Centrifugal Pump by Price Pump Company - Lab Report Example

CENTRIFUGAL PUMP LAB REPORT TABLE OF CONTENTS 1.0 Introduction 1 1.1 Theory 1 1.2 Uncertainty analysis: 4 1.3 Procedure 5 2.0 Results 6 2.1 Calibration 6 2.2 Relationship between flow rate and power 7 2.3 Relationship between flow rate and power 8 2.4 Relationship between flow rate and power 9 2.5 Error analysis 10 3.0 Discussion and Conclusions 11 References 12 APPENDIX A: CALIBARATION DATA 14 APPENDIX B:DATA FOR FIRST TRIAL 15 APPENDIX C: DATA FOR SECOND TRIAL 16 APPENDIX D: DATA FOR THIRD TRAIL 17 APPENDIX E:ERROR ANALYSIS 18 APPENDIX F:SAMPLE CALCULATIONS 20 1.0 Introduction This lab concentrated on exploration of a number of characteristics exhibited by a centrifugal pump, with the ultimate goal being the determination of how pressure and rate of flow interact with each other. a centrifugal pump manufactured by Price Pump Company was analyzed for a number of flow rates translating to a number of pressure differences. 1.1 Theory The general rule is that fluids will always move from high energy areas to low energy areas. A good example of this is shown where water will always from high grounds to lower grounds such that the Potential energy due to gravity is reduced. A similar phenomenon is exhibited when it comes to pressure where there can be pressurization of fluids so that they can be made to flow from the point where the high pressure in being created to the lower pressure region. One of the simplest ways of creating high pressure in liquids like water is the utilization of the weight of the water to initiate the force1. An increase in the depth of fluid results to a pressure build up in the lower areas in conformation to the equation  (1) The equation clearly indicates that the pressure at a particular point in the fluid will always depend on how deep is the point from the surface of the water and also the density of the liquid in question. This means that a column of fluid for example water in a tank , will exert a downward force and if a pipe can be connected at the lower side of the water column , then the water can easily be transported through the pipe. The other option of transporting water through pipes is by engaging the service of a pump. The principle behind the function of all pumps is that we have some devices in the pump which imparts energy into the system resulting to an increase in the pressure level. Centrifugal pump is one of the pumps that is commonly used. In this pump a fluid will usually be taken in the central point of a wide cylindrical chamber, and the water will undergo rotation courtesy of spinning impeller blades. By utilization of centrifugal forces the vanes in the pump directs the fluid outwards. There will be an increase in the fluid speed, due to the fact that with the impeller rotating at a certain angular velocity, a larger velocity will be realized as the distance from the axis of rotation is increased. When dealing with incompressible fluids such as in the case of water, we have the mass flow rate of the fluid when entering is the same as mass flow rate when the fluid is living the pump , in the case where we have the radius at the entry being the same as the radius at exit of the pump. This will mean that the increase in energy of the fluid will entirely be translated into an increased pressure and this will achieve forward movement of the fluid. Figure 1 Figure 1 give diagram of a typical centrifugal pump with the major parts being the impeller, vane, the inlet and the exit. The energy transfer into the fluid result to an increase in pressure head and the relationship is given as  (2)2 The power P is what is put into the system by the pump, m gives the mass flow rate, while g is the for of gravity, and Δℎ which is the head that is put into the system. The head of a pump can be though of as being the height to which water will be projected upwards, with the energy that has been provided would be matching the potential energy at the height. By obtaining the difference in pressure at fluid entry and at fluid exit from the pump. A bourdon tube is used to obtain pressures at the two points in question. The difference in the pressure  is divided by the product of density of fluid 𝜌 and the gravitation constant g and the obtained value can be compared to Δℎ Through rearrangement of eqn (2) we can have obtain an equation that gives a good reflection of the quantity of power desired putting into consideration the two values measured  (3)2 With the density passing as a constant, it is possible to obtain the power provided by the pump on the basis of conditions measurements at two points. This experiment will there will be adjustment and recording of rate of flow Q at different measurements as will be described in procedure. It will be adjusted by turning a valve connected to a rotameter, measuring in gallons per minute (GPM). This will act as the