Heat Transfer Theory 1 1 Multiple Transfer Mechanisms Most heat transfer processes used in production facilities involve combi- nations of conduction and convection transfer processes. For example, in heat exchangers the transfer of heat energy from the hot fluid to the cold fluid involves three steps. First, the heat energy is transferred from the hot fluid to the exchanger tube, then through the exchanger tube wall, and finally from the tube wall to the cold fluid. The first and third steps are convection transfer processes, while the second step is conduction process, To calculate the rate of heat transfer in each of the steps, the individual temperature difference would have to be known. It is difficult to measure accurately the temperatures at each boundary, such as at the surface of the heat exchanger tube. Therefore, in practice, the heat transfer calcula- tions are based on the overall temperature difference, such as the differ- ence between the hot and cold fluid temperatures. The heat transfer rate is expressed by the following equation, similar to the conductive/convec- tive transfer process: where q = overall heat transfer rate, Btu/hr U = overall heat transfer coefficient, Btu/hr-ft 2 -°F A = heat transfer area, ft 2 AT = overall temperature difference, °F Examples of overall heat transfer coefficient and overall temperature difference calculations are discussed in the following sections. Overall Temperature Difference The temperature difference may not remain constant throughout the flow path. Plots of temperature vs. pipe length for a system of two concen- tric pipes in which the annular fluid is cooled and the pipe fluid heated are shown in Figures 2-2 and 2-3. When the two fluids travel in opposite direc- tions, as in Figure 2-2, they are in countercurrent flow. When the fluids travel in the same direction, as in Figure 2-3, they are in co-current flow. The temperature of the inner pipe fluid in either case varies according to one curve as it proceeds along the length of the pipe, and the tempera- ture of the annular fluid varies according to another. The temperature dif- ference at any point is the vertical distance between the two curves. 12 Design of GAS-HANDLING Systems and facilities Figure 2-2. Change in AT over distance, counter-current flow of fluids. Since the temperature of both fluids changes as they flow through the exchanger, an "average" temperature difference must be used in Equation 2-3. Normally a log mean temperature difference is used and can be found as follows: where LMTD = log mean temperature difference, °F ATj = larger terminal temperature difference, °F AT 2 = smaller terminal temperature difference, °F Although two fluids may transfer heat in either counter-current or co- current flow, the relative direction of the two fluids influences the value of the LMTD, and thus, the area required to transfer a given amount of Heat Transfer Theory 13 Figure 2-3. Change in AT over distance, co-current flow of fluids. heat. The following example demonstrates the thermal advantage of using counter-current flow. Given: A hot fluid enters a concentric