Shell-and-Tube Heat Exchangers Unit Operations Laboratory - Sarkeys E111 February 11 th & 18 th, 2015 ChE 3432 - Section 3 Eric Henderson Eddie Rich Xiaorong Zhang Mikey Zhou
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ABSTRACT Shell-and-tube heat exchangers were the focal point of this experiment, and were examined to evaluate the properties of pressure drop and heat transfer. Tube-side pressure drop data for a single 1-4 heat exchanger was collected for flow rates between 1665.33 and 4662.08 lb/hr to determine the portion of the overall tube-side pressure drop that was due to tube boxes was between 26% and 45.6% respectively, while the overall tube-side pressure drop due to skin friction was between 74% and 55.4% respectively. Shell-side pressure drop data was collected for five heat exchangers with different number of baffles for flow rates ranging from 2610 to 10010 lb/hr to determine that there were approximately 9 baffles in a heat exchanger that had an unknown number of baffles. A 1-4 heat exchanger with no baffles was used as a steam condenser to find a linear relationship between the convective film heat transfer coefficient of water flowing tube-side, and the convective film heat transfer coefficient inside the long straight tubes of the condenser. This linear relationship was used to find that the heat transfer coefficient ranged from 1.86 to 263.6 BTU/hft 2 F for steam at 50% of its maximum flow rate, while the tube-side flow rate ranged from 4.8 to 772.8 lb/hr. Data was also collected for steam at 100% of its maximum flow rate to get a heat transfer coefficient range of 108.5 to 607.1 BTU/hft 2 F, while the tube-side flow rate ranged from 4.77 to 3864.2 lb/hr. 2
INTRODUCTION AND THEORY In this experiment, shell-and-tube heat exchangers were examined to better understand the causes of tube-side and shell-side pressure drop, and heat transfer of flowing water. This experiment was performed in two parts on separate occasions. The purpose of the first part of the experiment was to determine the amount of pressure drop due to skin friction and tube boxes for the tube-side flow, and to develop an equation correlating shell-side pressure drop to the number of baffles in heat exchangers. Tube boxes enclose each end of the shell of a heat exchanger and redirects flow so the tube-side fluid can make another pass. Baffles are metal plates inside the shell that alter shell-side flow to increase heat transfer. The purpose of the second part of the experiment was to evaluate the convective film heat transfer coefficient for water flowing through long straight tubes in a steam condenser. Tubular heat exchangers are used in a vast majority of industrial and chemical process, which is the reason their designs are so highly developed. 1 The basic function of heat exchangers is to transfer heat from a flowing fluid of high temperature, to a flowing fluid with a lower temperature. A typical shell-and-tube heat exchanger consists of a shell that is enclosed at each end by stationary heads as shown in Figure 1. Stationary heads are also known as tube boxes. Inside the shell are tubesheets at each end of the exchanger in which a guide rod and baffle spacers are attached to support the baffles and tubes. Two major aspects when designing shell-and-tube heat exchangers are determining if the tube-side and shell-side flows should be single-pass or multipass, and the number of baffles to place inside the shell along with their configuration. This experiment used 1-4 heat exchangers which indicate the number of passes the shell-side and tubeside fluid make through the system. For example, the shell-side made one pass through the heat exchanger, while the tube-side made four passes. There were twenty 3
FIGURE 1. Single pass 1-1 shell-and-tube heat exchanger. 2 FIGURE 2. 1-4 Shell-and tube heat exchanger. 11 copper tubes inside each heat exchanger, with each pass going through five of the tubes. Twenty solid dummy tubes were also placed inside the heat exchanger to prevent a path of lower resistance for the shell-side fluid to flow through from forming. The dummy tubes did not participate in heat transfer. The first part of the experiment was split between finding the tube-side pressure drop of a single heat exchanger, and finding the number of baffles in an unknown heat exchanger using pressure drop data from five heat exchangers of known number of baffles. Since all of the four pass heat exchangers only differed in the number of baffles, tube-side pressure drop data only needed to be recorded for one heat exchanger. Tube-side pressure drop is caused by skin friction inside the pipes, and change in flow direction inside the tube boxes. The skin friction of the tubes causes a pressure drop known as head loss h L, which can be calculated using the Fanning friction factor f f, length of tubes L, diameter of tubes D, velocity of fluid through tubes ʋ, and the gravitational constant g. 3 L ʋ h L = 2f 2 f = ΔP D g ρ (1.1) The Fanning friction factor can be calculated using equation (1.2), assuming that the flow is turbulent and the pipe is smooth. 4 1 f f = 4.0 log 10 (Re f f ) 0.40 (1.2) 4
The Reynolds number Re represents a dimensionless ratio of the inertial forces to the viscous forces in fluid flow. 5 L is the length of pipe, ʋ is the velocity of the fluid, ρ is the density of the fluid, and µ is the viscosity of the fluid. Re = Lʋρ µ (1.3) The tube-side mass flow rate was calculated using the tube-side Venturi meter calibration curve, and then was converted into the velocity of the fluid by knowing the density of water and the diameter of the tube. ln (y) = 0.506 ln (x) + 7.249 (1.4) y = water flowrate ( lb hr ) x = Δ P (cmhg) At each end of the heat exchanger, there are tube boxes that redirect the flow in the opposite direction so the fluid can make another pass through the exchanger. These tube sheets cause a significant pressure drop as well and can be calculated by subtracting the pressure drop due to head loss from the overall measured tube-side pressure drop. P tube boxes = P total P friction (1.5) The single-segmental baffles used in the heat exchangers for this experiment are semicircular metal plates attached to a guide rod and copper tubes in a perpendicular manner inside the shell of the exchanger. 6 Baffles are used to increase heat transfer by increasing the average velocity and causing crossflow of the shell-side fluid over the tubes. 1 Although baffles increase heat transfer, they cause a significant pressure drop. This pressure drop was used in the first part of the experiment to determine the number of baffles in an unknown heat exchanger using pressure drop data from heat exchangers with a known number of baffles. The Venturi meter calibration equation for the shell-side flow was used to calculate the shell-side mass flow rate. ln(y) = 0.52 ln(x) + 7.343 (1.6) 5
