Pipeline System Design - Research Paper Example

FLOW METERS TABLE OF CONTENTS TABLE OF CONTENTS ii 1.0 Introduction 1 1.1 Aims 1 2.0 Methodology 2 2.1 Operating procedure 2 2.2 Experimental Operation 2 2.3 Theory 2 2.3.1 Orifice and Venturi Meters 2 2.3.1 Weirs 3 3.0 Results 5 3.1 Calculation for weir 5 3.2 Relationship between flow rate and  QUOTE

5 3.3 Relationship between flow rate and  QUOTE

6 3.4 Relationship between flow rate and  QUOTE

7 3.5 Relationship between flow rate and  QUOTE

8 3.6 Relationship between flow rate and head loss for orifice 9 3.7 Relationship between flow rate and  QUOTE

10 3.8 Relationship between flow rate and head loss for venture 12 4.0 Discussion 14 5.0 Conclusions and recommendations 17 5.1 Conclusions 17 5.2 Recommendations 17 References 18 APPENDIX A 19 APPENDIX B 21 APPENDIX C 21 APPENDIX D 23 APPENDIX E 24 1.0 Introduction The pipe rig is constructed of a venturi, orifice and a weir all with associated pressure tappings as well as an Endress & Hauser electromagnetic flowmeter. The water flow is pumped using a variable speed inverter driven centrifugal pump. A diaphragm valve can be used in addition to the pump to adjust the flowrate. 1.1 Aims 1. Understand the principle of measure ΔP over different flow measuring devices. 2. To calibrate different ΔP flow devices and determine for the orifice and venturi the CD (coefficient of discharge) 3. To verify the theoretical Francis formulae for flow through different types of weir.. 2.0 Methodology 2.1 Operating procedure Start up It was to be ensured that the feed tank had sufficient volume. The diaphragm control valve was then to be opened fully. The flow path was then set as per the experimental aims. The centrifugal pump was started and the slow ramp up with the control valves being adjusted such that there was variation of flow on the targeted flow measuring devices. The pump started at 25%. Ramp up of the pump was affected using the control on the inverter, which was fixed directly on top of the pump. 12 different flowrates were taken for the venturi and orifice. 2.2 Experimental Operation Experiment: At varied flowrates (12 runs), measure the flowrate, ΔP of the in-line devices, and the pressure recovery. Shut Down 1. Stop pump shut all valves 2.3 Theory 2.3.1 Orifice and Venturi Meters Benouilli equation is used in the derivation of the coefficient of discharge CD for venturi as well orifice meter. This equation for a venturi meter, (Coulson and Richardson, 1999), is given by where Q stands for flow rate of the liquid,  is the density of the liquid, A1 is cross sectional area of pipe, A2 is the area at throat, p1 represents p2 is the pressure at the throat of the venturi meter. For convention in an orifice meter, instead of A2 we have A0 as its replacement which is the area that is bigger than the vena contracta area A2 of the orifice. This is majorly the reason why the discharge coefficient in an orifice will be lower than that of a venturi meter for the same A2. Figure 1: Venturi meter When the liquid passes through the contraction there will drop in pressure and after the vena contracta there is slow expansion of to the original velocity and cross-section. But recovery to initial pressure is not attained, as a result of existence of friction loss in the meter 2.3.1 Weirs The expression giving the coefficient of discharge for a rectangular notch by Coulson and Richardson (1999) as Figure 2 : Rectangular notch where Q is the volumetric flow rate of the liquid being measured, B is the width of the notch, g is gravitational acceleration and D is the total depth of liquid above the notch (see Figure 2). 3.0 Results 3.1 Calculation for weir D=H-h Where D is the head of water over weir; H is distance between the weir crest and the still water surface and h is distance of the water surface at point 2 below the still water surface The sample calculation is as shown in APPENDIX D 1 3.2 Relationship between flow rate and  weir 1 The relationship between flow rate and  for weir 1 is as shown in figure 3. From the figure it can be seen that the maximum  value was at a flow rate of 122.5 while at the lowest flow rate of the three where Q=85.7 the value of  was lowest at 0.342. The full table of results is in APPENDIX A1 Figure 3: Flow rate and  weir 1 3.3 Relationship between flow rate and  weir 2 For weir 2 the relationship between flow rate and  was as shown in figure 4. From the figure it can be seen that for this weir the value of  ranged between 0.52 and 