Fluid Meter and Tray Hydraulic Experiment free essay sample

According to Bernoullli’s equation, the slope of a log-log plot of flow rate vs pressure drop was expected to be 0. 5. After much experimentation of different flow rates and the pressure drop that came with these flow rates, the Venturi meter had a slope of 0. 53  ± . 03, and orifice meter data had a slope of 0. 46  ± . 02. The data showed as the water flow rate was increased, the pressure drop also increased, which is in accordance with Bernoulli’s equation. The discharge coefficient is a ratio of the efficiency of the actual discharge of the fluid over the theoretical discharge. The average calculated coefficient of discharge for the Venturi meter was 0. 984  ± 0. 001 and for the orifice meter has an average calculated coefficient of discharge of 0. 540  ± 0. 001. The discharge coefficient should theoretically be 0. 98 for the Venturi meter, and 0. 62 for the orifice meter. The percent error of the discharge coefficient was 0. 046% and 9. 2% for the Venturi and orifice meters, respectively. We will write a custom essay sample on Fluid Meter and Tray Hydraulic Experiment or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page The purpose of the second experiment, the Tray Hydraulics, was to examine the vapor and liquid tray hydraulics parameters for sieve type crossflow distillation trays. Water flow rates were varied in intervals of 15 in. H2O, ranging from 0 to 75 in. of H2O. For each water flow rate, 5 air flow rates were measured from 0. 01 to 0. 95 cm3/s. The pressure drop increased as the water flow rate increased if the air flow rate was held constant, and when the air flow rate was increased with the water flow rate being held constant. The data showed that the percent flooding was a maximum at maximum water flow rate and air flow rate with a value of 10. 3 ±0. Introduction and Theory – William Kwendi This experiment is divided into two sub-experiments, fluid flow meters and tray hydraulics. The purpose of the fluid flow meters experiment was to determine the operating characteristics of the Venturi and orifice meters. The purpose of the tray hydraulics experiment was to study the vapor and liquid tray hydraulics parameters for sieve, or perforated, trays in a distillation column. By performing experiments based on theory and comparing results to literature values, the objectives of this experiment can be achieved. Both the orifice and the Venturi meters produce a restriction in the flow and measure the pressure drop across the meter. The velocity of a fluid is expected to increase as the fluid flows from an open area, to a more constricted area. Assuming incompressible flow, a negligible height change, and steady state, Bernoulli’s equation can be simplified to show the correlation between the volumetric flow rate and the pressure drop. The equation for both meters is as follows: w=Q? =CYA22gc(p1-p2)? 1-? 4 (1) 1 where A2 is the cross-sectional area of the throat, C is the coefficient of discharge (dimensionless), gc is the dimensional constant, Q is the volumetric rate of discharge measured at upstream pressure and temperature, is the weight rate of discharge, p1 and p2 are the pressures at upstream and downstream static pressure taps, respectively, Y is a dimensionless expansion factor, ? is the ratio of the throat diameter to pipe diameter (dimensionless), and ? is the density at upstream pressure and temperature. By measuring the pressure drop across the meters and collecting the fluid leaving the syst em, one can find the discharge coefficients of each meter by using the equation explained above. The discharge coefficient is a ratio of the efficiency of the actual discharge of the fluid over the theoretical discharge. Figure 1: Schematic of Sieve tray showing where vapor flow enters. 2 Figure 1: Schematic of Sieve tray showing where vapor flow enters. 2 The other part of the experiment dealt with examining the vapor and liquid tray parameters for sieve type crossflow distillation trays. A schematic of a sieve tray is shown in Figure 1 (left). In a trayed tower, liquid flows across each tray, over an outlet weir, and into a downcomer, which takes liquid by gravity to the tray below. 