y = water flowrate ( lb hr ) x = Δ P (cmhg) An equation had to be developed to find the number of baffles in the unknown heat exchanger. Equations (1.7) and (1.8) were given in the lab manual 12, and utilized to develop the equation to find the number of baffles N, where a, b, y and z are constants. P = a (flow rate) z (1.7) a = b N y (1.8) Applying equations (1.7) and (1.8) to the calibration curves for shell-side flow, the number of unknown baffles can be evaluated once the constants are calculated. log( P) = log(a) + z log(flow rate) (1.9) log(a) = log(b) + y log (N) (1.10) For the second part of the experiment, water was passed tube-side through a heat exchanger while steam was passed shell-side to heat up the water. The convective film heat transfer coefficient for the water flowing tube-side was of interest. To calculate the heat transfer coefficient, a different form of the Dittus-Boelter equation was used. 7 Nu = h id k = αre0.8 Pr 1/3 (1.11) The Reynolds number is used in the calculations, and is found the same way as in part one of the experiment. The Prandtl number Pr, is a dimensionless ratio of the molecular diffusivity of momentum to the molecular diffusivity of heat, where µ is the viscosity of the fluid, c p is the heat capacity of the fluid, and k is the thermal conductivity of the fluid. 8 Pr = µc p k (1.12) The form of the Dittus-Boelter equation used was given in the lab manual 12, where U i is the overall heat transfer coefficient. 9 6
1 U i = 1 k (1.13) D Re0.8 Pr 1/3 The overall heat transfer coefficient is found by calculating the heat gained in the system using equation (1.14), and then solving for the overall heat transfer coefficient in equation (1.15). 9 Δq = m c p ΔT L (1.14) U = q AΔT (1.15) L The mass flow rate m of the water is found the same way as in the first part of the experiment. The heat capacity c p of water fluctuates slightly with temperature which must be accounted for. The logarithmic-mean temperature difference ΔT L is a very important fluid heat transfer equation to help determine how well a heat exchanger performs. 10 LMTD = ΔT L = ΔT 1 ΔT 2 ln ( ΔT 1 ΔT2 ) (1.16) From equation (1.13), a Wilson plot of 1 U i vs. 1 k D Re0.8 Pr 1/3 was created to find the slope of the trendline α, generated from the experimental data. The convective film heat transfer coefficient was then calculated using equation (1.17). Apparatus and Procedures 1 h = (1.17) α k D Re0.8 Pr 1/3 Equipment Description The heat exchanger unit is comprised of six, 1-4 pass shell-and-tube heat exchangers, a single-pass heat exchanger, and a steam condenser. In a 1-4 pass heat exchanger, water flows through the length of the shell four times before exiting. For a single-pass heat exchanger, water enters tube-side and just flows through the length of the shell once before exiting. In each of the heat exchangers there are a different number of baffles which, on average, are 0.041-inches thick. 7
FIGURE 3. Apparatus The distance between each baffle varies depending on the number of baffles in the exchanger. The tubes within the exchangers are made of copper, and have an outer diameter of 0.3 inches and an inner diameter of 0.25 inches. The walls of the tubes are 0.025 inches thick, and the center-to-center distance between tubes is 0.406 inches. Each tube is 30 inches long, measuring from tube-sheet to tube-sheet. Not all of the tubes in the exchangers are open-ended. Some solid, close-ended tubes are included to be used as dummy tubes, which serve to prevent short-circuiting of the shell-side flow. Since there is no flow through these dummy tubes, they provide no heat transfer surface. Shell-side, the outer and inner diameters are 3.125 and 3.06 inches, respectively. As for the steam condenser, there are no shell baffles and the tube-sheet to tube-sheet length is 23.3 inches. The condenser s role in the second week of the experiment is to use steam to heat up the process water; it is not used in the first week. There are three feeds into the heat exchanger unit: process water, cooling water, and steam. The manual valves (indicated in green in FIGURE 4) for each feed must first be opened before the user can manipulate the flow rate at which water will run through the valves via process control valves on the HeatX computer program, which is the software used in this experiment for data collection. 8
FIGURE 4. Schematic illustrating fluid flow excluding heat exchangers These process control valves generate a current signal that is sent to the current-topneumatic transducers, which then converts the signal to an air pressure between 3 and 15 psig. This pressure closes the valve the desired amount, which can range from 0% open to 100% open. Temperatures at the tube-in, tube-out, and shell-out locations of each heat exchanger can be read from the Thermo Electric thermocouple on the front of the apparatus. The Omega Engineering rotary thermocouple switch is used to control which exchanger s temperature reading is displayed. The figure above is a depiction of the front of the apparatus. The process water flows tube-side through the condenser where it is heated by steam that flows in shell-side. The process water then flows tube-side through the heat exchangers where it is cooled by the cooling water that flows in through the heat exchangers shell-side. There are two Venturi meters in the apparatus. One Venturi meter is placed at a location before the process water enters the condenser, and the other is placed at a location before the cooling water enters the heat exchangers. Two pressure transducers send signals to the computer that allow the pressure drop across these Venturi meters to be read continuously; this data is then used to calculate tube-side and shell-side flow rate. A third pressure transducer allows for the reading of pressure drop across any heat exchanger. To obtain these readings from the HeatX program, the heat exchanger s corresponding tubes must be attached to the appropriate pressure 9 FIGURE 5. Process control valves on HeatX program