independent variable which influences the dependent variable of pressure difference. Pressure difference will be acquired through the use of a bourdon tube before and after the pump. This will result in three recorded measurements for each of the 19 different flow rates. These values can then be utilized in equation 3 to solve for the power supplied by the pump. Once these values for power have been found, efficiency can be determined by comparing the power supplied by the pump to the power supplied to the pump3. The pump will be powered by a one horse power motor, so the power supplied should be about that much. It is possible to plot efficiency a long side the characteristic curves such that the intersection of the curves can be used in establishing the optimal operating point of the pump. To obtain efficiency we use the equation:  (4)5 1.2 Uncertainty analysis: With regards to uncertainty, there are two methods that will be used in the determination of the level of uncertainty for the final pressure values. In the first method, the actual data is looked into and the standard deviation of the repeated measurement is established. For each of the flow settings there will be a standard deviation. The second method will involve estimation of the uncertainty for each instrument on the basis of the ease of reading the instrument. With the three measured values being combined the following equations will result  (5)  (6) 1.3 Procedure In performing the experiment, first it was to be ensured that there was proper set up of the lab such that all the valves were position at the required position with the lab technician being consulted before going on with the experiment. Calibration of the rotameters is very important and this was done by the group. The pump was turned on so as to allow water circulatuion through the system. The low flow rotometer was adjusted to a flow rate of 2GPM, with one person directing the discharge to a 6L bucket at the same time another student used a timer to record the time required to collect the desired volume of water. There was a repeat of this process at 2, 4, 6, 8 and 10 for low flow rotameter while for the case of high flow rotameter the discharges involved were 12, 16, 20, 24 and 28. With this exercise undertaken, it was ensured that in performing the experiment, actual flow rate was used in the calculation of power output of the pump. Having calibrated the rotameter, it was time for data to be collected by the group. Two sets each having a total of 14 runs were obtained, with the flow rate, pressure at the inlet and at the outlet being recorded. there is assumption that the reading made had some errors; first because of it being impossible to make the exact reading of the two pressures (input and output) because of lack of finite precision. 2.0 Results 2.1 Calibration Calibration was undertaken as the first procedure in the lab, and part of process involved changing the units of volume in which the water was measured. The water collection involved use of a cylinder that its calibration was in liters and these was not rhyming with the units used on the rotameter scale. After this being done, next was to calculate the actual flow rate through division of the volume and the time used to collect it. In figure 2 it can be seen that we have a linear relationship between the flow rate by the rotameter and the actual flow obtained through calculation. Figure 2: Relationship between Rotameter rate vs Actual flow rate 2.2 Relationship between flow rate and power In this experiment there are three set of data which were obtained with each set having 14 runs , and in all the data sets there was calculation of the power delivered by pump according to equation 3. Appendix F calculation F1 is a sample of this calculation. The power of the motor is assumed to be constant at 1 hp and is equal to the value indicated on label of the pump motor. Figure 3: Relationship between flow rate vs Power 2.3 Relationship between flow rate and power In order to establish how to utilize the pump it important to understand the relationship and pressure. Figure 5 gives the relationship between the pressure transmitted into the system and the discharge. It can be seen that the pump exerts higher pressures when the discharge is low. It also be seen that at initial stages the pump pressure drop gradually with increasing discharge but at about 11GPM the drop in pressure is much drastic. Figure 4: Relationship between Flow rate vs pressure 2.4 Relationship between flow rate and power In order to put the pump at optimal use it is important to establish the point at which the pump functions most efficiently. It can be seen that the pump has maximum efficiency at a discharge of about 11 GPM where the efficiency is about 24%. Figure 5: Relationship between flow rate and Efficiency 2.5 Error analysis So as to have a better understanding of the data, there was utilization of some equations in performing error analysis. In order to obtain the mean value, equation 5 was used so as to come up with a solution. Here the value of  in the equation represent change in pressure. As an example this equation has been used in calculation F.3 in Appendix F.  (5) For calculation of variance8and standard deviation9 there was use of equation 6 and 7 respectively. The examples involving the application of these equations is found in appendix F, calculation F.4 and F.5 respectively.  (6)  (7) As it was already cited, there were errors present during the experiment. To be able to understand how these contribute to errors in the results, it was also necessary to do propagation error analyze. The same calculations were made for power, ΔP and efficiency. An example of each of these calculations can be found in appendix F. The equation provided in class was used in order to calculate these errors10. 3.0 Discussion and Conclusions There are many reasons to why centrifugal pumps are used widely globally. One of the reasons is that these pumps are associated with low maintenance cost. Centrifugal pumps are known to have high efficiency5. These pumps are because of low power consumption. In this experiment the , the operation of the pump has been shown to conform to Bernoulli principle, where reduction in velocity result to increased pressure and vise versa. During the experiment errors were incurred including instrumental errors. In reading the pressure from the gauge the pointer may settle somewhere in between two marks and this means that approximate values were taken when such situations were encountered. In the calibration process, the timing may have not been accurate since there could have some delay in stopping the watch while in other incidences could have involved the stop water being stopped prematurely. References 1 Schaschke, C. Dictionary of Chemical Engineering [Online]; Oxford University Press: New York, NY, 2014; pp 60. http://app.knovel.com/hotlink/toc/id:kpDCE00021/dictionary-chemicalengineering/dictionary-chemical-engineering (accessed Feb 19, 2017). 2 United States Department of Energy, Industrial Technologies Program. Improving Pumping System Performance: A Sourcebook for Industry, 2nd ed. [Online]; Golden, CO, 2006; p. 3. https://www1.eere.energy.gov/manufacturing/tech_assistance/pdfs/pump.pdf (accessed Feb 19, 2017). 3Schaschke, C. Dictionary of Chemical Engineering [Online]; Oxford University Press: New York, NY, 2014; pp 60. http://app.knovel.com/hotlink/toc/id:kpDCE00021/dictionary-chemicalengineering/dictionary-chemical-engineering (accessed Feb 20, 2017). 4 ASME Shale Shaker Committee. Drilling Fluids Processing Handbook [Online]; Elsevier: Burlington, MA, 2005; pp 239. http://app.knovel.com/hotlink/toc/id:kpDFPH0003/drillingfluids- processing/drilling-fluids-processing (accessed Feb 19, 2017). 5Allaby, M. A Dictionary of Earth Sciences, 3rd ed. [Online]; Oxford University Press: New York, NY, 2008; pp 61. http://app.knovel.com/hotlink/toc/id:kpDESE000X/dictionary-earthsciences/dictionary-earth-sciences (accessed Feb 20, 2017). 6Boljanovic, V. Applied Mathematical and Physical Formulas, 2nd ed. [Online]; Industrial Press: South Norwalk, CT, 2016; pp 351. http://app.knovel.com/hotlink/toc/id:kpAMPFE001/applied-mathematical/applied-mathematical (accessed Feb 20, 2017). 8Kahn, M. K. Fluid Mechanics and Machinery [Online]; Oxford University Press: New York, NY, 2015; pp 508. http://app.knovel.com/hotlink/toc/id:kpFMM00004/fluid-mechanicsmachinery/fluid-mechanics-machinery (accessed Feb 19, 2017). 9 Information gotten in during the lab at SCOB190 from the pump used. 10 Kahn, M. K. Fluid Mechanics and Machinery [Online]; Oxford University Press: New York, NY, 2015; pp 303. http://app.knovel.com/hotlink/toc/id:kpFMM00004/fluid-mechanicsmachinery/ fluid-mechanics-machinery (accessed Feb 8, 2017). 11Glass Tube Rotameter. http://www.rotameters.co.in/glass-tube-rotameter.html (accessed Feb 8, 2017). APPENDIX A: CALIBARATION DATA Run rate lpm Eror V(l) V(g) Error time error Ac(l/s) Ac(gpm) 1 2 7.58 0.1 1 0.26385224 0.1 8.09 0.1 0.123609 1.956877 2 4 15.16 0.1 0.8 0.21108179 0.1 3.33 0.1 0.24024 3.803276 3 6 22.74 0.1 0.8 0.21108179 0.1 2.09 0.1 0.382775 6.059764 4 8 30.32 0.1 0.8 0.21108179 0.1 1.44 0.1 0.555556 8.795075 5 10 37.9 0.1 0.8 0.21108179 0.1 1.15 0.1 0.695652 11.01296 6 12 45.48 0.1 6 1.58311346 0.1 8.18 0.1 0.733496 11.61208 7 16 60.64 0.1 6 1.58311346 0.1 6.03 0.1 0.995025 15.75237 8 20 75.8 0.1 6 1.58311346 0.1 4.22 0.1 1.421801 22.50872 9 24 90.96 0.1 6 1.58311346 0.1 3.9 0.1 1.538462 24.35559 10 25.5 96.645 0.1 6 1.58311346 0.1 3.37 0.1 1.780415 28.186 APPENDIX B:DATA FOR FIRST TRIAL APPENDIX C: DATA FOR SECOND TRIAL APPENDIX D: DATA FOR THIRD TRAIL APPENDIX E:ERROR ANALYSIS run GPM Pin(1) Pin(2) Pin(3) Pin(mean) Pout1 Pout2 Pout3 Pout(mean) Mean PSI-Mean PSI-Mean PSI-Mean (PSI-Mean)2 Var SD p(w) P(motor) Effi Increase p Error P Error (η) 1 2 0.9 0.8 0.9 0.8667 32 32 32 32 31.1 31.2 31.1 31.13333 -0.03333 0.066667 -0.03333 4.44444E-05 2.22E-05 0.004714 0.036289 1 0.036289 3.1734694 0.004444 0.066667 7.99262E-09 8.94015E-05 2 3.5 0.9 0.7 0.8 0.8 32 32 32 32 31.1 31.3 31.2 31.2 -0.1 0.1 0 0.0004 0.0002 0.014142 0.063711 1 0.063711 3.1836735 0.1225 0.35 0.1225 0.35 3 5 0.7 0.4 0.7 0.6 32 31.5 31.5 31.667 31.3 31.1 30.8 31.06667 0.233333 0.033333 -0.26667 0.016044444 0.008022 0.089567 0.089848 1 0.089848 3.1428571 3.027778 1.740051 3.027777778 1.740051085 4 6.5 0.5 0.2 0.4 0.3667 31 31 31 31 30.5 30.8 30.6 30.63333 -0.13333 0.166667 -0.03333 0.002177778 0.001089 0.032998 0.116044 1 0.116044 3.122449 0.751111 0.866667 0.751111111 0.866666667 5 8 0.3 0.1 0.2 0.2 31 30.5 30.5 30.667 30.7 30.4 30.3 30.46667 0.233333 -0.06667 -0.16667 0.007511111 0.003756 0.061283 0.141424 1 0.141424 3.0918367 7.751111 2.784082 7.751111111 2.784081736 6 9.5 0.1 0 0.1 0.0667 30 30 30 30 29.9 30 29.9 29.93333 -0.03333 0.066667 -0.03333 4.44444E-05 2.22E-05 0.004714 0.165723 1 0.165723 3.0510204 0.100278 0.316667 0.100277778 0.316666667 7 11 0 0 0 0 30 30 30 30 30 30 30 30 0 0 0 0 0 0 0.192532 1 0.192532 3.0612245 0 0 0 0 8 12 0.9901 0.2475 0.2475 0.495 30 30 30 30 29.613228 29.752475 29.7524752 29.70606 -0.09283 0.046416 0.046416 0.000167097 8.35E-05 0.00914 0.208302 1 0.208302 3.0359669 35.29066 5.940594 35.29065778 5.940594059 9 14 1.9802 0.7426 0.7426 1.1551 30 29 29 29.333 29.226455 28.257426 28.2574257 28.58044 0.64602 -0.32301 -0.32301 0.391891149 0.195946 0.442657 0.230807 1 0.230807 2.8834108 220.5403 14.8506 220.5402956 14.85059917 10 16 3.7129 1.4851 1.4851 2.2277 28 28 28 28 26.549604 26.514851 26.5148515 26.52644 0.023168 -0.01158 -0.01158 6.48247E-07 3.24E-07 0.000569 0.247513 1 0.247513 2.7055971 564.6505 23.76238 564.6505245 23.76237624 11 18 6.9307 1.9802 2.2277 3.7129 27 26 26 26.333 24.292593 24.019802 23.7722772 24.02822 0.264369 -0.00842 -0.25595 0.018352341 0.009176 0.095792 0.249651 1 0.249651 2.4257426 3498.818 59.15081 3498.818155 59.15080858 12 20 7.4257 2.4752 2.9703 4.2904 26 25 25.5 25.5 23.099207 22.524752 22.529703 22.71789 0.38132 -0.19314 -0.18818 0.047575988 0.023788 0.154234 0.26289 1 0.26289 2.2989493 4032.076 63.49863 4032.076376 63.49863287 13 22 8.4158 3.4653 3.4653 5.1155 25 24.5 25 24.833 21.712435 21.034653 21.5346535 21.42725 0.285188 -0.39259 0.107406 0.06100795 0.030504 0.174654 0.276407 1 0.276407 2.1974136 5285.259 72.69979 5285.258755 72.69978511 14 24 9.4059 3.9604 3.9604 5.7756 24 24 24 24 20.325662 20.039604 20.039604 20.13496 0.190706 -0.09535 -0.09535 0.002976023 0.001488 0.038575 0.280601 1 0.280601 2.0448575 7591.413 87.12871 7591.412607 87.12871287 APPENDIX F:SAMPLE CALCULATIONS F1Power from the pump to fluid F2 Efficiency F3 Mean   F4 Variance  F5 Standard deviation  POST REFLECTION Upon completion of this lab report I can confess that there has been a lot of improvement with regard to my knowledge on concepts on the subject matter. Combining the concept of calculation of power by use of discharge and change in pressure and putting into consideration the units that were being used was a very good learning experience. To complete the lab it was important to have a review of Bernoulli equation and the principles behind it. This was very important as it will come in handy in many other labs that I will undertake in future. In this lab I came to appreciate the need of working in a group and being at full alert during the time of undertaking the lab report. In the process of collecting data, there were several quantities which were supposed to be measured simultaneously including the targeted volume, the time taken to achieve this volume, the pressure at inlet and pressure at the outlet. This clearly shows that in order for this to be accomplished at least we had to have a minimum of four people in a group. It was important that the timing of collection of a certain volume be done very accurately as delaying in stopping the stop watch could mean errors. It is in the calculating of errors that I came to appreciate the implication of having inaccurate data being collected. The error in the calculated value can highly magnified due to the errors in the components of the equation. It is during this report that I appreciated the concept of instrument calibration and it came to my realization that most of the measurement we undertake in our daily life may not be accurate after all since the instruments are rarely calibrated. In this lab report I came to realize that when it comes to calculating the required values excel is a very powerful tool to be put into use. I learned a number of things in excel from my friends which previously I did not know, with regards to applying of equations in excel. I that working as a group of at least two is important when it comes to calculating the required quantities more so when using excel. Read More