2 Gas flows upward through the openings in the sieve tray, bubbling through the liquid on the tray. Depending on the water and air flow rates, spray, froth, emulsion, bubble, and cellular foam flow regimes can occur in a sieve tray. There are four instances that can reduce the operating efficiency of the sieve tray: entrainment flooding, entrainment, weeping, and downflow flooding. Entrainment flooding is where both downflow flooding and entrainment occurs because the ratio of the flow rate of vapor to the flow rate of air is too high. Entrainment is where vapor carries the liquid from one tray to the tray above. This lowers efficiency because liquid from a tray of lower volatility is carried to a tray with higher volatility. Weeping is where the gas pressure drop through the perforations of the sieve tray is not great enough to bubble through the tray, so instead the liquid â€Å"weeps† through the perforations of the tray. Downflow flooding is where a column floods because it cannot handle large quantities of liquid, or if there is too little space between each tray. 1 Figure 2, shown below, shows the operating conditions of the distillation tray. With regards to downflow flooding, the height that this flooding occurs at an actually be calculated. The following equation is solved for the theoretical height of the fluid in the downcomer Figure 2: Shows conditions where tray efficiency decreases and stable operating conditions. 1 Figure 2: Shows conditions where tray efficiency decreases and stable operating conditions. 1 hdc=ht+hw+how+hda+hhg (2)1 where hdc is the clear liquid height in the downcomer, ht is the total pressure drop across the plate, hw is the height of the liquid crest over the weir, had is the head loss due to liquid flow under the downcomer, and hhg is the liquid gradient across the plate. All of these heights are measured in inches. In order to prevent downflow flooding from happening, the space between trays must be increased, or the water flow rate must be decreased. By using the theoretical clear liquid height in the downcomer, calculated above, and the average relative froth density, which relates the liquid density to the froth density, the height of liquid and froth in the downcomer can be calculated. hdc=hdc? dc(3)1 where h’dc is the height of liquid and froth in the downcomer (inches), and ? c is the average froth density (dimensionless). The total pressure drop across a place, or tray, is defined by the following equation: ht=hd+hL (4)1 where ht is the total pressure across the plate, hd is the pressure drop across the dispersion unit, and h’L is the pressure drop through aerated mass over and around the disperser. The units of all of these variables are in mm, or inches, of liquid. Ht is important because it is a term used in the calculation of the aeration factor. The aeration factor equation is as follows: ? =ht-hhhw-how (5)1 here all of the heights have the units of inches of water, hh is the dry tray pressure drop, hw is the height of the weir, and how is the height of liquid and froth over the weir. As the height of the liquid and froth increases, the pressure drop is also expected to increase because pressure in a distillation usually increases with height, relatively speaking. The aeration factor is used because the height of the liquid on top of the tray may not entirely be clear because of the amount of froth on top of the liquid and this factor relates the height of the froth to the identical clear liquid height. Apparatus and Operating Procedures – Khanh Ho Part A: Fluid Flow The apparatus consisted of a holding tank, a pump, a set of pipes Type L drawn copper tubing of four differing-nominal sizes (1, 3/4, 1/2, and 3/8), an orifice flow meter, a venturi flow meter, a manometer, a visual observation tank, and controlling valves. A standard venturi meter consists of a converging cone to create the acceleration in the fluid. There are pressure taps attached to the upstream side of the cone or entrance of 1. 025 diameter and the throat of 0. 625. The orifice meter of 0. 