sockets on the front of the apparatus (FIGURE 6). As can be seen, there are nine pairs of highand low-pressure tubes. Although not shown in the figure, there is a sheet of paper in the laboratory pinned to the front of the apparatus that specifies which pair of tubes correspond to each particular FIGURE 6. Schematic of apparatus front panel exchanger. Operating Procedures: For week one of the experiment, the subject of interest was the pressure drop on the tubeside and shell-side of the exchanger. Because all the heat exchangers were similar in the tube-side direction, to analyze tube-side pressure drop it was only necessary to collect data for the 11-baffle exchanger. Shell-side pressure drop data was recorded for the 25, 21, 17, 13, 11, and X (unknown number) baffle heat exchangers. In order to measure the pressure drops, a pair of tubes corresponding to each exchanger has to be attached to the high pressure and low pressure sockets on the front of the apparatus. The high pressure socket is where the tube connected to the entrance of the heat exchanger is attached, and the low pressure socket is where the tube connected to the exit of the heat exchanger is attached. To turn on the water flow, the process water manual valve must first be opened. With this valve open, the process control valve on the HeatX program can be manipulated to vary the flow rate of water entering. In this lab, the process control valve was initially set to 100% open, and was decreased in increments of 10% until the valve was 0% open. 10
Pressure drop data across the heat exchanger and the Venturi was recorded at each process control valve setting. The pressure drop data fluctuated too quickly to get an accurate reading, so the data was exported to Excel to be averaged, and this value was then recorded. Collection of the pressure drop data is nearly identical for both the tube-side and the shell-side procedure. The only difference is that when examining shell-side pressure drop, the cold water feed is used instead of the process water. Consequently, on the HeatX program, the cold water valve is varied instead of the process water valve. Because the flow rates were being changed from trial to trial, it was important to make sure the system reached steady-state before collecting data. Thus, data was not recorded until the temperature reading on the HeatX program had stabilized. In week two, the objective was to determine the convective film heat transfer coefficient inside the tubes. In this part, the condenser and the steam feed would actually be used. Before the steam was allowed to flow through the unit, process water was run through the condenser and each heat exchanger. Cooling water was also run through each exchanger to lower the temperature of the exiting process water. After water had been flowing for a few minutes, steam was allowed to flow through the condenser to heat up the process water. On top of the condenser is a pressure gauge that was used to monitor the pressure within the condenser. This pressure had to be kept within 1-3 psig; if the limit was exceeded, the steam vent valve must be opened to release some pressure from the condenser. With each fluid running, the experiment began with the process water at 100% open. The steam temperature and the temperatures of the entering and exiting process water were read off of the thermocouple on the front of the apparatus. The pressure drop across the Venturi was acquired from the HeatX computer program, just as it was done in the first week. The process water valve was then closed in increments of 10% until the valve was completely shut, and the temperature and pressure drop data were recorded for each trial. After all runs were 11
completed, the steam supply valve was closed, allowing the condenser to cool down. Finally, the process water and cooling water supply valves were shut off. The primary safety concern with this experiment arises from working with steam. Because the temperature of the steam was so high, it was necessary to wear gloves while working with the condenser. RESULTS & DISCUSSION In order to obtain data for correlating pressure drop and water flow rate, varying pressure differentials and drops were recorded via computer, while the amount of water fed into the tube side of the 11 baffle heat exchanger was decreased from 100% to 0% in 10% increments. The results from data analysis showed that an increase in the water flow rate caused an increase in the pressure drop within the tubes, and consequently, a decrease in frictional head loss (Figure 7). This trend is consistent with the relationship in Equation 1.4. Pertaining to the pressure drop with the tube side feed, a greater total pressure drop than pressure drop due to friction was expected. As water flow rate varied from 1665.33 to 4662.08 lb/hr, the total pressure drop varied from 0.04 to 1.16 inches H2O, whereas the frictional pressure drop varied from 0.62 to 3.87 inches H2O. These ranges generate two curves, and by taking the difference between these two curves, the pressure due to boxes (Boxes P) could then be found. The pressure drop due to the boxes ranged between 0.25 to 0.57 inches H2O, increasing with increasing flow rate. Figure 7 shows an example of this. Shell side feed for a heat exchanger also involves a relationship between pressure drop and water flow rate, which is dependent on the number of baffles present in the heat exchanger. 12
Log P [in H2O] 1.3 1.1 0.9 0.7 0.5 0.3 0.1 y = 2.4237x - 7.6979 R² = 0.9867 0.83 y = 1.7786x - 5.9378 R² = 1-0.1 3.2 3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7-0.3 0.28 Log of Flow Rate [lb/hr] Boxes P = 0.55 Total Frictional FIGURE 7. A log-log plot for an 11 baffle heat exchanger with tube side feed showing the total and frictional pressure drops vs. the flow rate of water. A heat exchanger with an unknown number of baffles (X) was presented and by plotting the pressure drop vs. flow rate for heat exchangers with a known number of baffles (25, 21, 17, 13 & 11), an estimation for X could be deduced. Figure 4 indicates that increasing the number of baffles will increase pressure drop at a fixed flow rate. In order to calculate the actual number of baffles in X, a relationship between pressure drop and flow rate from Equations 1.7 and 1.8 must be used, along with the knowledge from Bernoulli s equation that the theoretical slope of the lines for the heat exchangers is two. Table 1 can then be constructed by taking slope (Z) and intercept (log(a)) values from Figure 4. By utilizing Equations 1.7, 1.8, and the linest values from Table 1, the number of baffles in the unknown heat exchanger, X, is calculated to be 8.53, or about 9 baffles. It may also be noted that the linest values of log(a) and log(baffles) in Table 1 correspond to the slope and the intercept values from Figure 9. The rounding up of X from 8.53 to 9 is caused from 13