0.63 with the value showing to be increasing as the flow rate increased. The full table of results is in APPENDIX A2 Figure 4: Flow rate and  weir 2 3.4 Relationship between flow rate and  weir 3 Figure 5 shows the relation between cd and flow rate for weir 3. It can be seen that the cd is lowest at the lowest flow rate and it increases when the flow rate is increased to 80  and then the cd drops when the flow rate is increased further to a value of 119.2. The full table of results is in APPENDIX A3 Figure 5: Flow rate and  weir 3 3.5 Relationship between flow rate and for orifice The calculation for the Cd of the orifice are as shown in sample calculation APPENDI D2 . The relationship between flow rate and  for the orifice is as shown in figure 6 and table 1 . From the figure it can be observed that almost all the  values ranged between 0.72 and 0.74 with the lowest flow rate registering an outlier value of less than 0.68. The full table of results is in APPENDIX B Table 1 Coefficient of discharge  Flow rate 0.669219 92.4 0.742508 192.6 0.73118 250.5 0.732352 285.3 0.733175 301.7 0.725654 277.1 0.732499 258.2 0.732214 261.8 0.73748 235.5 0.736412 190.7 0.728434 169.06 0.724388 144.6 Figure 6 : Flow rate and for orifice 3.6 Relationship between flow rate and head loss for orifice The relationship between flow rate through the orifice and head loss is as shown in Table 2 and figure 7. From the figure it can be seen that there is almost a direct linear relationship between flow rate and head loss. At the lowest flow rate of 92.4dm3/min we have head loss of 65mbar while at the highest flow rate of 301.7 m3/min the highest head loss of 359mbar is recorded. The full table of results is in APPENDIX B Table 2 Flow rate LOSS 92.4 65 192.6 147 250.5 240 285.3 316 301.7 359 277.1 302 258.2 265.5 261.8 273.3 235.5 221 190.7 157 169.06 123.2 144.6 93.2 Figure 7: Flow rate and head loss for orifice 3.7 Relationship between flow rate and for venturi The rest of the calculation for the venture have been calculated in excel as can be seen in table The results for relationship between flow rate and  for the venture are summarized in table 3 and figure 8. From the figure it can be seen that a good number of the calculated figures went beyond the theoretical figure of 0.98. The lowest Cd value was 0.848657 which occurs at a flow rate of 141.8dm3/min. From the figure it can be observed that almost all the  values ranged between 0.72 and 0.74 with the lowest flow rate registering an outlier value of less than 0.68. The full table of results is in APPENDIX C Table 3 Flow rate 0.848657 141.8 0.904041 166.3 0.919768 188.9 0.990025 213.3 0.991614 232.9 1.061194 258.2 1.018083 280.7 1.10283 290.3 1.038453 297.5 1.060003 303.3 1.038705 283.2 1.014868 234.7 Figure 8: Flow rate and for venturi 3.8 Relationship between flow rate and head loss for venture The results for relationship between flow rate and head loss for the venturi are summarized in table 4 and figure 9. From general look of the graph it can be seen that the graph has a small gradient or it is tending towards being horizontal. This shows that for the venturi increase in head loss with increasing discharge is small. The graph also show a direct linear relation between flow rate and head loss. At the lowest flow rate of 141.8 a head loss of 47.7 mbar is registered and the head loss increases to 63 mbar at the highest level of discharge of 303.3 dm3/min. The full table of results is in APPENDIX C Table 4 Flow rate Heat loss 141.8 47.7 166.3 48.3 188.9 56.4 213.3 56 232.9 68 258.2 63 280.7 74 290.3 47 297.5 62 303.3 63 283.2 60.4 234.7 57.4 Figure 9 4.0 Discussion This experiment first looked at coefficient of discharge Cd of a weir. There were 3 weirs which were looked at and from the result it was seen that the Cd for a weir varied with depending on the width B of the weir with the widest weir registering the lowest Cd. It was also seen that weirs Cd value varied with the rate of flow. It was seen that at very low flow the Cd value was low this increased to some degree as the flow rate was increased. The Narrowest weir with a width of 1 cm had the highest Cd but also this is the weir that had the highest fluctuation from a low of 0.49 for the a flow rate of 34.4 to a highest of 0.7 at a flow rate of 81.9. For this weir when the flow rate was increased to 127.7 the Cd dropped to 0.64. For the 5cm width level Cd remained relatively constant at about 0.34 when the discharge was varied from 85.7 to 159. The 1.2cm