25 diameter consists of a flat thin orifice plate with a circular hole drilled in it. Similarly, there is a pressure tap upstream from the orifice plate and another just downstream. The manometer contains flexible rubber hoses attached to pressure taps at the entrance and exiting of both orifice and venture meters, which allows measuring the pressure drop through each meter. Diagram of experimental system is shown in Figu re 3. Figure 3: Diagram of Fluid Flow System and Flow Path of Water3 Before beginning, all air bubbles were removed from the piping lines by following the given procedure in the laboratory manual. Then, the vertical tank was filled to eleven gallons of water. The valves V1, V3, V4 and V5 were closed for the entire experiment. Valve V2 was used to control the discharged water from the piping system. All of other valves were open in order to have a maximum flow through orifice and venturi meters. There are flexible hoses attached to the entrance and exiting of both orifice and venture meters, which allowed measuring the pressure drop through each meter. A bucket was placed under the exit stream of valve V2 with a graduated cylinder to measure the collected water. The pump was then turned on and valve V2 was opened to set a flow rate for the system. The exiting flow rates were varied from 0. 220 to 0. 613lbm/s by adjusting the valve V2. Data was recorded including the pressure drop across the two meters, the water draining out of system, and the collecting time. Part B: Tray Hydraulics In this part of experiment, the air was supplied into the rectangular tray test section (cross-sectional area 15 x 48) of a distillation tower by a centrifugal Chicago Blower Corp. Turbo Pressure Blower (Model B2-5-184). At the same time, water was pumped to the system by the Ingersoll-Rand Centrifugal pump (Model 2 x 1. 5 x 5). Two types of trays are contained in the test section: sieve tray and valve tray. For this particular experiment, stainless-steel sieve tray with thickness of 0. 078 and an active area of 11 ? x 34 ? was evaluated. A sieve tray consists of a large number of 3/16-diameter â€Å"holes† known as perforations drilled on 3/4 triangular pitches which allow the passage of air through the water. Pumped water flows across the tray and over the 2. 0 weir, and falls down a 15 x 4 downcomer into the bottom tray via a 1. clearance. The blower and the pump were powered by the on-off buttons. The water flow rate was varied by adjusting the valve behind the pump until the desired water differential pressure was obtained. This differential pressure of water was measured by an orifice meter of 1. 250 diameter. It was necessary to purge any air in the orifice meter before running the e xperiment. Besides, the flow rate of air was controlled by using the lever on the lower panel. The air differential pressure was obtained via a Pitot-static tube in circular duct of 7 7/8 diameter. From that, the mass flow rate of water would be determined by using the given equation of calibration in the lab manual; the air velocity could be estimated by methods in Perry’s Handbook. To begin the experiment, the water was allowed to fill to a minimum of six inches from the bottom of the tower test section. It was noticed to maintain the six inches height of water during the experiment in order to avoid cavitation. At this point, the pump was started and water was allowed to flow down the apparatus. The experiment was operated with five water flow rate of 0. 050, 0. 074, 0. 093, 0. 109, and 0. 124 ft3/s. A dry run, in which there was no liquid flowing, was also conducted. For each water flowrate and dry run, the experiment was run at 2. 161, 4. 515, 5. 682, 6. 385, and 6. 958 ft3/s for air flowrate. Data was recorded for this part of the experiment including tray pressure drop, height of clear liquid crest over weir, height of liquid at tray entrance, height of froth on the tray, height of liquid and froth leaving tray, height of clear liquid in downcomer, and height of liquid and froth in downcomer. The specifications of measured heights, which were determined by provided yardstick, are shown in Figure 4. Figure 4: Diagram of Tray Hydraulic Tower and Specifications of Height Measurements. 