log (a) Log P [psig] estimation of trends seen in Figure 8, and by the curvature in Figure 9, which can be attributed to 25 Baffles 21 baffles 17 Baffles 13 baffles 11 Baffles X Baffles y = 1.978x - 6.4411 y = 1.8869x - 6.4739 y = 1.9405x - 6.6565 y = 1.8565x - 6.0974 y = 2.3502x - 8.2966 y = 2.1733x - 7.8339 R² = 0.997 1.4 R² = 0.9994 R² = 0.9978 R² = 0.9992 R² = 0.995 R² = 0.9993 1.2 1 0.8 0.6 0.4 0.2 0 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1-0.2 Log of Flow Rate [lb/hr] -0.4 the pressure losses in both the entrance and exit nozzles for the heat exchangers. Other error considerations during this part of the experiment arose from uncertainty in measurement of the differential pressure measurements. The small sample size associated with Figure 7 led to error prorogation analysis in the range that data points should lie in, as illustrated by the vertical error bars shown in Figure 8. -6-6.5 1 1.1 1.2 1.3 1.4 Baffles Z a log baffles log a 14-7 -7.5 y = 3.4142x - 10.962 R² = 0.3329 25 1.978 3.62E-07 1.3979-6.4411 21 1.8869 3.36E-07 1.3222-6.4739-8 17 1.9405 2.21E-07 1.2304-6.6565 13 1.8565 7.99E-07 1.1139-6.0974-8.5-9 TABLE 11 1. Values 2.3502 used to 5.05E-09 ultimately determine 1.0414 the -8.2966 FIGURE 8. A log-log plot of the pressure drop vs. flow number rate FIGURE for 25, 17, 9. A 11, log-log and an plot unknown log of (# a of vs. Baffles) (X) the number of of baffles in a heat of baffles exchanger. X in X. 2.1733 1.65E-08 #VALUE! -7.78339 for each heat exchanger during shell side flow.
h (Btu/(h*ft2* F) h (Btu/(h*ft2* F) 1/Ui 1/Ui For the subsequent part of the experiment, the amount of water heated by steam within the condenser was varied. By doing this, the convective film heat transfer coefficient for the tube side could be evaluated, as quantified by Equation 1.17. For comparison, the amount of steam within the condenser was also varied. A Wilson plot (Figures 10) was then constructed using the inverse of the overall heat transfer coefficient in order to find a value for the alpha constant in Equation 1.11, which the slope of the plotted data. An average alpha value was used to calculate the convective film heat transfer coefficient, since the exchanger was run at several steam flow rates. Observed trends consisted of the amount of heat transferring from the steam to the water increased (228.1 to 263,010.8 BTU/hr for 50% steam) as the water flow rate increased (4.8 to 772.8 lb/hr). Another trend also showed the overall heat transfer coefficient increasing (1.86 to 263.6 BTU/hft 2 F for 50% steam) in relation to increasing water flow rate, which is consistent with the theory since Wilson Plot 50% Steam Wilson Plot 100% Steam 0.003 0.0025 0.002 0.0015 0.001 y = 96.331x - 0.0005 R² = 0.9882 0.01 0.008 0.006 0.004 y = 157.02x - 0.0012 R² = 0.9964 0.0005 0.002 0 0 0.00001 0.00002 0.00003 0.00004 (k/di*re0.8*pr1/3)-1 0 0 0.00002 0.00004 0.00006 0.00008 (k/di*re0.8*pr1/3)-1 300 250 200 150 100 50 0 Tube-Side Convective Heat Transfer Coefficient for 50% Steam y = 0.0628x + 24.953 R² = 0.985 0 1000 2000 3000 4000 5000 Water Flow Rate (lb/hr) Tube-Side Convective Heat Transfer Coefficient for 100% Steam 700 600 500 400 300 200 100 0 y = 0.1184x + 113.07 R² = 0.9893 0 1000 2000 3000 4000 5000 Flow Rate (lb/hr) FIGURE 10. 50% vs. 100% steam flow rate Wilson and tube-side convective heat transfer coefficient plots. 15
the coefficient is directly proportional to the amount of heat transferred. By comparison, the heat transferring from the steam to the water increased from 15,016.1 to 439,442.9 BTU/hr, and the coefficient increased from 108.5 to 607.1 BTU/hft 2 F for 100% steam flow rate. The experimental value for the overall coefficient was found to have an error of 11.3% for 50% steam and 47.1% for 100% steam, when compared to literature values 6. This error is in large part due to the roughness of the pipe and the uncertainty of the measurements. Other errors could arise from uncertainty in the measurement of the differential pressure across the heat exchanger, which would also result in error associated with calculated flow rates of water. CONCLUSION 1. Tube-side pressure drop attributed to the tube boxes was between 26% and 45.6% of the total pressure drop, while the pressure drop due to skin friction was between 74% and 55.4% of the total pressure drop, between flow rates of 1665.33 and 4662.08 lb/hr. 2. The unknown heat exchanger was found to have approximately 9 baffles by forming an equation correlating the shell-side pressure drop to the number of baffles. 3. The linear relationship between the convective film heat transfer coefficient and the tubeside flow rate was used to find that the heat transfer coefficient ranged between 1.86 and 263.6 BTU/hft 2 F, while the tube-side flow rate ranged from 4.8 to 772.8 lb/hr for steam at 50% of its maximum flow rate. For steam at 100% of its maximum flow rate, the heat transfer coefficient ranged from 108.5 to 607.1 BTU/hft 2 F, while the tube-side flow rate ranged from 4.77 to 3864.2 lb/hr 16
REFERENCES 1. McCabe, W. L., Smith, J. C., and Harriott, P. Unit Operations of Chemical Engineering, 7th ed. New York: McGraw Hill, 2005, p. 441-2 2. Mukherjee, R. Effectively Design Shell-and-Tube Heat Exchangers. CEP. Feb. 1998. p. 3. Print 3. Welty, J. R., Wicks, C. W., Wilson, R. E., and Rorrer, G. L. Fundamentals of Momentum, Heat, and Mass Transfer, 5th ed. New Jersey: Wiley, 2008, p. 169 4. Welty, J. R., Wicks, C. W., Wilson, R. E., and Rorrer, G. L. Fundamentals of Momentum, Heat, and Mass Transfer, 5th ed. New Jersey: Wiley, 2008, p. 172 5. Welty, J. R., Wicks, C. W., Wilson, R. E., and Rorrer, G. L. Fundamentals of Momentum, Heat, and Mass Transfer, 5th ed. New Jersey: Wiley, 2008, p. 128 6. Bouhairie, Salem. Selecting Baffles for Shell-and-Tube Heat Exchangers. CEP. Feb. 2012. p. 1-2. Print 7. McCabe, W. L., Smith, J. C., and Harriott, P. Unit Operations of Chemical Engineering, 7 th ed. New York: McGraw Hill, 2005, p. 358 8. Welty, J. R., Wicks, C. W., Wilson, R. E., and Rorrer, G. L. Fundamentals of Momentum, Heat, and Mass Transfer, 5 th ed. New Jersey: Wiley, 2008, p. 275-6 9. Welty, J. R., Wicks, C. W., Wilson, R. E., and Rorrer, G. L. Fundamentals of Momentum, Heat, and Mass Transfer, 5 th ed. New Jersey: Wiley, 2008, p. 340-1 10. McCabe, W. L., Smith, J. C., and Harriott, P. Unit Operations of Chemical Engineering, 7 th ed. New York: McGraw Hill, 2005, p. 333 11. "How Hot Is Too Hot?" Hydraulics & Pneumatics. N.p., 13 June 2007. Web. 22 Feb. 2015. 12. University of Oklahoma, Ch E 3432: Shell and Tube Heat Exchanger. Norman, Spring 2015. 17