weir had the Cd ranging from 0.52 to 0.63 with the flow rate increasing from 57.8 to 119.2. A weir is a device that is to be used in measurement of flow rate through open tunnels. For reliable measurement the Cd value of the weir must be relatively stable. This is important in the calibration of the weir. While weir 1 has a low Cd value the Cd is seen to change little on a wide range of flow rate. This shows that the weir can measure a wide range of discharge using a relatively uniform scale. In choosing a weir it is important to know the range of discharge that the flow rate will range with and then have a weir with relatively stable Cd value when the weir is operating in this range. From the weir the next device that was looked at was the orifice. With the rate of flow range from 92.1 to a maximum of 301.7 the Cd values were relatively stable ranging between 0.669 and 0.743. The highest Cd value of 0.743 was observed at a flow rate of 192.6. These values were relatively close to the values expected for orifice. The relatively small range of Cd values over a wide range of flow rate shows that the orifice can reliably be used to measure discharge over a wide range of discharge the connected pipe. It can be seen that the Cd value starts dropping beyond a certain rate of flow. In the process of calibration the acceptable discharge rate through the orifice is to be established. I high Cd level means that the device does not interfere with flow but this does not mean that the device should be operated at the maximum Cd but rather in a range where Cd is relatively stable. The venturi was also investigated with regard to the variation of Cd with flow rate and also the overall pressure drop with change in flow rate. It was interesting to note that for venturi with the flow rate range of between 141 to 303.3 some of the Cd values were slightly above 1. This is not practically possible. From literature a well design venturi with very low energy loss will have a Cd of about 0.98. This value is very close to 1 and with the calculation of the Cd value involving use of a number of variables which are taken using instruments that have some errors the obtained value may well be above 1. Some of the measurements that are made for calculations are the pressure and the rate of flow. The area at the throat and upstream are also used in calculation. Even though the value for Cd went above the expected value the range of the Cd was relatively stable for the wide range of flow rate under experiment. A Cd value that is very close to 1 show that the venturi can be used in a pipe line without much interference with flow. It also means that there can be accurate measurement of flow over a wide range of flow. In both the orifice and the venturi pressure drop was measured for the different flow rates. The graphs of pressure drop versus discharge were used in measuring pressure drop. It was seen that pressure drop generally increased with discharge. This is because as the range of flow is increased turbulence is increased and this means that some of the energy in the water is lost to other forms of energy majorly heat and also noise. The graphs of the orifice were found to have a higher gradient (was much more steep) than the venturi graph with the former having a gradient of 1.456 while the later gradient was 0.001. This means that increasing the rate of flow in the orifice by 1 unit resulted to a 1.456 pressure drop downstream while for a venturi there was only 0.001 drop in pressure when flow rate is increased by 1 unit. This clearly shows that the ventori is a more efficient device for measuring water discharge through a pipe than the orifice. 5.0 Conclusions and recommendations 5.1 Conclusions From the experiment we have seen that the weir, venturi and orifice are devices that can be used in measurement of liquids. The experiment has clearly shown the factors that are to be put into consideration when calibrating the devices. Stability in the Cd value in all the three devices will enable accurate measurement of flow rate over a wide range. With regard to the weir it was seen the wider it is the more stable it is but the lower the Cd value. A narrow (small breadth ) weir will not measure rate of flow over a wide range of flow. Comparing an orifice with a venturi it has been shown that a venturi with measure flow more accurate with interference and loss of pressure being almost zero. 5.2 Recommendations It is recommended that other experiments be done for similar devices with different dimension , with different flow ranges and different fluids other than water References Herschel, Clemens. (1898). Measuring Water. Providence, RI:Builders Iron Foundry. Adrian, R. J., editor (1993); Selected on Laser Doppler Velocimetry, S.P.I.E. Milestone Series, ISBN 978-0-8194-1297-3 Coulson, J.M. and Richardson, J.F. (1999), Chapter 6: Flow and Pressure Measurement, In: Chemical Engineering Volume 1, 6th Edition, Butterworth-Heinemann, Oxford, ISBN 0 7506 4444 3. Kahn, 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 March 14, 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 March 14, 2017). APPENDIX A Q1 Q2 B D Cd Q1 57.8 0.963333 0.000963 -3.01622 1.2 0.012 3 0.477121 0.052318 0.523179 57.8 80.6 1.343333 0.001343 -2.87182 1.2 0.012 3.5 0.544068 0.057894 0.578945 80.6 119.2 1.986667 0.001987 -2.70187 1.2 0.012 4.3 0.633468 0.062875 0.628749 119.2 Q1 Q2 B D Cd Q1 34.4 0.573333 0.000573 -3.24159 1 0.01 2.5 0.39794 0.049117 0.491172 34.4 81.9 1.365 0.001365 -2.86487 1 0.01 3.5 0.544068 0.070594 0.705939 81.9 127.7 2.128333 0.002128 -2.67196 1 0.01 5 0.69897 0.064465 0.644646 127.7 APPENDIX B Q Q P1 P2 P3 A1 A2 Cd LOSS 92.4 1.54 1178 1127 1113 0.002781 0.000698 0.062905 0.937095 937.0948 102 0.000230119 6692.189 0.669219 92.4 65 192.6 3.21 1350 1170 1203 0.002781 0.000698 0.062905 0.937095 937.0948 360 0.000432318 7425.083 0.742508 192.6 147 250.5 4.175 1077 763 837 0.002781 0.000698 0.062905 0.937095 937.0948 628 0.000570995 7311.798 0.73118 250.5 240 285.3 4.755 1370 964 1054 0.002781 0.000698 0.062905 0.937095 937.0948 812 0.000649278 7323.523 0.732352 285.3 316 301.7 5.028333 769 316 410 0.002781 0.000698 0.062905 0.937095 937.0948 906 0.00068583 7331.748 0.733175 301.7 359 277.1 4.618333 454 63.9 152 0.002781 0.000698 0.062905 0.937095 937.0948 780.2 0.000636437 7256.544 0.725654 277.1 302 258.2 4.303333 390 57.6 124.5 0.002781 0.000698 0.062905 0.937095 937.0948 664.8 0.000587487 7324.99 0.732499 258.2 265.5 261.8 4.363333 380 38 106.7 0.002781 0.000698 0.062905 0.937095 937.0948 684 0.00059591 7322.138 0.732214 261.8 273.3 235.5 3.925 312 39.2 91 0.002781 0.000698 0.062905 0.937095 937.0948 545.6 0.000532218 7374.796 0.73748 235.5 221 190.7 3.178333 217 37.6 60 0.002781 0.000698 0.062905 0.937095 937.0948 358.8 0.000431597 7364.119 0.736412 190.7 157 169.06 2.817667 175 30.9 51.8 0.002781 0.000698 0.062905 0.937095 937.0948 288.2 0.000386812 7284.34 0.728434 169.06 123.2 144.6 2.41 135.6 29 42.4 0.002781 0.000698 0.062905 0.937095 937.0948 213.2 0.000332695 7243.876 0.724388 144.6 93.2 APPENDIX C Q Q P1 P2 P3 A1 A2 Cd LOSS 141.8 2.363333 152.5 111 104.8 0.00278 0.000913 0.107858 0.892142 892.1421 83 0.000278479 8486.57 0.848657 141.8 47.7 166.3 2.771667 194 143.7 145.7 0.00278 0.000913 0.107858 0.892142 892.1421 100.6 0.000306586 9040.413 0.904041 166.3 48.3 188.9 3.148333 240 177.3 183.6 0.00278 0.000913 0.107858 0.892142 892.1421 125.4 0.000342297 9197.678 0.919768 188.9 56.4 213.3 3.555 285 216 229 0.00278 0.000913 0.107858 0.892142 892.1421 138 0.000359082 9900.253 0.990025 213.3 56 232.9 3.881667 338 256 270 0.00278 0.000913 0.107858 0.892142 892.1421 164 0.000391449 9916.138 0.991614 232.9 68 258.2 4.303333 393 305 330 0.00278 0.000913 0.107858 0.892142 892.1421 176 0.000405518 10611.94 1.061194 258.2 63 280.7 4.678333 458 345 384 0.00278 0.000913 0.107858 0.892142 892.1421 226 0.000459524 10180.83 1.018083 280.7 74 290.3 4.838333 363 260 316 0.00278 0.000913 0.107858 0.892142 892.1421 206 0.00043872 11028.3 1.10283 290.3 47 297.5 4.958333 334 212 272 0.00278 0.000913 0.107858 0.892142 892.1421 244 0.000477473 10384.53 1.038453 297.5 62 303.3 5.055 277 155.3 214 0.00278 0.000913 0.107858 0.892142 892.1421 243.4 0.000476885 10600.03 1.060003 303.3 63 283.2 4.72 220 109.5 159.6 0.00278 0.000913 0.107858 0.892142 892.1421 221 0.000454412 10387.05 1.038705 283.2 60.4 234.7 3.911667 162 82.5 104.6 0.00278 0.000913 0.107858 0.892142 892.1421 159 0.000385436 10148.68 1.014868 234.7 57.4 APPENDIX D D1 Sample calculation for weir To convert the units appropriately D2 Calculating  for the orifice Inlet pipe diameter (d1)  Now when the thickness is put into consideration From the provided data From Area  m2  m2  Considering units we have The rest of the calculation for the venture have been calculated in excel as can be seen in table APPENDIX E Calculating  for venturi Inlet pipe diameter (d1)  Now when the thickness is put into consideration Throat diameter  From Area  m2  m2  Considering units we have Read More

In the process of calibration the acceptable discharge rate through the orifice is to be established. I high Cd level means that the device does not interfere with flow but this does not mean that the device should be operated at the maximum Cd but rather in a range where Cd is relatively stable. The venturi was also investigated with regard to the variation of Cd with flow rate and also the overall pressure drop with change in flow rate. It was interesting to note that for venturi with the flow rate range of between 141 to 303.

3 some of the Cd values were slightly above 1. This is not practically possible. From literature a well design venturi with very low energy loss will have a Cd of about 0.98. This value is very close to 1 and with the calculation of the Cd value involving use of a number of variables which are taken using instruments that have some errors the obtained value may well be above 1. Some of the measurements that are made for calculations are the pressure and the rate of flow. The area at the throat and upstream are also used in calculation.

Even though the value for Cd went above the expected value the range of the Cd was relatively stable for the wide range of flow rate under experiment. A Cd value that is very close to 1 show that the venturi can be used in a pipe line without much interference with flow. It also means that there can be accurate measurement of flow over a wide range of flow. In both the orifice and the venturi pressure drop was measured for the different flow rates. The graphs of pressure drop versus discharge were used in measuring pressure drop.

It was seen that pressure drop generally increased with discharge. This is because as the range of flow is increased turbulence is increased and this means that some of the energy in the water is lost to other forms of energy majorly heat and also noise. The graphs of the orifice were found to have a higher gradient (was much more steep) than the venturi graph with the former having a gradient of 1.456 while the later gradient was 0.001. This means that increasing the rate of flow in the orifice by 1 unit resulted to a 1.

456 pressure drop downstream while for a venturi there was only 0.001 drop in pressure when flow rate is increased by 1 unit. This clearly shows that the ventori is a more efficient device for measuring water discharge through a pipe than the orifice. 5.0 Conclusions and recommendations 5.1 Conclusions From the experiment we have seen that the weir, venturi and orifice are devices that can be used in measurement of liquids. The experiment has clearly shown the factors that are to be put into consideration when calibrating the devices.

Stability in the Cd value in all the three devices will enable accurate measurement of flow rate over a wide range. With regard to the weir it was seen the wider it is the more stable it is but the lower the Cd value. A narrow (small breadth ) weir will not measure rate of flow over a wide range of flow. Comparing an orifice with a venturi it has been shown that a venturi with measure flow more accurate with interference and loss of pressure being almost zero. 5.2 Recommendations It is recommended that other experiments be done for similar devices with different dimension , with different flow ranges and different fluids other than water References Herschel, Clemens. (1898). Measuring Water.

Providence, RI:Builders Iron Foundry. Adrian, R. J., editor (1993); Selected on Laser Doppler Velocimetry, S.P.I.E. Milestone Series, ISBN 978-0-8194-1297-3 Coulson, J.M. and Richardson, J.F. (1999), Chapter 6: Flow and Pressure Measurement, In: Chemical Engineering Volume 1, 6th Edition, Butterworth-Heinemann, Oxford, ISBN 0 7506 4444 3. Kahn, 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 March 14, 2017).

6Boljanovic, V. Applied Mathematical and Physical Formulas, 2nd ed.

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