3 For safety in the laboratory, eye protection was worn all the time. Water and air were only materials used in this experiment, so there was no harmful toxic hazard. The only concerned hazard was mainly due to the spillage of water from transferring and leaking. To prevent the slipping and falling, the area was kept to be dry by removing water consistently into a nearby drain. Results and Conclusion – Tricia Heitmann In part A of the experiment pressure drops were recorded across a venture meter and across an orifice meter. The amount of water was collected and timed in order to find a flow rate for that particular pressure. A plot of log (flow rate) versus log (pressure drop) was made (Figure 5). Based on Bernoulli’s equation and equation 1 the slope of both lines should be equal to . 5. The slope stems from the square root in the equation. However the slopes of the lines were found to be . 53  ± . 03 for the venturi meter and 0. 46  ± . 02 for the orifice meter. The contribution of a frictional force from the metal pipe and the water would cause the water flow rate to be lower than ideal. The Bernoulli’s equation does not account for this friction. From Figure 5 it can be seen that the correlation coefficients are . 97 for the venturi meter and . 96 for the orifice meter. Since the correlation coefficients are close to one, the Bernoulli’s equation is a good model for the data. From the graph it can be seen that as the pressure drop increases, so does the flow rate. The venturi meter had a smaller pressure drop that than the orifice meter and also deviated more from the predicted . 5 slope. From this analysis it shows that venturi meter is better used at higher flow rates than the ones used during this experiment. The coefficient of discharge can be calculated from equation 1 for both the venturi and orifice meter. For the venturi meter the average calculated coefficient of discharge is 0. 984  ± 0. 001 and for the orifice meter has an average calculated coefficient of discharge of 0. 540  ± 0. 001. The percent error of Cd for the venturi meter is . 046% and 9. 2% error in the Cd of the orifice meter. The venturi meter behaved more ideally than the orifice meter. This is due to the venturi meter gradually constricting flow, rather than having a sudden flow constriction, like the orifice meter has. Because of this sudden constriction water lags at the entrance and does not discharge. For practical purposes it would be wiser to use the Venturi meter because the coefficient of discharge is higher than that of the orifice meter. For part B the pressure drop was plotted against the net airflow rate shown as figure 2. The pressure of water was varied from 15 in H2O to 75 in H2O. A dry run was also performed. As the airflow increases so does the pressure drop. From this plot it can also be seen that as the flow rate of the water is increased the pressure drop also increases. These results mirror what was expected, an increase in pressure drop with and increase in air velocity. Another thing to note from this plot is that as the net air velocity increases, the differences in the water flow rates become less pronounced and harder to distinguish one flow rate from another. A plot of change in pressure versus percent flooding was made. This graph is much like the previous graph. As the percent flooding increases so does the pressure drop and again, as the percent flooding increases the difference between the water pressures become harder to see. The percent flooding was found from a relation found in Perry’s. Figure 7 shows that the apparatus was not in flooding range during operation. It makes sense that the trends of Figure 2 and Figure 3 are similar because the percent flooding is linearly related to net air velocity. Next the aeration factor (beta) was plotted against the net airflow, shown below as figure 8. The solid lines are the calculated values and the individual points are the values that were experimentally found. Both decrease as net air velocity increases. The aeration is found (experimentally) through the height of the liquid and froth leaving the tray. Error can come from the change in the froth height. Although the calculated and measured aeration factors do not match up exactly, the trends are the same. Figure 9 shows ht versus the net airflow