Appendices Part 1 Sample Calculations To try to minimize the variations in the pressure readings from the HeatX software, after allowing a few seconds for the flow to become steady, the averages were recorded for each pressure reading. The average of the values was used to find the differential pressure in the pressure drop across each heat exchanger an meter. At 0% flow, there was still a pressure drop and differential pressure change because the flow was not completely obstructed by the actuator. The measurements at 0% flow on the HeatX software, the correction values, were subtracted from the appropriate pressure changes in the heat exchangers an meter. The units given from the readings were in psig, and were converted to cmhg using the conversion factor of: 76 cmhg 14.7 psig Tube-side The tube-side with 11 baffles sample data from our measurements will be used for 100% and 0% flow rates: The pressure corrections for Heat Exchanger (HX) using the 0% values: 100%: d = 13.632 ( 0.17) = 13.802 psig The pressure corrections for Venturi using the 0% values: 100%: d = 1.25 ( 0.14) = 2.065 psig The correcte dp is converted to cmhg: 100%: d = 2.065 psig 76cmHg = 10.676 cmhg 14.7 psig The tube-side flow rate was calculated using the tube-side flow rate equation for the Venturi meter, which was given in the lab instructions 12 : 18
ln(y) = 0.506 ln(x) + 7.249 Equation 1 y = e 0.506 ln(x)+7.249 where y = water flow rate ( lb ) and x = (cmhg) hr Total flow rate: y = e 0.506 ln(10.676)+7.249 = 4662.076 lb/hr The log base 10 was taken of the pressure drop for heat exchanger and total flow rate: log(corrected P) : log(13.802) = 1.140 log(total flow rate): log(4662.076) = 3.669 There are 5 separate tubes in each pass, so we divided the total flow rate by 5: Equation 2 m = Individual flow rate: m = lb 4662.076 hr = 932.552 lb 5 hr Total Flow Rate Density and viscosity values were obtained and interpolated for 60 C Welty 3. This data was used to find the volumetric flow rate (Q), velocity (v), and Reynolds number (Re). These equations were obtained from the same text: 5 Temp μ ρ Inner Tube CS Tube Tube ( F) (lb/s*ft) (lbm/ft 3 ) Diameter (ft) Area(ft 2 ) Length(in) 60 7.145E- 04 62.37 0.0208 3.4088E- 4 23.3 Table 2. Water properties for 60 Q ( ft3 ) = m s (lb m ) 1 hr 1 hr ρ ( lb m ft 3 ) 3600 s Equation 3 19
Q ( ft3 s ) = 932.552 (lb m hr ) 1 Re = 62.37 ( lb m ft 3) ft 3 s ) 1 hr ft3 = 0.00415 3600 s s v ( ft ) = Q ( π Equation 4 s [D (ft)]2 4 v ( ft ft 0.00415 ( 3 s ) = s ) ft π = 12.213 4 [0.0208 (in)]2 s Re = ρ (lbm ft3 ) D (ft) v (ft s ) Equation 5 μ ( lb m ft s ) 62.37 ( lb m ft3) 0.0208 (ft) 12.213 (ft s ) 7.145 10 4 ( lb = 2.218 104 m ft s ) The equation relating the Reynolds number and the Fanning friction factor for turbulent flow in a smooth pipe was obtained for Welty 2 : 1 f f = 4 log(re f f ) 0.4 Equation 6 All of the terms were moved to one side and the known Reynolds number and a guessed friction factor were plugged in. The Solver function in Excel was used to get as close to 0 as possible for this equation: 0 = 4 log (Re f f ) 0.4 1 f f 0 = 4 log (2.216 10 4 f f ) 0.4 1 f f = 6.315 10 3 The length of the tube was given in the lab instructions as 23.3 in. for one pass. The following head loss equation was also obtained from Welty 3 : f f 20
h L (ft H 2 O) = 2 f f h L (ft H 2 O) = 2 6.315 10 3 Length of pipe (in) D(in) 4 23.3 (in) 0.25 (in) [v ( ft s )] 2 [12.213 ( ft s )] 2 32.17 ( ft s 2) 1 g ( ft s 2) This head loss was converted to a pressure drop due to skin friction in psig with: P f (psig) = h L (ft H 2 O) ρ H2 O ( lb m ft 3) 1 ft2 144 in 2 = 21.830 ft H 2 O P f (psig) = 21.830(ft H 2 O) 62.370 ( lb m ft 3) 1 ft2 = 9.455 psig 144 in2 The graph for the log of the pressure drop due to skin friction was shown below and the difference between the total pressure drop and the pressure drop due to skin friction was calculated to equal the pressure drop due to the boxes. The pressure drop due to the boxes was divided by the total pressure drop and multiplied by 100% was the percentage of the total pressure drop: P boxes = log ( P total ) log ( P friction ) Equation 7 P boxes = log (13.802 psig) log (9.455 psig) = 0.572 psig Shell-side P boxes P total 100% 4.347 psig 100% = 31.5% 13.802 psig For the shell-side, the exact same calculations were used and the flow rate was found with a slightly different calibration equation as it is a separate Venturi meter: ln(y) = 0.52 ln(x) + 7.343 Equation 8 21
where y = flow rate ( lb ) and x = (cmhg) hr The flow rates and pressure drops were plotted log-log. The slope of the lines should be the same, so the intercepts for the trend lines were briefly adjusted so the slope was equalized to 2 across all 6 heat exchangers as this is the exponent shown in Bernoulli s equation: Figure 8: The log-log plot of the pressure drop versus flow rate through 6 heat exchangers with varying number of baffles, including the trend lines. The following equations relating the pressure drop, flow rate, and the number of baffles were given in the lab instructions: P = a (flow rate) z Equation 9 a = b N y Equation 10 where z, b, and y are constants and N is the number of baffles Applied to the equations 1 and 8: log( P) = log(a) + z log(flow rate) log(a) = log(b) + y log (N) Equation 11 Equation 11 was used as a template for the trend lines from figure 2. z = 2 The intercepts in the trend lines represent the log(a). These values were plotted against the log(baffles). Figure 9: The log-log plot of a-values versus the number of baffles. The plot shows curvature due to pressure drop at the entrance and exit but these were not incorporated to produce a linear trend. The a-values for calculated for all heat exchangers (using data from x baffles in this calculation): log(a) = 7.783 22
