series. These curves are created by graphing the head, pump efficiency and power versus the volumetric flow rate. The BEP is found along the head curve at the maximum efficiency point. The calculations for the head, pump efficiency, power, and volumetric flow rate are discussed in this report, and a pictorial representation of the BEP is shown. 7 2.0 Experimental Methodology 2.1.1 Equipment and Apparatus for Piping Systems Figure 4 shows the entire piping system examined. Figure 4: Piping Apparatus The water basin is shown on the left of Figure 4 (1). The water flowing through the pipes empties into this basin. A rod was placed in a drain in the basin to allow water to accumulate. The target volume for the water in the basin was 15 L. Figure 4 also shows the combination of bends and straights in the pipes. To measure pressure differences caused by the effects of head loss, plastic tubes were used to connect the pipes to the piezometer, which is shown on the right of Figure 4 (3). The water was extracted through the tubes and flowed into the piezometer. The piezometer mimics the function of a manometer and measures differences in pressure between two points in the pipe network. This pressure difference reading helped with the calculation of head loss using Equation 1. 8 2.1.2 Equipment and Apparatus for Pumps Figure 5 shows the front end of the pumping system. Figure 5: Front End of Pumping System As shown in Figure 5, water is drawn from the blue basin and fed into Pumps A and B, (2) and (3) respectively. The suction valves (4) can be opened or closed to control the water inlet to the pumps. After water flows through the pumps, it is discharged into the pipe network. The rate at which the water is discharged from the pumps is controlled by the red discharge valves (5). The values for the suction and discharge pressures are determined from the pressure-gauge board (6). The cross-over valve (1) is used in the second technical objective to transition from parallel to series operation. The pumping power is determined by the current and voltage (5) supplied to the pumps, which is shown in Figure 6. The power supply can be adjusted by the variac wheel (7) on the electrical box. While only one electrical box is visible in Figure 6, an additional box exists directly behind the one shown. Each of these two boxes controls the power supply for their respective pumps. The power given to the pumps rotates the pump blades, which directly affects the velocity of the fluid. 9 Figure 6: Back End of Pumping System The water entering the rest of the apparatus first travels through a venturi meter (6) as shown in Figure 6. Figure 7 shows the anatomy of the venturi meter. Figure 7: Venturi Meter The diameters of the inlet and throat areas for the venturi meter are 55.6 mm and 30.9 mm, respectively. After proceeding through the venturi, the water is expelled into the other side of the water tank from which it was drawn. The basin has a setup called the V-notch. The V-notch is used to measure and confirm the volumetric flow rate of water through the system and to assist in headpressure calculations. The basin is separated into two sections, the suction channel and the discharge channel. Naturally, the volume of water in the discharge channel should be higher as water is being recycled through the system via the suction channel. To quantify the flow of water 10 from discharge to suction, a partition with a v-shaped opening is inserted. Figure 8 shows the setup of the V-notch flow inside the water basin. This partition allows for a height difference, which is used for calculations shown in the Results section. Figure 8: V-notch Wier 2.2.1 Experimental Procedure for Piping Systems The first technical objective was to obtain head loss for flow through straight pipes. The second technical objective was to obtain head loss for flow through bends and elbows. To begin, the valve on the panel was turned 90 degrees counterclockwise to allow water to flow through the pipe network and into the basin. The rod was placed in the hole in the basin to allow the water level to rise. Once the water level in the basin reached 0 L, a stopwatch was started. The stopwatch was stopped and the rod was removed from the basin when the water level reached 15 L. The time for the water to accumulate 15 L was recorded to determine the volumetric flow rate. Plastic tubes were connected from the pipes of interest to the piezometer. Once the column heights settled on the piezometer, the values were recorded to the nearest millimeter. The valve was then turned to the next position, and the new flow rates and column heights were recorded for each trial for further analysis. The valve positions and configurations of interest are illustrated in Table 1. Table 1: Ports and Valve Positions for Piping System Run 1: Circuit Light Blue Valve Positions 0.25 0.50 0.75 1.00 1.50 Type Upstream Port Downstream Port 50mm bend 15 16 100mm bend 17 18 11 Run 2: Circuit Light Blue Run3: Circuit Dark Blue Run 4: Circuit Gray Valve Positions 0.25 0.50 0.75 1.00 1.50 Type Upstream Port Downstream Port 150mm bend 19 4 26.2mm Smooth 10 11 Valve Positions 0.75 1.00 1.50 2.00 Type 13.6mm Smooth Upstream Port 13 Downstream Port 14 Mitre Corner 20 21 Elbow Corner 22 23 Valve Positions 1/4 3/8 1/2 3/4 Type Upstream Port Downstream Port 17mm Smooth 7 8 17mm Rough 31 30 2.2.2 Experimental Procedures for Centrifugal Pumps Technical Objective 1: Determine BEP for single Pump A operation With the valves in the closed position, the power to the Pump A variac unit was turned on. The variac was set to 40 V. Then, the suction valve to Pump A was opened, followed by the exit valve downstream from the venturi meter. The variac input was slowly increased until the voltage achieved 130 V. The tachometer was used to ensure a shaft speed of 2000 RPM. The voltage was adjusted if the tachometer did not give a reading of 2000 RPM. The voltage, current, V-notch height, torque, shaft speed, venturi pressure, suction pressure, and discharge pressure were recorded at this condition. The discharge valve was opened via a ⅙ turn counterclockwise, and the voltage was readjusted to 130 V (if necessary). The tachometer, again, ensured a shaft speed of 2000 RPM and each of the eight measurements were recorded. The discharge valve continued to be opened by a ⅙ turn, the shaft speed and voltage were readjusted to their respective values (if necessary), and all data was recorded until the valve was opened two complete turns. After the valve was opened two full turns, the discharge valve was closed and the V-notch was allowed to settle to below 15 mm. This process was repeated for a shaft speed of 3000 RPM and a voltage of 195 V. 12 After the discharge valve was opened two full turns under these conditions, the exit valve downstream from the venturi meter and discharge valve were closed. The variac setting was gradually decreased until it achieved 40 V. Then, the suction valve to Pump A was closed and the variac was adjusted to zero volts. Finally, the power to the Pump A variac unit was turned off. Technical Objective 2: Determine characteristic curves for Pumps A and B operating in series and parallel With all the valves in the closed position, the power to the Pump A variac unit was turned on. The variac was set to 40 V. The suction valve to Pump A was opened, followed by the exit valve downstream from the venturi meter. Then, the power to the Pump B variac unit was turned on, the variac was set to 40 V, and the suction valve to Pump B was opened. The variac input for Pump A and Pump B was slowly increased until the voltage reached 195 V and 200 V for Pump A and Pump B, respectively. The tachometer was used to ensure a shaft speed of 3000 RPM for both pumps. The voltage was adjusted if this speed was not obtained. The voltage, current, Vnotch height, torque, shaft speed, venturi pressure, suction pressure, and discharge pressure were recorded for both pumps at this condition. For Pump A, the suction pressure (measured in bars) was negative, which means that a vacuum exists. For Pump B, the suction gauge is a vacuum gauge and measured the suction pressure in inches Hg vacuum. The discharge valves for both pumps were opened via a ⅙ turn counterclockwise, and the voltages were readjusted to obtain 195 V and 200 V for Pump A and Pump B, respectively. The tachometer verified that the shaft speed remained at 3000 RPM, and each of the eight measurements were recorded at the ⅙ turn. The discharge valves continued to be opened by a ⅙ turn, the shaft speed and voltages were readjusted to their respective values (if necessary), and all data was recorded until the valves were opened two complete turns. After the valves completed their two turns, the discharge valves from Pump A and Pump B were closed, and the V-notch reading was allowed to fall to below 15 mm. Once the V-notch reading fell below 15 mm, the suction valve to Pump B was closed, and the cross-over valve from Pump A to Pump B was opened. The process was repeated by only turning the discharge valve from Pump B. After the valve was opened two full turns, the exit valve downstream from the venturi meter and the discharge valve for Pump B were closed. The variac settings for both pumps were gradually decreased to achieve 40 V. The cross-over valve to Pump B was closed, and the Pump 13 B variac was adjusted to zero volts. Then, the suction valve to Pump A was closed, and the Pump A variac was adjusted to zero volts. Finally, the power to the respective variac units was turned off. 3.0 Results 3.1 Piping Systems Results Data for both the centrifugal pump and the head loss in piping systems was collected via two experiments. The head loss in piping systems required measurements of pressures at various points along the rig, as well as the amount of time needed to fill a basin to 15 L. All the pressures were determined in units of mm H2O. Table 13 in Appendix A-1 displays the data collected for the head loss experiment for the first and second lab session. The raw data was used to calculate values that led to the overall roughness of the straight pipes. These values satisfy technical objective 1 and are displayed in Table 2. Table 2: Straight Pipe Results Technical objective 1 also required a plot of the head loss per unit length vs. the Reynolds number for each pipe section at each of the valve positions. Figure 9 shows a positive 14 power-based trend between the head losses per unit length and the Reynolds numbers. The values for the section between 26.2 mm smooth are shifted due to lower Reynolds numbers. Figure 9: Straight Head Loss per Length vs Re The 26.2 mm smooth pipe also had the largest inside diameter (ID) at double the value for the other sections. Additionally, this large ID section displayed head loss per unit length values that were about one order of magnitude smaller than the other sections of pipe at most valve positions. It was also observed that the rough section, 17 mm pipe, had some of the largest head loss per unit length values compared to the smooth sections. Technical objective 2 for the head loss experiment required calculations that led to the overall bend loss coefficient. These values are displayed in Table 3. 15 Table 3: Bends/Elbow Results When comparing the values of the bend loss coefficient for the elbow, mitre corner, and radius bends, it was found that bends had the lowest loss coefficient values, the elbow had midrange values, and the mitre corner had the largest values. The second technical objective also required a graph of the bends and corners head loss per unit length versus the Reynolds numbers with the 13.6 mm smooth straight pipe data as reference. This graph is displayed in Figure 10. 16 Figure 10: Bends/Elbow Head Loss per Length vs Re The overall power-based trend shown in Figure 10 is similar to the trend in Figure 9. The smooth pipe data was included in this graph as a basis for comparison with the bends. The smooth pipe shows the lowest average head loss per unit length over the span of the Reynolds numbers, while the mitre corner has the highest average head loss per unit length over the span of the Reynolds numbers. The overall values of head loss per unit length, similar to the bend coefficient values, were highest in the mitre corner pipe and lowest in the bend pipes. 3.2 Centrifugal Pump Results The second experimental system dealt with centrifugal pumps both individually and in series and parallel. Data for this system was recorded in Tables 12 and 13 in Appendix A-1. Technical objective 1 dealt with single pump operations at 2000 RPM and 3000 RPM. This objective required the calculation of values for head pressure (m of H2O), flow rate in m3/hr (using the v-notch and venturi manometer readings), fluid power (W), pump mechanical power (W) and pump efficiency (thermodynamic efficiency). These values are displayed in Table 4 for 2000 RPM and Table 5 for 3000 RPM. 17 Table 4: 2000 RPM Single Pump Results Table 5: 3000 RPM Single Pump Results The head pressure, pump mechanical power, and pump efficiency were plotted against the flow rate in Figures 11 and 12 for the 2000 RPM and 3000 RPM runs, respectively, to determine the BEP. The values for the BEPs are displayed in Table 6. Technical objective 1 also required a “prediction” of the values for flow, head pressure, and pump power at 3000 RPM 18 using the affinity laws for a centrifugal pump and the data from the 2000 RPM experiment. The predicted BEP value for 3000 RPM is also displayed in Table 6. Figure 11: 2000 RPM Single Pump BEP Plot Figure 12: 3000 RPM Single Pump BEP Plot 19 Table 6: BEP Values for Single Pump Systems The predicted BEP values are similar to the values from the experimental data at 3000 RPM and thus reaffirmed the calculations based on 3000 RPM. Technical objective 2 of the centrifugal pump system dealt with Pumps A and B in parallel and in series with each other. The same initial calculations used in objective 1 were required for objective 2. These values are displayed in Table 7 for the parallel pumps and in Table 8 for the series pumps. Table 7: Results for Pumps A and B in Parallel 20 Table 8: Results for Pumps A and B in Series The same BEP plots were also required with the values from Tables 7 and 8 and are displayed in Figure 13 for parallel and Figure 14 for series. Figure 13: BEP Plot for Pumps in Parallel 21 Figure 14: BEP Plot for Pumps in Series With the plots for the different pump setups, the BEPs were determined and are displayed in Table 9. Table 9: BEP Values for 2 Pump Systems When the pumps were run in series, the head valve pressure increased dramatically with very little change in flow rate compared to the single pump at 2000 RPM and 3000 RPM. Conversely, when the pumps were run in parallel, the flow rate increased with only small changes in head valve pressure compared to the single pump systems. 4.0 Analysis and Discussion 4.1 Piping System Analysis In the first technical objective for Head Loss in Piping Systems, one of the goals was to calculate the head loss in straight-pipe flow. This value of head loss varied with changing parameters of pipe diameter and volumetric flow rate, which was determined by the position of the opening valve. The examples for trends will be explained using the 26.2 mm straight pipe data. As shown in Table 2, the position of the valve increasing from 0.25 to 1.5 turns led to an increase in linear velocity, from 0.309 m/s to 0.598m/s. This was determined through Equation 3, 22 u = Q/A, (3) where a constant diameter led to a constant area of 0.000539 m2. This constant area resulted in an increased velocity with increasing volumetric flow. Another factor that grew with increasing velocity was the Reynolds number. Using Table 2, a change in velocity from 0.309 m/s to 0.598 m/s resulted in a linear increase of the Reynolds number from 4047 to 7838. The three other piping systems had diameters of 13.2 mm and 17.0 mm. These differences in diameter resulted in smaller cross-sectional areas of 0.000227 m2 and 0.000145 m2. These smaller areas would result in a larger change in velocity between the two valve positions, but still follow the same trend as the 26.2 mm pipe. The head loss was calculated through Equation 1 by using the height difference of water on the piezometer. Following a similar trend, the head loss of the piping systems increased with increasing linear velocity. Using Table 2 for the 26.2 mm pipe, head loss increased from 0.005 m to 0.023 m with increasing velocity, from 0.309 m/s to 0.598 m/s. The four straight pipes followed similar trends regarding head loss per length and Reynolds number, and this can be better represented through Figure 9. As the Reynolds number increased, so too did the head loss per unit length. In terms of the friction factor, the pipes had different trends. For the 13.6 mm smooth and the 17.0 mm smooth pipes, the friction factor decreased as velocity increased. With the 26.2 mm smooth and the 17.0 mm rough pipes, the friction factor increased, reached a maximum, and then decreased. The friction factor was calculated using Equation 4, Fd=HL/((L/D)*(u2/2g)). (4) The trends in area and Reynolds numbers do not correlate with the friction abnormalities. A possible source of error could have occurred with the piezometer not being calibrated properly. The final parameter analyzed for objective 1 was pipe roughness. These values were directly obtained using the Darcy friction factor in conjunction with the Moody chart. Therefore, the pipe roughness follows the same exact trend as the friction factors. With this, it is observed that increasing pipe roughness leads to decreasing head loss per unit length. The second technical objective for Head Loss in Piping Systems analyzed similar parameters to objective 1. However, the target changed from straight pipe flow to the bends/elbows of the system, which resulted in analysis of hbend and k-values. The bends/elbows followed the same initial trends as the straight pipes. As the volumetric flow rate increased, so too did the velocity. This ultimately led to increasing values of head loss and Reynolds number. Using the values for 50 mm radius bend from Table 3, increasing velocity from 1.13 m/s to 2.19 23 m/s led to an increase in head loss from 0.117 m to 0.402 m. These values of head loss also accounted for the geometry of the bend. For the elbow, mitre corner, and 100 mm radius bend, the head loss of the bend increased with increasing velocity and Reynolds number. For the elbow using Table 3, with increasing velocity from 0.63 m/s to 2.02 m/s, the bend head loss increased from 0.027 m to 0.26 m. However, for the 50 mm and 150 mm radius bends, there was an error as these values were determined to be negative. These values were calculated using Equations 5, 6, and 7, Ff = FD / 4, (5) Hfriction = Ff * (L/D) * u2/2g, (6) Hbend = HL - Hfriction. (7) A possible source of error could have been through an inaccurate piezometer reading or there could have been internal issues within the pipe and its walls. Finally, for all bends/corners, the value of friction factor decreased with increasing Reynolds number. Using Table 3 for the elbow system, with increasing velocity from 0.63 m/s to 2.02 m/s, the friction factor decreased from 0.033 to 0.025. When comparing the experimental k-values calculated in Table 3 to the literature values, there were major discrepancies. Due to the error of a negative bend loss calculation, the 50 mm and 150 mm bend resulted in a negative k-value. However, the elbow, mitre corner, and 100 mm bend produced viable values. The literature value of the elbow is 0.75 and the mitre corner is 1.3. The values comparing head loss per length and Reynolds number is shown in Figure 10, showing a similar trend to the straight pump experiments. 4.2 Centrifugal Pump Analysis The second experiment that was analyzed was the Centrifugal Pump system. The first technical objective focused on single pump operation at RPM’s of 2000 and 3000. Looking at Table 4 for 2000 RPM, upon opening the valve, the flow rate of water increased. With this, the head loss value decreased, starting at a maximum of 19.16 m and decreasing to a minimum of 4.82 m. The 3000 RPM run, using Table 5, followed a similar route, starting at 25.6 m and decreasing to 9.41 m. This occurred because the suction pressure was decreasing at a slower rate than the discharge pressure, resulting in overall head loss. Looking at the fluid power produced, with increasing flow rate, both 2000 RPM and 3000 RPM increased to a max and then started to decrease. The 2000 RPM experiment increased to 214 W at a 1/6 turn, then slowly decreased to ranges of 165-170 W from one rotation to two valve rotations. The 3000 RPM experiment 24 increased to a max of 681 W at a half turn, then slowly decreased to a value of 447 W at two full rotations. For both RPM’s, mechanical power steadily increased as the valve became more open. This power changed from 138 W to 435 W and 435 W to 1425 W for 2000 and 3000 RPM respectively. As the volumetric flow rate increased, so too did the torque, resulting in an overall increase in mechanical power. Finally, the thermodynamic efficiency was produced by comparing the fluid power versus the mechanical power. The trend followed that of the fluid power, increasing to a max and then decreasing further. The values were plotted against the flow rate in Figures 11 and 12. Using these charts, the BEP was determined through the efficiency curve and displayed in Table 6. The 2000 RPM BEP was calculated at 8.10 m3/hr and the 3000 RPM BEP was calculated at 9.47 m3/hr. When comparing the affinity laws prediction results to the actual experimental values for 3000 RPM, using Table 6, the values are fairly similar. The prediction yielded a flow rate of 12.2 m3/hr and a pressure head of 21.9 m, while the experiment produced a flow rate of 9.47m3/hr and a pressure head of 23.1 m. This resulted in a higher predicted efficiency of 65.5% compared to the experimental at 56.4%. The second technical objective looked at dual pump operation, with pump A and B running in series and in parallel. Beginning with series, the head loss had the same effect as single pump operations. The head loss started high and continued to decrease with increasing valve position. However, the quantitative value was much larger due to having two pumps in operation. At a closed position as seen in Table 8, the head loss reached a high of 52.7 m. This value would decrease to 8.5 m at two full rotations. The flow rate of the series pumps resembled that of a single pump at 3000 RPM, reaching a max at 18.9 m3/hr. The trend of the fluid power and mechanical power matched the single pump, however these values were doubled due to two pumps being operated; fluid power reached a high of 1584 W before decreasing to 438 W and mechanical power steadily increased to a max of 2929 W. Using Figure 14, the BEP of series pumps was reached at a flow rate of 18.1 m3/hr. This flow rate is greater than that of single pump operation with a larger head loss and much larger mechanical power produced. Because of this high mechanical power value, the thermodynamic efficiency is low value at 32.7%. In terms of parallel operation, a trend opposite to that of series occurred. The head loss of parallel operation resembled that of the single pump, yet the flow rate increased by a factor of two. Using Table 7, the head loss started at a high of 25.1 m and decreased to 12.5 m. Meanwhile, the flow rate increased steadily to a total of 37.9 m3/hr. In terms of fluid power, parallel followed a similar trend to single pump and series operations. However, due to having a 25 flow rate approximately double that of the single pump operation, the fluid power value was also doubled. The fluid power peaked at 1575 W, but only decreased down to 1294 W afterwards. In terms of mechanical power, the trend follows that of series pump operation due to having two pumps in operation. Because of this, the thermodynamic efficiency was calculated to be relatively high, going no lower than 45.4%. Using Figure 13, the BEP was determined to be at 20.8 m3/hr. Comparing parallel and series to single pump operation, the BEP’s have a higher flow rate in conjunction with a slightly lower thermodynamic efficiency, while being at similar head loss values. 5.0 Summary and Conclusions The centrifugal pump converts rotational kinetic energy into fluid pressure energy. An electric motor provides a fluid flow into an inlet duct which is then rotated by the blades of an impeller, which then flows into an expanding valve called the volute. The decrease in fluid velocity allows the pump to produce both pressure head and volumetric flow rate. The first experiment consisted of three circuits: Gray, Dark Blue, and Light Blue. The Light Blue circuit featured a smooth straight pipe with varying bends, roughnesses, and diameter sizes. Meanwhile, the Gray and Dark Blue Circuits featured a series of bends and elbows. These factors found in the pipe circuits affected the fluid head loss, the energy lost due to friction, flow direction, and pipe size. In the first lab session, the light blue circuit was used. The upstream/downstream port pressure (mm H2O) and drainage times were measured for each incremented valve position for the following designs: 50 mm, 100 mm, 150 mm bends and 26.2 mm smooth. In the second lab session, two different circuits were used, the Dark Blue and Gray circuits. Similarly, the upstream/downstream port pressures (mm H2O) and drainage times were measured for each incremented valve position for the following designs in the Dark Blue Circuit: 13.6 mm Smooth, Mitre Corner, and Elbow Corner. Lastly, the upstream/downstream port pressure (mm H2O) and drainage times were measured for each incremented valve position for the following designs in the Gray Circuit: 17 mm Smooth and 17 mm Rough pipe types. The objective for the first lab session was completed by calculating the volumetric flow rate (m3/sec), flow velocity, Reynolds Number, head loss, head loss per unit length, and friction factor based on the head loss for each valve position. The relative roughness of the pipe surface was determined by using the Moody chart. A figure showing the head loss per unit length versus 26 the Reynolds Number was prepared. These calculations determined the effects of pipe diameter size and surface area roughness on the head loss of a straight pipe. According to the calculations, as the Reynolds number increased, the head loss increased too. This trend was apparent throughout the graphs plotting head loss per unit length as a function of Reynolds number for all four pipe designs. Additionally, as the valve opened, the pipe allowed a larger volume of water to pass through. This phenomenon increased the linear velocity of the fluid which increased head loss. Lastly, the head loss increased as the pipe roughness increased; however, a few inconsistencies showed otherwise. This flaw was attributed to human error or the piezometer not being calibrated properly. The same variables were calculated for the second lab session in addition to the overall loss coefficient for the bends and elbows. A figure showing the head loss per unit length versus Reynolds number for each bend or elbow was prepared. The figure and calculations determined the head loss across a series of bends and elbows of varying geometry in the pipe circuits. The bends and elbows in this pipe system resulted in varying head losses for the fluid. The results showed the highest k-coefficient was associated with the mitre corner, followed by the elbow, and then the 100 mm bend. Negative k-coefficient values were calculated for the 50 mm and 150 mm bend type due to the error of a negative bend loss calculation. Similar to the straight pipe, the head loss increased with an increasing Reynolds number because the velocity of the fluid is greater, resulting in more resistance force from pipe walls, especially in sharp bends. The other experiment began by the operation of one centrifugal pump. The pump was configured and operated at two different shaft speeds, 2000 and 3000 RPM. As the pump operated, the voltage, current, venturi pressure, V-notch, torque, and suction/discharge pressure measurements were recorded with each 1/6 turn increment of the discharge valve. With this data, the experiment was guided by several objectives to help understand the usefulness of the pump. The head pressure was determined by calculating the difference between the suction and discharge pressure. The flow rate was found by using the V-notch and venturi manometer readings. Pump performance curves were made by plotting the head pressure, pump efficiency, and mechanical power versus flow rate. The BEP was determined for both 2000 and 3000 RPM along with the head pressure, pump efficiency, and pump mechanical power at that point. Lastly, scale-up predictions were made for 3000 RPM based on the experimental results from the data obtained at 2000 RPM for comparison. 27 As the flow rate increased, the head loss decreased because the suction pressure decreased at a slower rate than the discharge pressure. Fluid power increased to a max for both RPM’s, then decreased. Mechanical power steadily increased as the flow increased because the torque increased. The BEP for 2000 RPM was calculated at 8.10 m3/hr and for 3000 RPM, the BEP was calculated at a greater value of 9.47 m3/hr to match the higher mechanical power. The affinity law prediction for 3000 RPM was similar to the actual data collected. The pressure head predicted value was only 1.2 m H2O lower than the experimental value while the flow rate predicted value was 2.73 m3/hr higher than the experimental value. These calculations resulted in a higher predicted efficiency of 65.5% compared to the experimental at 56.4%. Next, both pumps were used in parallel and series with the same shaft speed of 3000 RPM. For the series operation, the suction valves were opened and the cross-over valve from Pump A to B was opened. Similar to the single pump procedure, the voltage, current, venturi pressure, V-notch, torque, and suction/discharge pressure readings were recorded with each 1/6 turn increment turn of the discharge valve. When the centrifugal pump was in series, the head loss was double the single pump’s head loss at 3000 RPM because the flow rate remained the same. Whereas in parallel, the head loss values were around that of the single pump’s because the flow rate doubled- causing a lower pressure difference between the discharge pressure and suction pressure. For series and parallel, the trend of the fluid and mechanical power matched the trend of the 3000 RPM single pump, but yielded different values. In parallel and series, two pumps delivered twice as much mechanical power than that of the 3000 RPM single pump. However, the fluid power for series and the 3000 RPM single pump were the same while the parallel pumps delivered twice the fluid power due to the doubled flow rate. Thermodynamic efficiency greater than 100% was detected for both series and parallel. The mishap was most likely due to the human error of inaccurately reading the torque values. This error led to a higher fluid power being calculated by mistake. Comparing parallel and series to single pump operation, the BEP’s have a higher flow rate in conjunction with a slightly lower thermodynamic efficiency, while being at the same head loss value. After analyzing the data from the centrifugal pump and piping systems, several conclusions were drawn. For the a single pump, as flow rate increased, head loss decreased and the BEP increased as RPM increased. Additionally, the affinity law was useful in predicting the flow rate, head loss, and efficiency of another RPM. In series, head loss increased by a factor of 2 compared to the single pump while in parallel the head loss stayed the same. The pumps in 28 series and parallel produced the most mechanical power but only the pumps in parallel produced the most fluid power because of the increased flow rate. For the piping systems, head loss increased with an increase in either the Reynolds Number or the pipe roughness. The pipe design with the highest roughness was the mitre corner, followed by the elbow, and then by the 100 mm bend. 6.0 References [1] P. Staff, "The history of pumps: Through the years," in Pumps and Systems. [Online]. Available: http://www.pumpsandsystems.com/topics/pumps/pumps/history-pumps-throughyears. [2] M. McMahon, "Pumping and Head Loss in Piping Systems," Michael McMahon, University of Pittsburgh, Jul. 2016. 29 Appendix A-1: Experimental Data and Results Table 10: Minor Loss Values for Various Pipe Fittings 30 Table 11: Centrifugal Pump Raw Data Session 1 Table 12: Centrifugal Pump Raw Data Session 2 31 Head Loss Piping Data Table 13: Head Loss in Piping Systems Data Session 1 & 2 32 Appendix A-2: Example Calculations Piping Systems: P31-P30 ¼ turn 1) Calculate Volumetric flow rate: Q =V/t Q = 0.015 m3/73.04s Q = 0.000205 m3/s 2) Calculate linear velocity u=Q/A u= 0.000205 m3/s / (pi * (0.007m)2) u= 1.33 m/s 3) Calculate Reynolds number Re = u*d/ν Re = 1.33 m/s * .014m/ (1.0x10-6 m2/s) Re = 18620 4) Calculate head loss HL = H1 – H2 HL = .590 m - .550 m HL = 0.04m 5) Calculate Friction Factor Fd = HL/ ((L/D) * (u2/2g)) Fd = 0.04m/ ((0.2m/0.014m) * (1.33(m/s)2/2*9.81m/s2)) Fd = 0.0310 - use chart to gather roughness data Bends & Elbows: P22-P23 elbow ¾ turn Steps 1-4 same as above 5) Calculate Ff Ff = FD / 4 Ff = 1.316 / 4 Ff = 0.0329 6) Calculate Hfriction Hfriction = Ff * (L/D) * u2/2g Hfriction = 0.0329 * (0.912m/0.0136m) * 0.63 (m/s)2/2* 9.81m/s2 Hfriction = 0.0446m 33 7) Hbend calculation Hbend = HL - Hfriction Hbend = 0.072m – 0. 0446m Hbend = 0.0273m 8) KB Calculation KB = 2*g/u2 * Hbend KB = 2 * 9.81(m/s2) / (0.63 (m/s)2 * 0.273m KB = 1.349 Centrifugal Pump: Single pump operation 2000 RPM 1/6 turn 1) Calculate HL HL = Hd – Hs HL = -1 * -0.12 * 10.1974428892 – 14* 0.7030889074 HL = 11.07 m H2O 2) Calculate volumetric flow Q = A* √2(𝜌𝐻𝐺 – 𝜌)𝑔𝛥𝑧/𝜌[(𝐴/𝑎)2 − 1]. Q = (PI*(0.0556/2)^2)*SQRT((2*(13600-1000)*9.81*0.5/100)/ (1000*(((PI()*(0.0556/2)^2)(PI()*(0.0309/2)^2))^2-1)))*3600 Q = 3.16 m3/hr 3) Calculate Fluid Power Pfluid = g * Q * HL * ρ Pfluid = 9.81 (m/s2) * 3.16 m3/hr * 1/3600 h/s * 11.07 m * 1000 kg/m3 Pfluid = 95.17 W 4) Calculate Mechanical Power Pmechanical = 2 * pi * N * 0.165 * F / 60 Pmechanical = 2 * pi * 2000 RPM * 0.165 * 6.5 N / 60 Pmechanical = 224.62 W 5) Calculate thermodynamic efficiency ηthermodynamic = Pfluid/ Pmechanical * 100% ηthermodynamic = 95.17 W/ 224.62 W * 100% ηthermodynamic = 42.37% 34
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