rate. Like the previous plot, the calculated values are the solid lines and the experimentally found data are individual points. The trends for the calculated and experimentally found values are not the same. For the calculated values, as the net air velocity increases, the pressure drop increases, but then starts to increase and for the experimental values, as the net air velocity increases, so does the pressure drop. Once ht has been either found/calculated, h’dc, the height of the froth and liquid of the downcomer, can be calculated. Figure 10 shows the relationship of h’dc to the height of liquid and froth in the downcomer and figure 11 shows the relationship of h’dc to the height of clear liquid. H’dc was found from using equation 3. When using this equation, ? dc was assumed to be . 5. This assumption is made based on low viscosity for liquids and low viscosity of the gas. Both water and air have low viscosities, so this assumption is valid. Desired separation will not happen if the h’dc is higher than the tray spacing. The tray spacing for this experiment is 24 inches. While there were two points of the measured that were above the 24 inches, they were at the highest water pressure and the highest two air flow rates. The calculated h’dc values never exceeded the 24 inches. Figure 11: Height of clear liquid vs. net air velocity Figure 11: Height of clear liquid vs. net air velocity Conclusion and Recommendations – Tricia Heitmann The fluid flow part of the experiment overall had relatively low error. This can be stated by the low error in the slopes of the log-log plot (figure 5) and the . 46% error of the coefficient of discharge for the venturi meter. The largest error of this part of the experiment was from the coefficient of discharge of the orifice meter. The coefficient of discharge of the orifice meter had an error of 9. 2 percent. This error can be traced back to the determination of the pressure drop. When the hose that was used for measuring the volumetric flow rate was adjus ted, the pressure drop fluctuated. Because of the fluctuation it was very important to keep the hose steady and at the same level when the pressure drops were read. In the second part of the lab, biggest source of error came from the measured values. This is due the fluctuation of the heights of the froth and the water. References – Alex Long 1. Perry, Robert H. , Don W. Green, and James OHara. Maloney. Perrys Chemical Engineers Handbook. New York: McGraw-Hill Book, 1984. Print. 2. Henley, Ernest J. , J. D. Seader, and D. Keith. Roper. Separation Process Principles. Chichester: John Wiley amp; Sons, 2011. Print. 3. â€Å"Fluid Flow Meters/Tray Hydraulics†. Unit Operations Laboratory Information Sheets, 2013. Appendix A: Raw Data – Alex Long Fluid Flow Meters Table 1: Flow measurements and calculations for multiple combinations of pipes with three trials each Table 2a: Measurements and calculations for a Venturi flow meter. This is an extension of Table 1. Table 2b: Measurements and calculations for a Orifice flow meter. This is an extension of Table 1. Tray Hydraulics Area Calculations: Table 3: Important calculated areas of the column. Dry Run: Table 4: Differential pressure measurements and important calculated values for a dry run with no water flow. Wetted Runs: Table 5: Measured differential pressures and heights for 5 air flow rates at 3 different water flow rates. Table 6: Calculated values for the air flow rates and water flow rates shown in Table 5. Table 7: Additional calculated values for the water flow rates and air flow rates shown in Table 5. Appendix B: Data Plots – Alex Long Fluid Flow Meters Figure 5: A log-log plot of the water mass flow rate vs. the pressure drop in both a Venturi and Orifice meter. Tray Hydraulics Figure 6: A plot of the pressure drop across the sieve tray vs. the air velocity based on the net area for vapor flow. Figure 7: A plot of the pressure drop across the sieve tray vs. the percent of the flood point. Figure 8: A comparison of measured pressure drop across the sieve tray and the pressure drop across the tray calculated according to Perrys 7th Edition Handbook. Both are plotted as functions of net air velocity. Lines represent