fa14c081-4f23-40e1-9727-fba48bb94336 10 4 5 true true 0 decimal

&[DATE] &[TIME] - &[FILENAME]

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

Data PT 0.01 6.97 0.05 32.88 0.1 45.81 0.25 64.96 0.5 81.32 0.75 91.76 1 99.61 2.5 127.41 5 151.84 10 179.98 25 223.96 50 263.94 100311150 342.16 200 365.75 220 373.71 162 mat :

Xk PT 1 col :

Yk PT 2 col :

XY Xk Yk . 10 black plotG :

Assigning the direct values of Y i 1 Yk rows range φ i 1 el Yk i el : for

Calculation of the table of inverse differences j 2 Yk rows range i j Yk rows range φ i j el Xk j 1 - el Xk i el - φ j 1 - j 1 - el φ i j 1 - el - / : cont j : 21 line break try for for

With the Try / on error function, division by zero is avoided when the inverse differences of a column are all the same, and the loop is exited.

Inverse Differences φ 697100 / 00000000082225 / 42591 / 000000004581100 / 93884 / 2.5159 106^* 38915 / 0000000162425 / 81933 / 5.0084 106^* 64980 / 7.5861 107^* 6.2843 109^* / 000000203325 / 497435 / 3.4675 107^* 3.8888 105^* / 6.0532 109^* 3.7103 1011^* / 7.1157 1016^* 1.2077 1015^* / 00000229425 / 748479 / 1.5378 108^* 1.5782 106^* / 7.9839 109^* 4.028 1011^* / 3.2187 1015^* 4.9887 1013^* / 6.8493 1014^* 1.5343 1016^* / 00009961100 / 333088 / 3.8005 107^* 3.6576 105^* / 1.708 109^* 7.4502 1010^* / 2.1432 1016^* 3.1016 1014^* / 6.6539 1013^* 1.3546 1015^* / 3.6918 1016^* 6.6153 1014^* / 00012741100 / 24912044 / 3.8227 108^* 2.9849 106^* / 4.6463 109^* 1.2278 1011^* / 2.6489 1016^* 3.0342 1014^* / 3.2546 1014^* 4.6186 1015^* / 3.9336 1015^* 5.8049 1013^* / 4.0928 1014^* 3.2627 1015^* / 00379625 / 49914487 / 3.716 109^* 2.4699 107^* / 9.4195 1011^* 1.6494 1013^* / 1.1739 1015^* 1.113 1013^* / 2.9846 1013^* 3.0873 1014^* / 3.576 1016^* 4.378 1014^* / 4.1157 1014^* 2.6624 1015^* / 9.6442 1015^* 1.1242 1014^* / 0899950 / 3335767 / 2.9735 109^* 1.6795 107^* / 1.4378 1011^* 1.6325 1012^* / 9.5391 1016^* 7.4362 1014^* / 3.7887 1014^* 2.7661 1015^* / 2.3559 1015^* 2.3515 1013^* / 2.6527 1013^* 1.3081 1014^* / 9.0978 1015^* 9.3829 1013^* / 1.4991 1014^* 3.3514 1014^* / 559925 / 8337233 / 9.3516 109^* 4.2587 107^* / 8.2533 1012^* 5.1355 1013^* / 4.3281 1016^* 2.5993 1014^* / 5.3575 1013^* 2.3527 1014^* / 7.7747 1016^* 5.8695 1014^* / 4.1384 1014^* 1.3217 1015^* / 3.4472 1015^* 2.8752 1013^* / 1.4699 1014^* 2.5072 1014^* / 1319750 / 499925697 / 2.2171 1010^* 8.5664 107^* / 3.327 1013^* 1.2946 1014^* / 4.4346 1015^* 2.1832 1013^* / 3.2843 1014^* 9.5679 1014^* / 6.4214 1017^* 3.8935 1015^* / 7.0059 1014^* 1.5602 1015^* / 2.1476 1016^* 1.4631 1014^* / 2.3375 1014^* 3.1686 1014^* / 311999930403 / 1.5747 1011^* 5.1572 108^* / 4.4553 1013^* 1.0734 1014^* / 7.162 1016^* 2.8934 1014^* / 1.7156 1014^* 3.252 1014^* / 4.3983 1016^* 2.14 1014^* / 7.78 1014^* 1.1766 1015^* / 8.311 1016^* 4.5671 1014^* / 4.3324 1014^* 4.3867 1014^* / 855425 / 1499933519 / 2.6046 1011^* 7.7457 108^* / 4.5183 1013^* 8.187 1013^* / 5.7403 1017^* 2.0693 1015^* / 5.9255 1014^* 8.6597 1014^* / 2.9354 1017^* 1.258 1015^* / 6.8832 1014^* 8.2015 1014^* / 2.191 1016^* 1.0603 1014^* / 7.6761 1014^* 6.3978 1014^* / 14634 / 1999935878 / 1.8587 1011^* 5.1674 108^* / 8.0395 1014^* 1.1866 1015^* / 8.6705 1016^* 2.8884 1014^* / 8.2412 1014^* 9.9663 1014^* / 4.2282 1017^* 1.66 1015^* / 8.6649 1014^* 8.6607 1014^* / 3.3045 1015^* 1.4641 1013^* / 2.2807 1014^* 1.6365 1014^* / 37371100 / 2199936674 / 2.09 1011^* 5.6853 108^* / 3.2434 1014^* 4.4686 1014^* / 5.1087 1016^* 1.6593 1014^* / 7.8133 1014^* 8.8621 1014^* / 6.6194 1017^* 2.5271 1015^* / 5.0807 1014^* 4.7823 1014^* / 1.0047 1017^* 4.3283 1014^* / 4.6461 1014^* 3.1626 1014^* / 1610 mat