log (a) a = 10 a = 10 7.783 = 1.647 10 8 Applying equation 4 to the trend line in Figure 9, we can find b and y. The intercept is log(b) and the slope is y: y = 3.414 log(b) = 10.962 log (b) b = 10 b = 10 10.962 = 1.091 10 11 Based on the b and y values and equation 2, the number of baffles in the x heat exchanger can be estimated: a = b N y (eq. 10) N = ( a b ) 1 y 1 1.647 10 8 3.414 N = ( 1.091 10 11) = 8.534 baffles Shell-side error propagation Shell Side(25 Baffles) (psig) (cmhg) 100% Trial 1 4.5 23.627 100% Trial 2 4.47 23.111 average 4.52 23.369 Table 3. Shell-side trials for average P and calculations. 23
The standard deviation formula can be applied to data: σ = (x i x ) 2 N 1 Equation 12 where x i is the measured data point, x is the mean, and N is the number of data points Applying the standard deviation to the sample data above: σ = (4.5 4.52)2 + (4.47 4.52) 2 2 1 = 0.0706 psig The standard deviation of must be converted to cmhg from psig using the previous conversion: σ = 0.0706 psig 76 cmhg = 0.365 cmhg 14.7 psig For a function, F, dependent on two variables, the error can be propagated using: σ F = F 2 x σx 2 + F 2 y σy 2 Equation 13 Error propagation was needed for the flow rate because of the fluctuations in the pressure drop. y = FR and x = ln y = 0.52 ln x + 7.343 y = e 7.343 x 0.52 y x = e7.343 0.52 x 0.48 σ y = y 2 σ2 x x σ FR = [e 7.343 0.52 (29.1) 0.48 ] 2 0.365 2 = 18.468 lb h 24
Since flow rate and pressure had discrepancies, error propagation for a was done: a = where z = 2 from Figure 8 FRz a P = 1 FR 2 and a FR = 2 FR 3 σ a = a 2 σ 2 P P + a 2 2 σ FR FR 1 σ a = 7956.33 2 2 0.365 2 + ( 2 23.369 7956.33 3 )2 18.468 3 = 9.353 10 9 N error can be found by using the formula below: 1 N = a y and b and y are be constant b N a = 1 1 1 y b1 a y 1 y σ N = N 2 σ2 a a 1 1 σ N = ( (1.091 10 11 ) 1 1.647 10 8 3.414 3.414 2 1 3.414 1 ) (9.353 10 9 ) 2 = 1.42 25
Part 2 Sample Calculations Trial 1 Trial 2 Tube Side (psig) Temp. In ( F) Temp. Out ( F) Temp. Steam( F) (psig) Temp. In ( F)) Temp. Out ( F) Temp. Steam( F) 100% 1.425 61 73 136 1.415 62 73 135 Table 4. Tube-side condenser trial data for average and T bulk calculations. The averaged pressures: 100%: Average = 1.425 + 1.415 2 = 1.42 psig The pressures were converted to cmhg: 100%: average in cmhg = 1.42 psig 76cmHg 14.7 psig = 7.367cmHg The average temperatures: 100%: Average T steam = 100%: Average T in = 136 + 135 2 61 + 62 2 = 135.5 = 61.5 100%: Average T out = 73 + 73 2 = 73 The bulk temperatures for the process water in and out: 100% T bulk1 = T bulk = T in + T out 2 61 + 73 2 26 = 67
100% T bulk2 = 62 + 73 2 The average of the two T bulk values was used for our T: 100% average T bulk = 67 + 67.5 2 = 67.5 Plugging average into Equation 2, the flow rate can be found as: = 67.25 Total flow rate: y = e 0.506 ln(7.354)+7.367 = 3864.205 lb hr single flow rate: m = lb 3860.77 hr = 772.841 lb 5 hr Water Properties ρ (lb/ft 3 ) cp (Btu/lbm* F) µ (lbm/ft*s) k (Btu/h*ft* F) Pr T=60( F) 62.3 1 0.00076 0.34 8.08 T=80( F) 62.2 0.9999 0.000578 0.353 5.89 Table 5. Water properties of water at different temperatures Using interpolation method to find the water properties at 67.25( F) which is the bulk temperature: y = y 1 y 0 x 1 x 0 (x x 0 ) + y 0 Equation 14 ρ = 62.2 lb m ft 3 62.3 lb m ft 3 (67.25 60 ) + 62.3 lb m 80 60 ft 3 = 62.264 lb m ft 3 0.999 BTU lb cρ = m 1 BTU lb m (67.25 60 ) + 1 BTU 80 60 lb m = 0.9996 BTU lb m 27
μ = 0.000578 lb m ft s 0.00076 lb m ft s (67.25 60 ) + 0.000578 lb m 80 60 ft s = 0.000694 lb m ft s BTU 0.353 hr ft 0.34 BTU hr ft BTU k = (67.25 60 ) + 0.34 67.25 60 hr ft Pr = BTU = 0.345 hr ft 5.89 8.08 (67.25 60 ) + 5.89 = 7.286 67.25 60 Tube Side Temp. In ( F) Temp. Out ( F) Steam Temp. ( F) 100% 61.5 73 135.5 Table 6. tube-side temperature LMTD expression: LMTD trial 1 = LMTD = ((T steam T out ) (T steam T in )) ln((t steam T out )/(T steam T in )) ((135.5 73 ) (135.5 61.5 )) ln((135.5 73 ) (135.5 61.5 )) = 68.088 Using Equation 3, 4, and 5, volumetric flow rate, velocity and Re become: Q ( ft3 s ) @ 100% = 772.15 (lb m hr ) 1 62.264 ( lb m ft 3) v ( ft ft 3.44 10 3 ( 3 s ) @ 100% = s ) ft π = 10.115 4 [0.0208 (in)]2 s 28 1 hr ft3 = 3.44 10 3 3600 s s
Re @ 100% = 62.264 ( lb m ft3) 0.0208 (ft) 10.115 (ft s ) 0.000694 ( lb = 1.89 104 m ft s ) Calculating for the Wilson Plot, k D i, Re 0.8, Pr 1 3 and heat gained by the water are necessary: k D i @ 100% = BTU 0.345 hr ft 0.0208 (ft) = 16.546 BTU hr Re 0.8 @ 100% = 1.89 10 40.8 = 2637.856 Pr 1 3 @ 100% = 7.286 1 3 = 1.939 Heat Gained = Flowrate cp avg LMTD Heat Gained = 3864.205 ( lb hr ) 0.999 ( BTU lb m ) 68.088 = 2.63 105 BTU/hr The Wilson Plot is necessary for the calculation of h and to check data accuracy: Wilson plot: 1 k Re D 0.8 1 Pr3 i vs 1 U i where 1/U i = avg LMTD contact area/heat gained contact area = D i π L 4passes 5 tubes = 0.0208(ft) π 1.942(ft) 4 5 = 2.542 ft 2 for 100%: 1 U i = 68.088 2.542ft2 1.46 10 5 BTU/hr = 6.58 10 4 hr ft 2 /BTU 1 for 100%: k D Re 0.8 Pr 1 = 3 i 1 16.546( BTU hr ) 2637.856 1.939 = 1.18 10 5 Figure 10. Wilson Plot was used for h calculations. 29
Linest 320.9946-0.00429 0.906021 0.000457 0.999928 0.00143 125521.7 9 Table 7. Computation of linest values. for 100%: h = = Heat-transfer error propagation 1 320.9946 k D i Re 0.8 Pr 1 3 1 BTU 320.9946(ft 2 16.546( ) 2637.856 1.939 ) hr = 263.603BTU/(hr ft 2 ) Using Equations 12 and 13 to find the errors in the flow rate with the following sample data: Tube Side (psig) Temp. In ( F) Temp. Out ( F) Steam Temp. ( F) Bulk Temp. ( F) 67 100% Trial 1.425 61 73 136 1 100% Trial 67.5 1.415 62 73 135 2 average 1.42 61.5 73 135.5 67.25 Table 8. The measured pressures and temperatures of the condenser water in and out and steam. from Equation 12 σ = (1.425 1.42)2 +(1.415 1.42) 2 = 0.0071 psig and from Equation1 2 1 ln y 1 = 0.506 ln ( x ) was obtained y 2 x+σ Total flow rate:ln 3864.205 = 0.506 ln ( y 2 Then y 2 =3866.089 lb hr 7.367 ) 7.367+0.0071 σ FR = y 2 y 1 = 3866.089 3864.205 = 1.884 lb hr For single flow: σ SFR = σ FR lb =0.377 5 hr 30
Standard deviation for bulk temperature was obtained using equation 12: σ Bulk Temp = (67 67.25)2 + (67.5 67.25) 2 2 1 = 0.354 Equation 14 was used to interpolate the physical properties of water. To find the error in these properties due to the estimated error in the bulk temperature, the partial derivative of this general equation is found to be: y x = y 1 y 0 x 1 x 0 where y is the physical property and x is the temperature σ y = y 2 σ x 2 x = ( y 1 y 2 0 ) σ2 x 1 x x 0 σ ρ = 0.00177 lb m ft 3 σ cp = 1.77 10 5 Btu lb m σ μ = 3.221 10 6 Using the Equation 13 on Equations 3, 4, and 5: lb m ft s σ k = 2.301 10 4 Btu hr ft σ Pr = 0.0388 σ v = 0.00205 ft s σ h = 0.0896 σ Re = 4.146 Btu hr ft 2 31
Flow Rate % d HX Venturi Tube Side - 11 Baffles d Venturi d Venturi (cm Hg) d Flow Rate (lb/hr) log of flow rate HX T ( F) 100 13.632 14.462 1.925 2.065 10.67619048 4662.076053 1.16022836 3.6685794 60 90 13.62 14.45 1.9 2.04 10.54693878 4633.430684 1.15986785 3.6659027 60 80 13.6 14.43 1.88 2.02 10.44353741 4610.389299 1.15926633 3.6637376 60 Was -0.17 70 12.54 13.37 1.68 1.82 9.40952381 4373.467746 1.12613141 3.6408259 60 60 10.73 11.56 1.46 1.6 8.272108844 4097.458059 1.06295783 3.6125145 60 50 8.53 9.36 1.18 1.32 6.824489796 3717.407877 0.97127585 3.5702402 60 40 5.95 6.78 0.81 0.95 4.911564626 3147.443552 0.83122969 3.4979579 60 ln (y) = 0.506 ln (x) +7.249 where y = water flowrate (lb/hr), x = D P (cm Hg) 30 3.55 4.38 0.48 0.62 3.205442177 2536.179574 0.64147411 3.40418 60 20 1.53 2.36 0.31 0.45 2.326530612 2156.529173 0.372912 3.3337553 60 10 0.269 1.099 0.13 0.27 1.395918367 1665.32833 0.04099769 3.2214999 60 0-0.83 0-0.14 0 0 60 Tube Water Diameter Density (ft) (lb m /ft 3 ) 0.0208333 62.37 Water Viscosity (lb m /ft*s) 0.0007145 CS Tube Area (ft 2 ) 0.00034088 HX Hot Correction Correction -0.83-0.14 D/e 4166.66667 Flow Rate % Flow Per Tube (lb/hr) Volumetric Flow Rate (ft 3 /s) Velocity (ft/s) Re Fanning Head Loss H L ΔP f (inches log of ΔP f ΔP Friction Factor boxes (ft) H 2 O) 100 932.4152106 0.004152705 12.18214314 22154.19488 0.008085391 8.943423816 3.87362044 0.5881171 0.57211 0.03956 1 90 926.6861367 0.00412719 12.10729194 22018.07203 0.008094933 8.844283771 3.83068041 0.5832759 0.57659 0.039903 1 80 922.0778598 0.004106666 12.04708412 21908.57932 0.008102675 8.764913892 3.79630333 0.5793609 0.57991 0.040187 1 70 874.6935491 0.00389563 11.42800106 20782.72762 0.008185887 7.968226275 3.45123801 0.5379749 0.58816 0.043991 1.000001 60 819.4916117 0.003649776 10.70677956 19471.12903 0.008292016 7.084892025 3.06864386 0.4869465 0.57601 0.049828 1 50 743.4815753 0.00331125 9.713697149 17665.12979 0.008457482 5.947926204 2.57619554 0.4109788 0.5603 0.059861 1 40 629.4887103 0.002803559 8.224363446 14956.65816 0.00876066 4.41668863 1.91297826 0.28171 0.54952 0.08105 1 30 507.2359148 0.002259081 6.627112525 12051.93049 0.009194604 3.009796135 1.30361795 0.1151503 0.52632 0.120165 1 20 431.3058346 0.00192091 5.635074756 10247.83102 0.009552959 2.260958788 0.97927778-0.009094 0.38201 0.161867 1.000001 10 333.0656661 0.001483377 4.35155237 7913.643612 0.010187219 1.43780317 0.6227485-0.205687 0.24669 0.224463 1.000001 0 0 0 0 0 0.006 0 0 0 0 #DIV/0! #DIV/0! % Total ΔP f Solver for ff 32
Flow Rate % Hg) (lb/hr) 100 19.72 19.26 4.99 4.57 23.62721088 8002.00574 1.284656 3.9031989 64 90 19.83 19.37 5.18 4.76 24.60952381 8173.31148 1.28713 3.912398 64 80 19.66 19.2 5.22 4.8 24.81632653 8208.955057 1.283301 3.9142879 64 70 18.55 18.09 4.68 4.26 22.0244898 7714.991041 1.257439 3.8873354 64 60 17.58 17.12 4.69 4.27 22.07619048 7724.403101 1.233504 3.8878649 64 50 15.39 14.93 3.87 3.45 17.83673469 6913.665508 1.17406 3.8397084 64 40 12.92 12.46 3.51 3.09 15.9755102 6528.611773 1.095518 3.8148208 64 30 9.92 9.46 2.61 2.19 11.32244898 5458.500749 0.975891 3.7370734 64 20 6.56 6.1 1.89 1.47 7.6 4436.571128 0.78533 3.6470474 64 10 2.84 2.38 1.05 0.63 3.257142857 2855.614117 0.376577 3.4556995 64 0 0.46 0 0.42 0 0 64 Flow Rate % Hg) (lb/hr) 100 11.11 11.246 6.71 6.47 33.45034014 9587.660793 1.050998 3.9817127 59.5 90 10.87 11.006 6.18 5.94 30.71020408 9170.887922 1.04163 3.9624114 80 10.94 11.076 6 5.76 29.77959184 9025.309958 1.044383 3.9554621 70 10.16 10.296 5.955 5.715 29.54693878 8988.575623 1.012669 3.9536909 60 9.245 9.381 5.71 5.47 28.28027211 8786.093977 0.972249 3.9437958 50 8.13 8.266 4.787 4.547 23.50829932 7981.03859 0.917295 3.9020594 40 6.722 6.858 3.973 3.733 19.29986395 7202.986309 0.836197 3.8575126 30 5.118 5.254 3.135 2.895 14.96734694 6311.021939 0.72049 3.8000997 20 2.926 3.062 1.925 1.685 8.711564626 4762.932045 0.486005 3.6778744 10 1.183 1.319 0.992 0.752 3.887891156 3130.946968 0.120245 3.4956757 0-0.136 0 0.24 0 0 Flow Rate HX HX HX d HX d HX d HX Venturi Venturi Venturi 25 Baffles d Venturi 17 Baffles d Venturi 11 Baffles d Venturi d Venturi (cm d Venturi (cm d Venturi (cm d Flow Rate d Flow Rate d Flow Rate log of flow rate log of flow rate log of flow rate % Hg) (lb/hr) 100 11.603 11.075532 6.825 6.527041 33.74524599 9631.522238 1.044365 3.9836949 60 90 11.581 11.053532 6.7645 6.466541 33.43245687 9584.995051 1.043501 3.9815919 80 11.41056 10.883092 6.621 6.323041 32.69055211 9473.794356 1.036752 3.976524 70 10.669 10.141532 6.21456 5.916601 30.58922966 9152.084505 1.006104 3.96152 60 9.73 9.202532 5.6956 5.397641 27.90617116 8725.463627 0.963907 3.9407885 50 8.4278 7.900332 4.99115 4.693191 24.26411673 8113.456531 0.897645 3.9092059 40 6.87495 6.347482 4.12266 3.824701 19.77396435 7294.459696 0.802601 3.8629931 30 5.180323 4.652855 3.194 2.896041 14.97272898 6312.2019 0.66772 3.8001809 20 3.189597 2.662129 2.091818 1.793859 9.274373061 4920.535308 0.425229 3.6920124 10 1.2448 0.717332 1.02253 0.724571 3.746081361 3071.033313-0.14428 3.4872845 0 0.527468 0 0.297959 0 0 T ( F) T ( F) T ( F) 33
Flow Rate % Hg) (lb/hr) 100 7.714336 7.236671 7.086818 7.029903 36.34507673 10010.50732 0.859539 4.0004561 60 90 7.672158 7.194493 7.02208 6.965165 36.01037687 9962.46405 0.857 3.9983668 80 7.628141 7.150476 6.9484 6.891485 35.62944626 9907.523211 0.854335 3.9959651 70 7.155942 6.678277 6.548936 6.492021 33.5641902 9604.615662 0.824664 3.98248 60 6.487356 6.009691 5.915847 5.858932 30.29107701 9105.588766 0.778852 3.959308 50 5.656944 5.179279 5.221242 5.164327 26.6999219 8527.261393 0.714269 3.9308096 40 4.587698 4.110033 4.336059 4.279144 22.12346558 7733.000233 0.613845 3.888348 30 3.438375 2.96071 3.326054 3.269139 16.90167102 6722.762914 0.471396 3.8275478 20 2.075 1.597335 1.967783 1.910868 9.879317551 5084.899715 0.203396 3.7062824 10 1.0757765 0.5981115 0.807877 0.750962 3.882524626 3128.698936-0.223218 3.4953638 0 0.477665 0 0.056915 0 0 Flow Rate d Venturi % Hg) (lb/hr) 100 10.355 9.955 6.435 5.825 30.11564626 9078.128335 0.998041 3.9579963 59 90 10.265 9.865 6.37 5.76 29.77959184 9025.309958 0.994097 3.9554621 59 80 9.995 9.595 6.215 5.605 28.97823129 8898.191649 0.982045 3.9493018 59 70 9.42 9.02 6.133 5.523 28.55428571 8830.259304 0.955207 3.9459735 59 60 8.7 8.3 5.42 4.81 24.86802721 8217.84365 0.919078 3.9147579 59 50 7.495 7.095 4.835 4.225 21.84353741 7681.965023 0.850952 3.8854723 59 40 6.32 5.92 4.105 3.495 18.06938776 6960.412338 0.772322 3.842635 59 30 4.79 4.39 3.085 2.475 12.79591837 5817.03317 0.642465 3.7647015 59 20 3.07 2.67 2.155 1.545 7.987755102 4552.86996 0.426511 3.6582852 59 10 1.405 1.005 1.18 0.57 2.946938776 2710.799267 0.002166 3.4330974 59 0 0.4 0 0.61 0 0 59 Flow Rate HX HX HX d HX d HX d HX Venturi Venturi Venturi X (unknown) Baffles 13 Baffles d Venturi 21 Baffles d Venturi d Venturi (cm d Venturi (cm d Venturi (cm d Flow Rate d Flow Rate d Flow Rate log of flow rate log of flow rate log of flow rate % Hg) (lb/hr) 100 15.415 14.91 5.345 4.865 25.15238095 8266.573162 1.173478 3.9173255 60 90 15.505 15 5.4 4.92 25.43673469 8315.038951 1.176091 3.9198643 80 15.335 14.83 5.29 4.81 24.86802721 8217.84365 1.171141 3.9147579 70 14.325 13.82 4.975 4.495 23.23945578 7933.446118 1.140508 3.8994619 60 13.31 12.805 4.6 4.12 21.30068027 7582.090902 1.10738 3.879789 50 11.885 11.38 3.965 3.485 18.01768707 6950.049238 1.056142 3.8419879 40 10.19 9.685 3.64 3.16 16.33741497 6605.104872 0.9861 3.8198797 30 7.51 7.005 2.75 2.27 11.73605442 5561.294326 0.845408 3.7451759 20 5 4.495 1.89 1.41 7.289795918 4341.465689 0.65273 3.6376364 10 2.295 1.79 1.015 0.535 2.765986395 2622.928193 0.252853 3.4187864 0 0.505 0 0.48 0 0 T ( F) T ( F) T ( F) 34
Flow Rate % (cm Rate 100 19.3256 18.8656 4.8902 4.4702 23.11124 7910.655 1.275671 3.898212 64 90 19.4334 18.9734 5.0764 4.6564 24.0739 8080.32 1.278145 3.907429 64 80 19.2668 18.8068 5.1156 4.6956 24.27657 8115.622 1.274315 3.909322 64 70 18.179 17.719 4.5864 4.1664 21.54057 7626.375 1.248439 3.882318 64 60 17.2284 16.7684 4.5962 4.1762 21.59124 7635.697 1.224492 3.882849 64 50 15.0822 14.6222 3.7926 3.3726 17.43657 6832.571 1.165013 3.834584 64 40 12.6616 12.2016 3.4398 3.0198 15.61257 6451.06 1.086417 3.809631 64 30 9.7216 9.2616 2.5578 2.1378 11.05257 5390.454 0.966686 3.731625 64 20 6.4288 5.9688 1.8522 1.4322 7.404571 4376.877 0.775887 3.641164 64 10 2.7832 2.3232 1.029 0.609 3.148571 2805.714 0.366087 3.448043 64 0 0.4508-0.0092 0.4116-0.0084-0.04343 64 Flow Rate % Venturi 25 Baffles - Trial 2 (cm Rate 100 10.8878 10.7886 6.5758 6.3358 32.75652 9483.73 1.032965 3.976979 59.5 90 10.6526 11.0238 6.0564 5.8164 30.07118 9071.156 1.042331 3.957663 80 10.7212 10.8572 5.88 5.64 29.15918 8927.042 1.035718 3.950708 70 9.9568 10.0928 5.8359 5.5959 28.93118 8890.676 1.004012 3.948935 60 9.0601 9.1961 5.5958 5.3558 27.68985 8690.227 0.963604 3.939031 50 7.9674 8.1034 4.69126 4.45126 23.01332 7893.209 0.908667 3.897254 40 6.58756 6.72356 3.89354 3.65354 18.88905 7122.847 0.827599 3.852654 30 5.01564 5.15164 3.0723 2.8323 14.64318 6239.573 0.711946 3.795155 20 2.86748 3.00348 1.8865 1.6465 8.512517 4706.028 0.477625 3.672655 10 1.15934 1.29534 0.97216 0.73216 3.785317 3087.717 0.112384 3.489638 0-0.13328 0.00272 0.2352-0.0048-0.02482 Flow Rate % HX HX HX d HX d HX d HX Venturi Venturi 17 Baffles - Trial 2 11 Baffles - Trial 2 (cm Rate 100 11.37094 10.84347 6.6885 6.390541 33.03953 9526.251 1.035168 3.978922 60 90 11.34938 10.82191 6.62921 6.331251 32.733 9480.189 1.034304 3.976817 80 11.18235 10.65488 6.48858 6.190621 32.00593 9370.1 1.027549 3.971744 70 10.45562 9.928152 6.090269 5.79231 29.94664 9051.6 0.996868 3.956725 60 9.5354 9.007932 5.581688 5.283729 27.31724 8629.219 0.954625 3.935972 50 8.259244 7.731776 4.891327 4.593368 23.74803 8023.257 0.888279 3.904351 40 6.737451 6.209983 4.040207 3.742248 19.34768 7212.26 0.79309 3.858071 30 5.076717 4.549249 3.13012 2.832161 14.64247 6239.413 0.65794 3.795144 20 3.125805 2.598337 2.049982 1.752023 9.058076 4860.524 0.414695 3.686683 10 1.219904 0.692436 1.002079 0.70412 3.64035 3025.651-0.15962 3.480819 0 0.516919-0.01055 0.292-0.00596-0.03081 35 d Flow d Flow d Flow log of flow rate log of flow rate log of flow rate T ( F) T ( F) T ( F)
Flow Rate % (cm Rate 100 7.560049 7.082384 6.945082 6.888167 35.61229 9905.042 0.850179 3.995856 60 90 7.518715 7.04105 6.881638 6.824723 35.28428 9857.497 0.847637 3.993767 80 7.475578 6.997913 6.809432 6.752517 34.91097 9803.126 0.844969 3.991365 70 7.012823 6.535158 6.417957 6.361042 32.88702 9503.359 0.815256 3.977877 60 6.357609 5.879944 5.79753 5.740615 29.67937 9009.503 0.769373 3.954701 50 5.543805 5.06614 5.116817 5.059902 26.16004 8437.161 0.704677 3.926196 40 4.495944 4.018279 4.249338 4.192423 21.67511 7651.107 0.60404 3.883724 30 3.369608 2.891943 3.259533 3.202618 16.55775 6651.278 0.46119 3.822905 20 2.0335 1.555835 1.928427 1.871512 9.675846 5030.17 0.191964 3.701583 10 1.054261 0.576596 0.791719 0.734804 3.798989 3093.512-0.23913 3.490452 0 0.468112-0.00955 0.055777-0.00114-0.00589 Flow Rate % (cm Rate 100 10.1479 9.7479 6.3063 5.6963 29.45026 8973.27 0.988911 3.952951 59 90 10.0597 9.6597 6.2426 5.6326 29.12093 8920.949 0.984964 3.950411 59 80 9.7951 9.3951 6.0907 5.4807 28.33559 8795.027 0.972901 3.944237 59 70 9.2316 8.8316 6.01034 5.40034 27.92013 8727.732 0.946039 3.940901 59 60 8.526 8.126 5.3116 4.7016 24.30759 8121.013 0.909877 3.90961 59 50 7.3451 6.9451 4.7383 4.1283 21.34359 7590.03 0.841679 3.880243 59 40 6.1936 5.7936 4.0229 3.4129 17.64493 6874.905 0.762949 3.837267 59 30 4.6942 4.2942 3.0233 2.4133 12.47693 5741.169 0.632882 3.759 59 20 3.0086 2.6086 2.1119 1.5019 7.764925 4486.377 0.416407 3.651896 59 10 1.3769 0.9769 1.1564 0.5464 2.824925 2651.844-0.01015 3.423548 59 0 0.392-0.008 0.5978-0.0122-0.06307 59 Flow Rate % HX HX HX d HX d HX d HX X (unknown) Baffles - Trial 2 Venturi Venturi Venturi 13 Baffles - Trial 2 21 Baffles - Trial 2 (cm Rate 100 15.1067 14.6017 5.2381 4.7581 24.5997 8171.615 1.164403 3.912308 60 90 15.1949 14.6899 5.292 4.812 24.87837 8219.62 1.167019 3.914852 80 15.0283 14.5233 5.1842 4.7042 24.32103 8123.348 1.162065 3.909735 70 14.0385 13.5335 4.8755 4.3955 22.72503 7841.637 1.13141 3.894407 60 13.0438 12.5388 4.508 4.028 20.82503 7493.573 1.098256 3.874689 50 11.6473 11.1423 3.8857 3.4057 17.6077 6867.359 1.046975 3.83679 40 9.9862 9.4812 3.5672 3.0872 15.96103 6525.535 0.976863 3.814616 30 7.3598 6.8548 2.695 2.215 11.4517 5490.815 0.835995 3.739637 20 4.9 4.395 1.8522 1.3722 7.094367 4280.549 0.642959 3.631499 10 2.2491 1.7441 0.9947 0.5147 2.661034 2570.695 0.241571 3.410051 0 0.4949-0.0101 0.4704-0.0096-0.04963 36 d Flow d Flow d Flow log of flow rate log of flow rate log of flow rate T ( F) T ( F) T ( F)