the calculated values, whereas points represent the measured values. Figure 9: A comparison of the aeration measured aeration factors and the calculated aeration factors. Both are plotted as functions of net air velocity. Lines represent calculated values and points represent measured values. Figure 10: A comparison of the measured height of clear liquid in the owncomer and the calculated headloss under the downcomer apron in terms of inches of water. Both are plotted as functions of net air velocity. Calculated headloss is represented by lines and can be seen to be constant with net air velocity and measured heights are represented by points that vary with net air velocity. Figure 11: A comparison of the height of the liquid and froth in the downcomer and th e calculated downcomer backup in terms of inches of water. Both are plotted as functions of net air velocity. Lines represent calculated downcomer backup and point represent measured heights. Appendix C: Sample Calculations – Alex Long Fluid Flow Meters All sample calculations are based on #Run 1. Pressure drop: Venturi ?PV=PV,in-PV,out*(0. 036lbmin2*144in2ft2) ?PV=4. 25 in H2O-6. 25 in H2O*0. 036lbmin2*144in2ft2 ?PV=0. 072 psi Orifice ?PO=PO,in-PO,out*(0. 036lbmin2*144in2ft2) ?PO=2. 00 in H2O-8. 50 in H2O*0. 036lbmin2*144in2ft2 ?PO=0. 230 psi Volumetric flow rate of water: q=Vt q=2000 mL*0. 00000353ft3mL9. 57 s q=0. 0074ft3s Mass flow rate of water: m= q? m=0. 0074ft3s? 64. 2lbmft3 m=0. 461lbms Water velocity: v=q? 4*D2*144in21ft2 v=0. 0074ft3s? 4*(0. 0854 ft)2*144in21ft2 v=1. 29 ft/s Reynolds number for water flow: Re=? Dv? Re=64. 2lfmft3*0. 0854 ft*1. 9fts0. 000002344lbmft s Re=2. 93*105 Logarithm of the pressure drop for graphical analysis: Venturi log? Pv=log0. 072 psi log? Pv=-1. 1 psi Orifice log? PO=log0. 230 psi log? PO=-0. 63 psi Logarithm of the volumetric flow rate for graphical analysis: logq=log0. 0074ft3s logq=-0. 337ft3s Discharge coefficient Cd: m=q? =CYA22gc? P? 1-? 4 * For venture: Cd= 0. 461lbms 2*(32. 2lbm*fts)*(10. 405lbft2)*(62. 2lbmft3)1-(0. 625in1. 025in)4*1*(0. 0012305ft2) = 0. 981 * For orifice: Cd= 0. 461lbms2*(32. 2lbm*fts)*(10. 405lbft2)*(62. 2lbmft3)1-(0. 625in1. 025in)4*1*(0. 0012305ft2) = 0. 544 Error Considerations for Fluid Flow Pressure Drop: Venturi Pv= ? Pv? Pv,in2*? v,in2+? Pv? Pv,out2*? v,out2 Pv= 1*0. 036lbmin22*. 1252+-1*0. 036lbmin22* . 1252 Pv= . 00002025+0. 00002025 Pv= 0. 0000405 Pv= . 006 psi Orifice Po= ? PO? PO,in2*? O,in2+? PO? PO,out2*? O,out2 Pv= 1*0. 036lbmin22*. 1252+-1*0. 036lbmin22* . 1252 Pv= . 00002025+0. 00002025 Pv= 0. 0000405 Pv= . 006 psi Volumetric flow rate of water: ?q= ? q? V2*? V2*0. 00003532+? q? t2*? t2*0. 00003532 ?q= 1t2*? V2*0. 00003532+qt22*? t2*0. 00003532 ?q= 19. 572*202*0. 00003532 +20009. 5722*. 012*0. 00003532 ?q= 5. 4424*10-9+5. 94734*10-11 ?q= 5. 50181*10-9 ?q= . 00007 ft3/s Mass flow of water: ?m= ? m? q2*? q2+? m 2* 2 ?M= ±V2 2+? 2 2 ?M= ±. 00738 2. 012+62. 42. 00072 ?M= ±2. 198*10-5 ?M= ± 0. 005 lbm/s Water Velocity: ?v= ? v? q2*? q2+? v? D2*? D2 ?v= 1? 4*(D)22*? q2+-2q? 4*D32*? D2 ?v= 1? 4*(1. 025)22*. 000072*1442+-2*. 00738? 4*(1. 025)32*. 0012*1442 ? v=  ± 0. 01 ft/s Reynolds number for water flow: ?Re= ? Re? v2*? v2+? Re 2* 2+? Re? D2*? D2+? Re 2* 2 ? Re= 64. 2*0. 0854 0. 0000023442*. 012+0. 0854 *1. 290. 0000023442*. 12+6. 2*1. 290. 0000023442*8. 3E-52+64. 2*0. 0854*1. 290. 00000234422*. 000000012 ? Re=  ±2. 93*105 Logarithm of the pressure drop for graphical analysis: Venturi ?v= 1/P2*? P2 ?v= 1. 722*. 0062 ?v= . 09 psi Orifice (same equation as Venturi) Logarithm of the volumetric flow rate for graphical analysis: ? v= 1/m2*? m2 ?v= 1/. 4612*. 0052 ?v=  ±. 01 psi Coefficient of discharge: ?Cd= ? Cd? m2*? m2+? Cd? P2*? P2 ?Cd= . 003 Tray Hydraulics Area Calculations: For these calculations all dimensions were given in the experiment assignment sheet. Additionally, all areas are converted into square feet. Net area for vapor flow: Anet for vapor flow =Test section W*Test Section L144in2ft2 Anet for vapor flow =15 in*48 in144in2ft2 Anet for vapor flow =5. 0 ft2 Active area: Aactive=active W*active L144 in2/ft2 Aactive=11. 75 in*34. 5 in144 in2/ft2 Aactive=2. 