pipe at a temperature of 300°F and is to be cooled to 20Q°F by a cold fluid entering at 100°F and heated to 150°F. Co-current Flow: Side Hot Fluid Inlet Hot Fluid Outlet Hot Fluid °F 300 200 Cold Fluid °F 100 150 AT op 200 50 14 Design oj GAS-HANDLING Systems and Facilities Counter-current Flow: Side Hot Fluid Inlet Hot Fluid Outlet Hot Fluid °F 300 200 Cold Fluid °f 150 100 AT °F 150 100 Equation 2-4 assumes that two fluids are exchanging heat energy while flowing either co-current or counter-current to each other. In many process applications the fluids may flow part of the way in a co-current and the remainder of the way in a counter-current direction. The equa- tions must be modified to model the actual flow arrangement. For pre- liminary sizing of heat transfer areas required, this correction factor can often be ignored. Correction factors for shell and tube heat exchangers are discussed in Chapter 3. Overall Heat Transfer Coefficient The overall heat transfer coefficient is a combination of the internal film coefficient, the tube wall thermal conductivity and thickness, the external film coefficient, and fouling factors. That is, in order for the energy to be transferred through the wall of the tube it has to pass through a film sitting on the inside wall of the tube. That film produces a resistance to the heat transfer, which is represented by the inside film coefficient for this convective heat transfer. It then must pass through the wall of the tube by a conduction process which is controlled by the tube- wall's thermal conductivity and tube-wall thickness. The transfer of heat from the outside wall of the tube to the bulk of the fluid outside is again a convective process. It is controlled by the outide film coefficient. All of these resistances are added in series, similar to a series of electrical resis- tance, to produce an overall resistance. The heat transfer coefficient is similar to the electrical conductance, and its reciprocal is the resistance. Therefore, the following equation is used to determine the overall heat transfer coefficient for use in Equation 2-3. Heal Transfer Theory 1 5 where hj = inside film coefficient, Btu/hr-ft 2 -°F h 0 = outside film coefficient, Btu/hr-ft 2 -°F k = pipe wall thermal conductivity, Btu/hr-ft-°F L = pipe wall thickness, ft Rj = inside fouling resistance, hr-ft 2 -°F7Btu R 0 = outside fouling resistance, hr-ft 2 -°F/Btu Aj = pipe inside surface area, ft 2 /ft A () = pipe outside surface area, ft 2 /ft Rj and R 0 are fouling factors. Fouling factors are normally included to allow for the added resistance to heat flow resulting from dirt, scale, or corrosion on the tube walls. The sum of these fouling factors is normally taken to be 0.003 hr-ft 2 -°F/Btu, although this value can vary widely with the specific service. Equation 2-5 gives a value for "U" based on the outside surface area of the tube, and therefore the area used in Equation 2-3 must also be the tube outside surface area. Note that Equation 2-5 is based on two fluids exchanging heat energy through a solid divider. If additional heat exchange steps are involved, such as for finned tubes or insulation, then additional terms must be added to the right side of Equation 2-5. Tables 2-1 and 2-2 have basic tube and coil properties for use in Equation 2-5 and Table 2-3 lists the conductivity of different metals. Inside Film Coefficient The inside film coefficient represents the resistance to heat flow caused by the change in flow regime from turbulent flow in the center of the tube to laminar flow at the tube surface. The inside film coefficient can be calculated from: 16 Design of GAS-HANDLING Systems and Facilities Table 2-1 Characteristics of Tubing Tube OD In, !4 !4 !/ 14 >^ •)H yfc y» 14 'X '/2 J4. )<: % ;i/ % % /i /i .V ,/H % 3 / -X4 % % /i /'4 ;/4 •% /'i 3/; | s I i 1 1 1 1 B.W.G. Gauge 22 24 26 27 18 20 22 24 16 18 20 22 12 13 14 15 16 17 18 19 20 10 11 12 13 14 15 16 17 18 20 8 10 11 12 13 14 15 16 Thickness In. .028 .022 .018 .016 .049 .035 ,028 .022 .065 .049 .035 .028 .109 .095 .083 .072 .065 .058 .049 .042 .035 ,134 .120 .109 .095 .083 .072 .065 .058 .049 .035 .165 .134 .120 .109 .095 .083 .072 .065 internal Area !n. 2 .0295 .0333 .0360 .0373 .0603 .0731 .0799 .0860 .1075 .1269 .1452 .1548 .1301 .1486 . 1 655 .1817 .1924 .2035 .2181 .2298 .2419 .1825 .2043 .2223 .2463 .2679 .2884 .3019 .3157 .3339 .3632 .3526 .4208 .4536 .4803 .5153 .5463 .5755 ,5945 Ft 2 External Surface PerFf Length .0655 .0655 .0655 .0655 .0982 .0982 .0982 .0982 .1309 .1309 .1309 .1309 .1636 .1636 .1636 .1636 .1636 .1636 .1636 .1636 .1636 .1963 .3963 .1963 .1963 . 1 963 .3963 .1963 .3963 .1963 .1963 .2618 .2618 .2618 .2618 .2618 .2618 .2618 .2618 Ft 3 Internal Surface Per Ft Length .05U8 .0539 .0560 .0570 .0725 .0798 .0835 .0867 .0%9 .1052 . 11 2o .1162 .1066 . 1 ! 39 .1202 . ! 259 . i 296 .1333 .1380 .1416 .!453 .1262 .1335 . 1 393 .1466 .1329 .1587 . i 623 .1660 . 1 707 . 1 780 i 754 .1916 .1990 .2047 .212! .21 S3 .224! .2278 Heat Transfer Theory 1 7 Table 2-1 (Continued) Characteristics of Tubing Tube OD In. 1 1 VA V/4 VA VA 114 114 VA VA VA 1!4 1!* V/i VA. VA 2 7 2 2 8.W.G. Gauge 18 20 1 8 10 11 12 13 14 16 18 20 10 12 14 16 11 12 13 14 Thickness In. .049 .035 .180 .165 .134 .120 .109 .095 .083 .065 .049 .035 .134 .109 .083 .065 .120 .109 .095 .083 Internal Area In, 2 .6390 .6793 .6221 .6648 .7574 .8012 .8365 .8825 .9229 .9852 1 .042 1.094 1.192 1.291 1 .398 1.474 2.433 2.494 2.573 2.642 Ft 2 External Surface Per Ft Length ,2618 .2618 .3272 .3272 .3272 .3272 .3272 .3272 .3272 .3272 .3272 .3272 .3927 .3927 .3927 .3927 .5236 .5236 .5236 .5236 Ft 2 Internal Surface Per Ft Length .2361 .2435 ,2330 .2409 .2571 .2644 .2702 .2775 .2,838 .2932 .3016 .3089 .3225 .3356 .3492 .3587 .4608 .4665 .4739 .480! where h ; - inside film heat transfer coefficient, Btu/hr-ft 2 -°F DJ = tube inside diameter, ft k = fluid thermal conductivity, Btu/hr-ft-°F G = mass velocity of fluid, lb/hr-ft 2 C = fluid specific heat, Btu/lb-°F fi e = fluid viscosity, lb/hr-ft ju ew = fluid viscosity at tube wall, lb/hr-ft (The viscosity of a fluid in lb/hr-ft is its viscosity in centipoise times 2.41.) The bulk fluid temperature at which the fluid properties are obtained should be the average temperature between the fluid inlet and outlet tem- peratures. The viscosity at the tube wall should be the fluid viscosity at the arithmetic average temperature between the inside fluid bulk temper- (text continued on page 20) 18 Design of GAS-HANDLING Systems and Facilities Table 2-2 Pipe Coil Data Norn, Size Sch. OD in. No. in. 1 S40 1.315 X80 160 XX 2 S40 2.375 X80 160 XX 2 1 A XXX 2.875 3 S40 3.50 X80 160 XX 4 S40 4.50 X80 160 XX !D in. 1 .049 0.957 0.815 0.599 2.067 1 .939 1.687 1 .503 1.375 3.068 2.900 2.624 2.300 4.026 3.826 3.438 3.152 Internal Surface Area (f^/ft) 0.275 0.25 1 0.213 0.157 0.541 0.508 0.442 0.394 0.360 0.803 0.759 0.687 0.602 1.054 1 .002 0.900 0.825 External Surface Area (fP/ft) 0.344 0,622 0.753 0.916 1.19 Table 2-3 Thermal Conductivity of Metals at 200°F Material Aluminum (annealed) Type 11 00-0 Type 3003-0 Type 3004-0 Type 606 1-0 Aluminum (tempered) Type 1 100 (all tempers) Type 3003 (all tempers) Type 3004 (all tempers) Type 606 1-T4&T6 Type 6063-T5 & T6 Type 6063-T42 Cast iron Carbon steel Conductivity Btu/hr-rr-°F 126 111 97 102 123 96 97 95 116 111 31 30 Heat Transfer Theory 19 Table 2-3 (Continued) Thermal Conductivity of Metals at 200°F Material Carbon rnoly ( [ A%) steel Chrom moly steels l%Cr, M%Mo 2'4%Cr, l%Mo 5% Cr, M% Mo 12% Cr Austenitic stainless steels 18%Cr, 8%Ni 25% Cr, 20% Ni Admiralty Naval brass Copper Copper & nickel alloys 90% Cu, 10% Ni 80% Cu, 20% Ni 70% Cu, 30% Ni 30% Cu, 70% Ni alloy 400 Muiitz Aluminum bronze alloy D alloy E Copper silicon alloy B Alloy A, C, D Nickel Nickel-chrome-iron alloy 600 Nickel-iron-chrome alloy 800 Ni-Fe-Cr-Mo-Cu alloy 825 Ni-Mo alloy B Ni-Mo-Cr alloy C-276 Cr-Mo alloy XM-27 Zirconium Titanium grade 3 Cr-Ni-Fe-Mo-Cu-Cb alloy 20 CB Conductivity Btu/hr-ft-°F 29 27 25 21 14 9,3 7.8 70 71 225 30 22 18 15 71 46 22 33 21 38 9.4 7.1 7.0 6.4 11.3 12.0 11.3 7.6 20 Design of GAS-HANDLING Systems and Facilities (text continued from page 17} ature and the tube wall temperature. The tube wall temperature may be approximated by taking the arithmetic average between the inside fluid bulk temperature and the outside fluid bulk temperature. The thermal conductivity of natural and hydrocarbon gases is given in Figure 2-5. The value from Figure 2-4 is multiplied by the ratio of k/k. A from Figure 2-5. The thermal conductivity of hydrocarbon liquids is given in Figure 2-6. The viscosity of natural gases and hydrocarbon liquids is discussed in Volume 1. Figure 2-4. Thermal conductivity of natural and hydrocarbon gases at 1 atmosphere, 14.696 psia. {From Gas Processors Suppliers Association, Engineering Data Book, 10th Edition.) [...]... 1. 99 02 1. 9 428 1. 89 72 1. 85 31 20 4 98 20 4 ,67 2. 0360 20 8 07 1 9 826 60 70 80 90 10 0 11 09.5 11 13.7 11 17.9 11 22 ,0 11 26 .1 0 .14 71 0 .16 45 0 .18 16 0 ,19 84 0. 21 4 9 1. 810 6 1. 7694 1. 729 6 1. 6 910 1. 6537 1. 9577 1. 9339 1. 911 2 1. 8894 1, 8685 11 0 12 0 13 0 14 0 15 0 Sat Liquid hfg kg Sf Evap % 10 75,8 10 74 .1 10 71. 3 10 68,4 10 65.6 10 75.8 10 77 .1 1079.3 10 81. 5 10 83.7 000 00 006 01 0. 016 2 0. 026 2 0,03 61 28 .06 38.04 48, 02 57.99 67.97 10 59.9... 15 7.95 16 7.99 10 02. 3 996.3 9 02 9 984 .1 977,9 11 30 .2 11 34 .2 11 38 .1 1 14 2. 0 1 145.9 0 .2 311 0 .24 72 0 .26 30 0 .27 85 0 ,29 38 1. 617 4 1. 5 822 1, 5480 1. 514 7 1, 4 824 1. 8485 1. 829 3 1. 810 9 1. 79 32 ! 77 62 16 0 17 0 18 0 19 0 20 0 21 0 21 2 14 12 3 14 .696 0. 016 70 0. 016 72 I 27 ,80 26 .78 27 . 82 26.80 17 8.05 18 0.07 9 71. 6 970,3 11 49.7 1 1.50.4 0.3090 ] 0. 3 12 0 ; 1. 4446 1. 7598 1. 7566 21 0 -7 j •-) Table 2- 6 (Continued) Properties of Dry... 1. 3609 1. 7440 1. 728 8 1. 714 0 22 0 23 0 24 0 21 6 .48 22 8.64 23 8.84 29 0 4.6 25 9. 31 945.5 938.7 9 31. 8 947 2 917 .5 11 64.0 1 167.3 1 170.6 11 73.8 11 76.8 0.3675 0.3 817 0.3958 049 06 0. 423 4 1. 3 323 1. 3043 1. 27 69 1. 25 01 1 22 38 1. 6998 1. 6860 1. 6 727 1. 6597 1. 64 72 250 26 0 27 0 28 0 29 0 6.466 5. 626 4, 914 4.307 3.788 26 9.59 27 9. 92 2 02 9.8 306 0.8 311 .13 910 .1 9 02. 6 849 9 887.0 879.0 1 179.7 11 82. 5 11 85 .2 11 87.7 11 90 .1 0.4369... 90 1. 1980 1. 1 727 1. 1478 1. 123 3 1. 09 92 1. 6350 1. 62 31 1. 611 5 1. 60 02 1 58 91 300 310 320 330 340 3.3 42 2.957 2. 625 2. 335 2. 0836 3 21 . 63 3 32 .18 3 42, 79 353.45 364 .17 870,7 8 62. 2 853.5 844.6 835.4 1 1 92, 3 11 94.4 11 96.3 11 98 .1 1 19 9.6 0 52 09 0. 515 8 0. 528 6 0.5 413 0.5539 1. 0754 1. 0 519 1. 028 7 1 0059 0.98 32 1. 5783 1. 5677 1. 5573 1. 54 71 1.53 71 350 350 370 380 390 Evap 23 .15 19 .3 82 16 . 323 18 8 .13 19 8 .23 20 8.34 13 .804... 0. 016 06 0. 016 08 0. 016 10 0. 016 13 12 06.6 867.8 633 .1 480 6 350.3 12 06.7 867,9 633 .1 480 6 350.4 11 0 12 0 13 0 14 0 15 0 1. 27 48 1. 6 924 2, 222 5 2. 8886 3. 718 0. 016 17 0. 016 20 0. 016 25 0. 016 29 0. 016 34 26 5.3 20 3 .25 15 7. 32 12 2. 99 9,6 70 Vf Entropy Enthalpy Temp, F t Evap v% ** Sot Vapor sg 2 .18 77 2 .17 09 2 .14 35 2 ,11 67 2. 0903 2 .18 77 2 .17 70 2 .15 97 2 ,14 29 2 , 12 64 32 35 40 45 50 0.0555 004 75 0.09 32 0 .11 15 0 . 12 95 2. 0393 1. 99 02. .. 10 59.9 10 54.3 10 48.6 10 42. 9 10 37 .2 10 88.0 10 92, 3 19 066 11 00.9 11 05 .2 265.4 20 3 .27 15 7.34 12 3, 01 97.07 77.94 87. 92 97.90 10 7.89 11 7.89 10 31, 6 10 25 .8 10 20 .0 10 14 .1 1008 .2 v g 3306 Sat Vapor Temp F t Evap Sat Vapor Sat Liquid 16 0 17 0 18 0 19 0 20 0 4.7 41 5.9 92 7. 510 9,339 1 1. 526 0. 016 39 0. 016 45 0. 016 51 0. 016 57 0. 016 63 77 .27 6.4 20 50, 21 4.4 09 33. 62 77 .29 6.6 20 50 .23 4.6 09 33.64 12 7.89 13 7.90 14 7. 92 15 7.95... Sat Liquid 400 410 420 430 440 24 7. 31 27 6.75 308.83 343. 72 3 81. 59 0. 018 64 0. 018 78 0. 018 94 0. 019 10 0. 019 26 1. 8447 1. 6 5 12 1. 4 811 1. 3308 1. 1979 1. 8633 1. 6700 1. 5000 1. 3499 1. 21 7 1 374.97 385.83 396.77 477 0.9 418 .90 826 .0 816 .3 806.3 796.0 785.4 12 01. 0 12 02 .1 120 3 .1 120 3.8 12 04.3 0.5664 0.5788 0.5 9 12 0.6035 0. 615 8 090 68 098 36 0. 916 6 0.8947 0.8730 1. 527 2 1. 517 4 1. 5078 1. 49 82 1. 4887 400 410 420 430 440 450... Liquid 20 23 0 24 0 17 .18 6 20 .780 24 .969 0. 016 77 0. 016 84 0. 016 92 23 .13 19 .365 16 .306 25 0 26 0 27 0 28 0 29 0 29 . 825 35. 429 41. 858 49 .20 3 57.556 0. 017 00 0. 017 09 0. 017 17 0. 017 26 0. 017 35 300 310 320 330 340 67. 013 77.68 89.66 10 3.06 11 8. 01 350 360 370 380 390 13 4.63 15 3.04 17 3.37 19 5.77 22 0.37 Sat Liquid Sf Evap % Sat Vapor s t Temp F t 965 .2 958.8 9 52. 2 11 53.4 11 57.0 11 60.5 0. 323 9 0.3387 0.35 31 1. 42 01 1.39 01 1.3609... 27 006 20 007 28 0.0305 0 .24 32 0 .19 55 0 .15 38 0 .11 65 0.0 810 0 .26 68 0 .22 01 0.798 0 .14 42 0 .11 15 617 .0 667 4 678.6 714 .2 757.3 548.5 503.6 4 52. 0 390 .2 309.9 11 65.3 11 50.3 11 30.5 11 04.4 10 67 .2 0. 813 1 0.8398 087 69 0.8987 0.93 51 j 0. 517 6 048 64 0. 411 0 0.3485 0 .2 719 1. 3307 1, 30 62 1 ,27 89 1. 24 72 1. 20 71 600 620 640 660 680 0 0369 000 5^ 0.03 92 0.07 61 0.0503 823 * 9 02. 7 17 2 1 o 3093.7 700 705.4 | 320 6 .2 L _J?... 13 25 .8 000 24 000 29 0.0 21 5 0. 02 21 0. 022 8 0.6545 0.5385 043 44 0.3647 0 .29 89 064 79 0.5594 044 69 0.3868 0.3 21 7 487.8 511 .9 536.6 5 62. 2 588.9 713 .9 686.4 656.6 624 .2 588.4 12 01. 7 11 98 .2 1 193 .2 11 86.4 11 77.3 068 87 0. 713 0 0.7374 0,76 21 0.78 72 0.7438 070 06 0.6568 0. 6 12 1 0.5659 1. 4 325 1. 413 6 1. 39 42 1. 37 42 1. 35 32 500 520 540 560 580 600 620 640 660 680 15 42. 9 17 86.6 20 59.7 23 65.4 27 08 .1 0. 023 6 004 27 . / -X4 % % /i /'4 ;/4 •% /'i 3/; | s I i 1 1 1 1 B.W.G. Gauge 22 24 26 27 18 20 22 24 16 18 20 22 12 13 14 15 16 17 18 19 20 10 11 12 13 14 15 16 17 18 20 8 10 11 12 13 14 15 16 Thickness In. . 028 . 022 . 018 . 016 .049 .035 , 028 . 022 .065 .049 .035 . 028 .10 9 .095 .083 .0 72 .065 .058 .049 .0 42 .035 ,13 4 . 12 0 .10 9 .095 .083 .0 72 .065 .058 .049 .035 .16 5 .13 4 . 12 0 .10 9 .095 .083 .0 72 .065 internal Area !n. 2 . 029 5 .0333 .0360 .0373 .0603 .07 31 .0799 .0860 .10 75 . 12 69 .14 52 .15 48 .13 01 .14 86 . . 26 .78 Sot. Vapor v g 3306 29 47 24 44 20 36,4 17 03 .2 12 06.7 867,9 633 .1 468.0 350.4 26 5.4 20 3 .27 15 7.34 12 3, 01 97.07 77 .29 62. 06 50 .23 40.96 33.64 27 . 82 26.80 Enthalpy Sat. Liquid 0.00 3. 02 8.05 13 .06 18 ,07 28 .06 38.04 48, 02 57.99 67.97 77.94 87. 92 97.90 10 7.89 11 7.89 12 7.89 13 7.90 14 7. 92 15 7.95 16 7.99 17 8.05 18 0.07 Evap. hfg 10 75,8 10 74 .1 10 71. 3 10 68,4 10 65.6 10 59.9 10 54.3 10 48.6 10 42. 9 10 37 .2 10 31, 6 10 25 .8 10 20 .0 10 14 .1 1008 .2 10 02. 3 996.3 990 .2 984 .1 977,9 9 71. 6 970,3 Sat. Vapor kg 10 75.8 10 77 .1 1079.3 10 81. 5 10 83.7 10 88.0 10 92, 3 10 96.6 11 00.9 11 05 .2 11 09.5 11 13.7 11 17.9 11 22 ,0 11 26 .1 113 0 .2 11 34 .2 11 38 .1 1 14 2. 0 1 14 5.9 11 49.7 1 1. 50.4 Entropy Sat. Liquid Sf 0.0000 0.00 61 0. 016 2 0. 026 2 0,03 61 0.0555 0.0745 0.09 32 0 .11 15 0 . 12 95 0 .14 71 0 .16 45 0 .18 16 0 ,19 84 0. 21 4 9 0 .2 311 0 .24 72 0 .26 30 0 .27 85 0 ,29 38 Evap. % 2 .18 77 2 .17 09 2 .14 35 2 ,11 67 2. 0903 2. 0393 1. 99 02 1. 9 428 1. 89 72 1. 85 31 1. 810 6 1. 7694 1. 729 6 1. 6 910 1. 6537 1. 617 4 1. 5 822 1, 5480 1. 514 7 1, 4 824 0.3090 . 1. 50.4 Entropy Sat. Liquid Sf 0.0000 0.00 61 0. 016 2 0. 026 2 0,03 61 0.0555 0.0745 0.09 32 0 .11 15 0 . 12 95 0 .14 71 0 .16 45 0 .18 16 0 ,19 84 0. 21 4 9 0 .2 311 0 .24 72 0 .26 30 0 .27 85 0 ,29 38 Evap. % 2 .18 77 2 .17 09 2 .14 35 2 ,11 67 2. 0903 2. 0393 1. 99 02 1. 9 428 1. 89 72 1. 85 31 1. 810 6 1. 7694 1. 729 6 1. 6 910 1. 6537 1. 617 4 1. 5 822 1, 5480 1. 514 7 1, 4 824 0.3090