cont 16

Obtaining the diagonal of the Matrix of the inverse differences i 1 cont range Yφ i el φ i i el 4 round : for

Rounding the values of the inverse differences for the purpose of presenting the equation to make it shorter

Thiele Function s P p size T i size 2 range i size ≡ T s i 1 - el eval p P i 1 - el eval - s i el eval / (+ : T T : 21 line T s i 1 - el eval p P i 1 - el eval - T / (+ : T T : 21 line if for s P p size T T : 21 line :

Thiele Size size 10 :

Xk 0.01000 0.05000 0.1000 0.2500 0.5000 0.7500 1.000 2.500 5.000 10.00 25.00 50.00 100.0 150.0 200.0 220.0 161 mat

Yφ 6.970 0.001500 64.65 0.01210 58.92 0.04460 55.81 0.1254 85.78 0.4473 107.9 0.8389 113.6 2.815 92.59 3.030 - 161 mat

p Tbar Yφ Xk p size T :

Data to build the equation

The equation in continuous fractions is p Tbar 6.97 p 0.01 - 0.0015 p 0.05 - 64.6502 p 0.1 - 0.0121 p 0.25 - 58.9206 p 0.5 - 0.0446 p 0.75 - 55.8065 p 1 - 0.1254 p 2.5 - 85.7831 p 5 - 0.4473 / + / + / + / + / + / + / + / + / +

Optimiz => numeric Tbar p 0.01 10 0.025 range : i 1 p rows range u i el p i el : ρ i el p i el Tbar eval : 21 line for u ρ augment 31 line :

1.333 Tbar 1.667 Tbar 2 Tbar 31 mat 108.152 114.8236 120.4606 31 mat

108.2 114.8 120.5 31 mat

Tbar 1 99.6 + 20 green 1 5 mat XY 3 1 sys

p 0.01 10100 logpts :

Optimiz => numeric Tlogpts i 1 p rows range u i el p i el : ρ i el p i el Tbar eval : 21 line for u ρ augment 21 line :

low high N logpts linear-log populate step high low / log10 N / : i 1 N range x i el low 10 step i *^* : for x 41 line :

Water saturation temperature °C <= p[bar]

1 99.6 + 20 green 1 5 mat Tlogpts XY 3 1 sys