82 ft2 Downcomer area: Adowncomer=downcomer W*downcomer L144in2ft2 Adowncomer=15 in*4 in144in2ft2 Adowncomer=0. 42 ft2 Area of holes and valves: Aholes and valves=Aactive*Aopen Aholes and valves=2. 82 ft2*0. 057 Aholes and valves=0. 159 ft^2 Total cross-sectional area of tower: ACS=Anet for vapor flow+Adowncomer ACS=5. 0 ft2+0. 42 ft2 ACS=5. 42 ft2 Open area of downcomer apron: ADC apron=downcomer W*downcomer clearance144in2ft2 ADC apron=15 in*1. 5 in144in2ft2 ADC apron=0. 15 ft2 Lab Worksheet Calculations: The following calculations are those specifically requested to be included in the laboratory worksheet by the experiment assignment sheet. Physical property data was obtained from the website Engineeringtoolbox. com. A constant air temperature of 70  °F and a constant water temperature of 65  °F were assumed over the course of all experiments. Liquid water is considered to be incompressible and the density varies inconsequentially over the range of 55 to 75  °F. Physical properties for air vary more significantly, but they do not vary by a significant amount over the likely temperature range of the air in the lab. Finally, all calculations are completed for a differential pressure measurement for air of 0. 095 in. H2O and a differential pressure measurement for water of 75 in. H2O. Maximum air velocity: vmax=2*gc*dPair*? w? a*1ft12in vmax=2*32. 17lbm fts2 lbf *0. 095 in H2O*62. 275 lbm/ft30. 07495 lbm/ft3*1ft12in vmax=20. 6 ft/s Reynolds number for air: Re=? a*Dair valve*vmax? a Re=0. 07495lbmft3*7. 875in*1ft12in*20. 6 ft/s1. 225*10-5lbmft s Re=82600 Average air velocity: vavg=vmax2 vavg=20. 6 ft/s2 vavg=10. 3 ft/s Mass flow rate of water: m=dPw1. 2178*10-611. 7525 m=75 in H2O1. 2178*10-611. 7525 m=27800lbmh Volumetric flow rate of air: qair=vmax*Dair valve12inft*? 4 qair=20. 6fts*7. 875 in12inft2*3. 141594 qair=6. 96 ft3/s Volumetric flow rate of water: qwater=m3600*? w qwater=27800lbmh3600*62. 275 lbm/ft3 qwater=0. 124ft3s Net Air velocity: vnet=qairAnet for vapor flow vnet=6. 96 ft3/s5. 0 ft2 vnet=1. 39 ft/s Ratio defined in the experiment assignment sheet which will be designated FLG (as defined in Perry’s): FLG=qwaterqair? a? w FLG=0. 124 ft3/s6. 96 ft3/s0. 07495 lbm/ft362. 275 lbm/ft3 FLG=0. 001 Capacity parameter: Csbf=0. 0105+8. 127*10-4*Tray spacing*25. 40. 755*e1. 463*FLG0. 842 Csbf=0. 0105+8. 27*10-4*24 in*25. 40. 755*e1. 463*0. 0010. 842 Csbf=0. 113ms Net air velocity at the flooding point (? is the surface tension and the value is from the website listed at the beginning of this section): Unf=Csbf*? 200. 2*? w-? a? a*3. 281 ft/m Unf=0. 113ms*62. 275lbmft3-0. 07495lbmft3 0. 07495lbmft3*3. 281ftm Unf=13. 6fts Percent flooding: %Flood=vnetUnf*100% %Flood=1. 39fts13. 6fts *100% %Flood=10. 3% Additional Calculations for Comparison from Perry’s Handbook: These additional calculations were not specifically asked for in the experiment assignment sheet, but they are needed for many of the requested plots. They generally are used to provide a literature comparison for our experimental findings. As above, all calculations are completed for a differential pressure measurement for air of 0. 095 in. H2O and a differential pressure measurement for water of 75 in. H2O. Linear gas velocity based on net area: Un=qairAholes and valves*1m3. 281ft Un=6. 96ft3s0. 159 ft2*1m3. 281ft Un=13. 3ms Constant used to calculated K2: Cv=0. 74*Aholes and valvesAactive+e0. 29*Tray thicknessDhole-0. 56 Cv=0. 74*0. 159 ft22. 82 ft2+e0. 29*0. 416 in0. 1875 in-0. 56 Cv=0. 686 Constant K2 used to calculate the pressure drop across the sieve tray: K2=50. 8Cv2 K2=50. 80. 862 K2=108 Pressure drop across the sieve tray: hd=K1+K2*? a? w*Un2*1 mm25. 4 in hd=0+108*0. 07495 lbm/ft362. 275 lbm/ft3*(13. 3 m/s)2*1 mm25. 4 in hd=0. 907 in F-factor for flow through holes: Fch=Un*? air Fch=13. 3 m/s*1. 20 kg/m3 Fch=14. 6mskgm30. 5 Calculated aeration factor: ?calc=0. 0825*lnqwaterLweir-0. 269*lnFch+1. 679 ?calc=0. 0825*ln0. 124 ft3s*1m3(3. 281ft)315in*1ft12in*1m3. 281ft-0. 269*ln14. 6+1. 679 ? calc=0. 571 Measured aeration factor (here hh is the dP in the dry bed. The given denominator term is hw + how, weir height + height over weir which has been equivalated to the height of the liquid and froth leaving the tray): ? eas=dPtray-hhhliq and froth leaving tray ?meas=5. 