Figure 1 Figure 1 give diagram of a typical centrifugal pump with the major parts being the impeller, vane, the inlet and the exit. The energy transfer into the fluid result to an increase in pressure head and the relationship is given as  (2)2 The power P is what is put into the system by the pump, m gives the mass flow rate, while g is the for of gravity, and Δℎ which is the head that is put into the system. The head of a pump can be though of as being the height to which water will be projected upwards, with the energy that has been provided would be matching the potential energy at the height.

By obtaining the difference in pressure at fluid entry and at fluid exit from the pump. A bourdon tube is used to obtain pressures at the two points in question. The difference in the pressure  is divided by the product of density of fluid 𝜌 and the gravitation constant g and the obtained value can be compared to Δℎ Through rearrangement of eqn (2) we can have obtain an equation that gives a good reflection of the quantity of power desired putting into consideration the two values measured  (3)2 With the density passing as a constant, it is possible to obtain the power provided by the pump on the basis of conditions measurements at two points.

This experiment will there will be adjustment and recording of rate of flow Q at different measurements as will be described in procedure. It will be adjusted by turning a valve connected to a rotameter, measuring in gallons per minute (GPM). This will act as the independent variable which influences the dependent variable of pressure difference. Pressure difference will be acquired through the use of a bourdon tube before and after the pump. This will result in three recorded measurements for each of the 19 different flow rates.

These values can then be utilized in equation 3 to solve for the power supplied by the pump. Once these values for power have been found, efficiency can be determined by comparing the power supplied by the pump to the power supplied to the pump3. The pump will be powered by a one horse power motor, so the power supplied should be about that much. It is possible to plot efficiency a long side the characteristic curves such that the intersection of the curves can be used in establishing the optimal operating point of the pump.

To obtain efficiency we use the equation:  (4)5 1.2 Uncertainty analysis: With regards to uncertainty, there are two methods that will be used in the determination of the level of uncertainty for the final pressure values. In the first method, the actual data is looked into and the standard deviation of the repeated measurement is established. For each of the flow settings there will be a standard deviation. The second method will involve estimation of the uncertainty for each instrument on the basis of the ease of reading the instrument.

With the three measured values being combined the following equations will result  (5)  (6) 1.3 Procedure In performing the experiment, first it was to be ensured that there was proper set up of the lab such that all the valves were position at the required position with the lab technician being consulted before going on with the experiment. Calibration of the rotameters is very important and this was done by the group. The pump was turned on so as to allow water circulatuion through the system.

The low flow rotometer was adjusted to a flow rate of 2GPM, with one person directing the discharge to a 6L bucket at the same time another student used a timer to record the time required to collect the desired volume of water. There was a repeat of this process at 2, 4, 6, 8 and 10 for low flow rotameter while for the case of high flow rotameter the discharges involved were 12, 16, 20, 24 and 28. With this exercise undertaken, it was ensured that in performing the experiment, actual flow rate was used in the calculation of power output of the pump.

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