6 in H2O-3. 8 in H2O4. 75 in H2O ?meas=0. 379 Height over the weir: how=664qwater2/3Lweir25. 4in1mm how=6640. 124ft3s*1m3(3. 281ft)32/315in*1ft12in*1m3. 281ft25. 4in1mm how=1. 12 in H2O Calculated height of clear liquid over dispersers (hhg is the hydraulic gradient and is assumed to be negligible): hds=how+hw+hhg hds=1. 12 in H2O+2 in+0 hds=3. 12 in Pressure drop through aerated liquid: hL=? meas*hds hL=0. 379*3. 12 in hL=1. 18 in Calculated total pressure drop across the sieve tray: ht calc=hL+hd ht calc=1. 18 in+0. 907 in ht calc=2. 09 in Headloss under the downcomer apron: hda=qwater2ADC apron hda=165. 2*0. 124ft3s0. 156 ft2 hda=16. 3 in Downcomer backup in terms of equivalent clear liquid: hdc=ht calc+hw+how+hda+hhg hdc=2. 09 in+2 in+1. 12 in+16. 3 in+0 hdc=21. 5 in Corrected downcomer backup (? dc is equal to 0. 5 according to Perry’s because of the rapid bubble rise of the system): hdc=hdc? dc hdc=21. 5 in0. 5 hdc=43. 0 in Error Considerations for Tray Hydraulics: In the second day of lab, the experiment will be repeated at each set of flowrates. Using these trials, error in the measurments will be estimated from the standard deviation: ? 1Ni=1Nxi-xavg2 This error will then be propagated through all calculations using the propagation of error: ? f=? f? x2*? x2+? f? y2*? y2+? f? y2*? y2+†¦ For this preliminary experiment, an error in the measurements was assumed based on the smallest resolution of the measuring device. In the case of measuring heights, the measuring device was a ruler that could measure to 1/8th of an inch. Thus the error in all height measurements is assumed to be 0. 125 inches. Each differential pressure gauge had a different resolution. For tray pressure drop the error is assumed to be 0. 2 in H2O. For the differential pressure of the air the error is assumed to be 0. 005 in H2O. Finally, for the differential pressure of the water the error is assumed to be 1 in H2O. Maximum air velocity: ?Vmax, air= ? Vmax air? P2*? P2+? Vmax air w2* w2+? Cd a2*? a2 ? Vmax, air= ± . 009 ft/s Reynolds number for air: Please see above Reynolds number in fluid flow Average air velocity: ?V, air= ? Vair? m2*? m2+? Cd? P2*? P2 ?V, air=  ± 0. 0004 ft/s Mass flow rate of water: ?m= ? m? P2*? P2 ?m=  ± 1 lbm/s Volumetric flow rate of air: ?V,air= ? V? D2*? D2 ?V, air=  ± 0. 003 ft3/s Volumetric flow rate of water: ?V,water= ? V,water? m2*? m2 ?V, water=  ± 0. 0003 ft3/s Net Air velocity: See velocity in fluid flow Ratio defined in the experiment assignment sheet which will be designated FLG (as defined in Perry’s): ? F= ? F? qw2*? qw2+? F? qa2*? qa2 ?F=  ± 3*10-7 Capacity parameter: ?Csbf= ? Csbf? FGL2*? FGL2 ?Csbf=  ± 1*10-7 m/s Net air velocity at the flooding point (? is the surface tension and the value is from the website listed at the beginning of this section): ? Unf= ? Unf? Csbf2*? Csbf2 ?Unf=  ± 1*10-5 ft/s Percent flooding: ?%F= ? %F? vnet2*? vnet2+? %F? Unf2*? Unf2 ?V, air=  ± 1*10-3 % Linear gas velocity based on net area: Un= ? Un? q2*? q2+? Un? a2*? A2 ?Un=  ± 0. 002 m/s Pressure drop across the sieve tray: ?hd= ? hd? Un2*? Un2 ?hda=  ± 0. 0003 in F-factor for flow through holes: ?Fch= ? Fch? Un2*? Un2 ?Fch=  ± 0. 00010 mskgm30. 5 Calculated aeration factor: calc= cal? Fch2*? Fch2 calc=  ± 0. 02 Measured aeration factor (here hh is the dP in the dry bed. The given denominator term is hw + how, weir height + height over weir which has been equivalated to the height of the liquid and froth leaving the tray): ,M= ,M? dP2*? dP2+ ,M? hh2*? hh2+ ,M? lf2*? lf2 meas=  ± 0. 06 Height over the weir: ?how= ? how? water2*? qwater2+ ,M? Lweir2*? Lweir2 ?how=  ± 2*10-5 in H2O Calculated height of clear liquid over dispersers (hhg is the hydraulic gradient and is assumed to be negligible): ? hds= ? hds? how2*? how2+? hds? hw2*? hw2+? hds? hg2*? hg2 ? hds=  ± 2*10-5 in Pressure drop through aerated liquid: ? hL= ? hL m2* m2+? hL? hds2*? hds2 ?hL=  ± 0. 02 in Calculated total pressure drop across the sieve tray: ?htc= ? htc? hL2*? hL2+? htc? hd2*? hd2 ?htc=  ± 0. 02 in Headloss under the downcomer apron: ?hda= ? hda? q2*? q2+? hda? Adc2*? Adc2 ?hda=  ± 0. 06 Downcomer backup in terms of equivalent clear liquid: