plot(data,a,b,c)

cca838d0-97bb-4a0c-b57d-1102048fe642 24 4 5 decimal

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

Water Saturation Temperature ... bar(°C)

t0 1 time :

°C 1 :

bar 1 :

n 1167.0521452767 724213.16703206 - 17.073846940092 - 12020.82470247 3232555.0322333 - 14.91510861353 4823.2657361591 - 405113.40542057 0.23855557567849 - 650.17534844798 101 mat :

K 273.15 : t v t K + (n 9 el t K + (n 10 el - / + : t A t v n 1 el + (t v * n 2 el + : t B n 3 el t v * n 4 el + (t v * n 5 el + : t C n 6 el t v * n 7 el + (t v * n 8 el + : t bar_1 102 t C * t B - t B 2^4 t A * t C * - (0.5^+ / (4^* : u 0 x ≤ (x 373.946 ≤ (* : 71 sys

373.946 bar_1 bar 220.64

a 348.05185628969 1.1671859879975 - 0.0010192970039326 572.54459862746 13.918839778870 51 mat :

K 273.15 : t bar_2 10 a 3 el t K + (* a 2 el + (t K + (* a 1 el + (* : w 350 x ≤ (x 590 ≤ (* : 31 sys

x bar_1 u / x bar_2 w / 373.95 220.64 + 40 black 1 5 mat 3 1 sys

critical °C 373.946 ≡ bar 220.64 ≡ 21 sys

X t bar_1 100 - 0 ≡ t 250350 solve :

X °C 311

sterilized units X °C * bar_1 450 °C * bar_2 21 mat bar 100 370.39 21 mat

conversion 101325 Pa * 1 atm * ≡ 100000 Pa * 1 bar * ≡ 21 sys

=========================================================================================

Water Saturation Pressure ... °C(bar)

bar u 10 :

K 273.15 : p β p 10 / (0.25^: p E p β n 3 el + (p β * n 6 el + : p F n 1 el p β * n 4 el + (p β * n 7 el + : p G n 2 el p β * n 5 el + (p β * n 8 el + : p D 2 p G * p F - p F 2^4 p E * p G * - (0.5^- / : p °C n 10 el p D + n 10 el p D + (2^(4 n 9 el n 10 el p D * + (* - (0.5^- 2 / K - : x c 1 0.006117 x ≤ (x 220.64 ≤ (& cases : 81 sys

user 4 - 322432 u u °C 32 mat :

x °C x c * user 2 1 sys

u u °C 12 mat °C 10 179.89 12 mat

sanity 1.01325 °C °C 100.0

triple point 0.006117 °C °C 0.01

Y bar °C 0.01 ≡ bar 0.005 0.007 solve :

Y 0.006117

plot(data,a,b,c)

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

0. Water masse volumique kg/m^3/°C

Thiele(X,Y,Δ)

X Y Δ Thiele ε 1018 -^: n X rows : i 1 n range M i 1 el Y i el : for j 2 n range i j n range dM M i j 1 - el M j 1 - j 1 - el - : dM dM abs ε < ε M i j el X i el X j 1 - el - dM / : if : 21 line for for i 1 n range c i 1 el X i el : c i 2 el M i i el : 21 line for Δ 0 ≡ c M if 61 line :

"data" source: M.P. WUKALOWITSCH [1958] Russian, German, English, French

X Y 0 Thiele generate Thiele vector ≡ X Y 1 Thiele generate Thiele table ≡ 21 line

step 0 => reduce the data Y

WUKALOWITSCH [1958] data 10 999.65 50 988.01 100 958.35 150 917.01 200 864.67 250 798.89 300 712.14 325 654.32 350 574.69 360 527.84 370 450.03 374322122 mat :

0 999.8 4100010 999.7 20 998.2 30 995.7 40 992.2 50 988.1 60 983.2 70 977.8 80 971.8 90 965.3 100 958.4 122 mat

X data 1 col : Y data 2 col : 21 line

X kg m 3^* ≡ Y °C ≡ 21 line

reduce i 1 data rows range R i el 1 999.9 Y i el - / : for R 21 line :

An expansion tank is required on all closed loop boiler systems. As a boiler heats the system water, the water will expand in volume. Water cannot be compressed but air can, so an expansion tank uses air (or an inert gas like nitrogen) that acts like a cushion or spring against this force.

step 1 => Thiele vector of the "reduced"

X reduce 0 Thiele 10450 10.214777 - 100 4.025304 - 150 6406.546109 200 0.023623 250 3.923232 105^* - 300 0.000572 325 9.306911 105^* - 350 0.000314 360 76987.173805 - 370 0.000284 - 374 35984.735995 - 122 mat

TK 10450 10.214777 - 100 4.025304 - 150 6406.546109 200 0.023623 250 3.923232 105^* - 300 0.000572 325 9.306911 105^* - 350 0.000314 360 76987.173789 - 370 0.000284 - 374 35984.735997 - 122 mat :

reduce 4 0.0841 0.02407 0.01206 0.00739 0.00497 0.00348 0.00289 0.00235 0.00212 0.00182 0.00148 121 mat

step 2 => Thiele continued fraction of the "reduced"

T TK 1 col : ρ TK 2 col : 12 mat

r(t)

t r ρ 1 el x T 1 el - ρ 2 el x T 2 el - ρ 3 el x T 3 el - ρ 4 el x T 4 el - ρ 5 el x T 5 el - ρ 6 el x T 6 el - ρ 7 el x T 7 el - ρ 8 el x T 8 el - ρ 9 el x T 9 el - ρ 10 el x T 10 el + ρ 11 el x T 11 el + ρ 12 el / + / + / + / + / + / + / + / + / + / + / + :

step 3 => Recast/Reverse Engineer the "reduced"

recast as function of 'x' x kgm3 999.9 1 x r / - :

Optimiz => numeric W t 0.01 3741 range : i 1 t rows range ρ i el t i el kgm3 eval : 11 line for t ρ augment 31 line :

Notes: 1. the triple point of water 273.16 K, 0.01 °C 2. max density @ approx: 4 °C 3. "surfusion" water droplet may be as low as - 10°C 4. any & all kg/m^3 formulas are approximation. 5. this Thiele is of exceptional quality [Jean Giraud]. 6. Thiele is exact @ the support points

W W :

step 4 =>Plot discrete, Interpolate kg/m^3 vs °C

XY data . 10 black plot :

Water masse volumique ... kg/m^3 vs °C critical range

322 W XY 3 1 sys

kg m 3^/

kg_m³ 1 :

Interpolate in-situ 100 kgm3 200 kgm3 325 kgm3 31 mat kg_m³ 958.35 864.67 654.34 31 mat

1 time t0 - 13 s *

data W 2 1 sys x 0.9 - kgm3 x kgm3 x 0.9 - kgm3

Optimiz => numeric v t 0.01 3741 range : i 1 t rows range specificvolume i el t i el kgm3 eval (1 -^: 11 line for t specificvolume augment 31 line :

support pts specific vol xy i 1 Y rows range spec i el 1 Y i el / : for X spec augment 21 line :

xx xy 1 col : yy xy 2 col : 21 line

uv xy . 10 black plot :

uv v 2 1 sys rho-Steam

WUKALOWITSCH [1958] Water/Steam data 10 999.65 0.009398 50 988.01 0.08306 100 958.35 0.5977 150 917.01 2.547 200 864.67 7.862 250 798.89 19.98 300 712.14 46.21 325 654.32 70.57 350 574.69 113.6 360 527.84 144370 450.03 203374322288123 mat :

ρs 0.009398 543.020824849 0.128192581 - 651.141760016 - 1.682165726 117.019936457 19.46537573 - 302.928543896 - 0.064612944 270.341818192 6.346153635 - 1.040581502 121 mat :

X data 1 col : Y data 3 col : 12 mat

t ρSteam ρs 1 el t X 1 el - ρs 2 el t X 2 el - ρs 3 el t X 3 el - ρs 4 el t X 4 el - ρs 5 el t X 5 el - ρs 6 el t X 6 el - ρs 7 el t X 7 el - ρs 8 el t X 8 el - ρs 9 el t X 9 el - ρs 10 el t X 10 el - ρs 11 el t X 11 el - ρs 12 el / + / + / + / + / + / + / + / + / + / + / + :

X data 1 col : Y data 3 col : 12 mat XY X Y augment : ρSteam XY . 12 black plot : 31 line

v 5 x ≤ (x 374 ≤ (* :

374 ρSteam kg_m³ 288

Steam masse volumique kg/m³ ... up to critical point.

ρSteam x ρSteam v / 2 1 sys

ice sublimation [-90 ... 0.01 °C] ... empirical from source t mbar 0.009316586 t * 2.168177 + 180.4903 t 31.5538 - 986.407 t 12.10429 + 62.33773 t 97.41639 + / + / + / + :

x sublim 190 - x ≤ (x 0.01 ≤ (& cases :

x mbar x sublim * 90 - 2 90 - 2 - 2 2 mat 2 1 sys

mbar 1 :

0.01 mbar mbar 6.11

Enthalpy saturation

Enthalpy Water ke 599.3 2.06612 87.70865 0.28073 444.5461 0.29356 - 849.96936 - 2.0626 - 74.12943 2.66168 33.49078 1.58508 - 23.12122 0.87324 - 141 mat :

Enthalpy Steam kv 5.02 0.99602 5025.02 0.00624 16324.23113 - 0.01094 12803.75677 0.10107 5186.36809 0.0063 3795.17033 - 0.05921 9707.2127 - 0.00044 141 mat :

Hev 5 5.02 599.3 10 10.04 601.72 25 25.04 608.24 50 50.00 618.93 100 100.10 639.06 150 151.01 655.86 200 203.59 666.88 250 259.32 669.02 300 321.20 656.74 325 356.69 641.19 350 399.08 612.31 360 420.73 592.58 370 452.06 557.36 374 498.54 499.61 143 mat :

X Hev 1 col : Y Hev 3 col : 12 mat EnthalWater X Y augment . 12 black plot : 21 line

X Hev 1 col : Y Hev 2 col : 12 mat EnthalpySteam X Y augment . 12 black plot : 21 line

Enthalpy Water

t He ke 1 el t 5 - ke 2 el t 10 - ke 3 el t 25 - ke 4 el t 50 - ke 5 el t 100 - ke 6 el t 150 - ke 7 el t 200 - ke 8 el t 250 - ke 9 el t 300 - ke 10 el t 325 - ke 11 el t 350 - ke 12 el t 360 - ke 13 el t 370 - ke 14 el / + / + / + / + / + / + / + / + / + / + / + / + / + :

Enthalpy Steam

t Hs kv 1 el t 5 - kv 2 el t 10 - kv 3 el t 25 - kv 4 el t 50 - kv 5 el t 100 - kv 6 el t 150 - kv 7 el t 200 - kv 8 el t 250 - kv 9 el t 300 - kv 10 el t 325 - kv 11 el t 350 - kv 12 el t 360 - kv 13 el t 370 - kv 14 el / + / + / + / + / + / + / + / + / + / + / + / + / + :

kcal_kg 1 :

300 Hs 300 He 21 mat kcal_kg 32165721 mat

v 5 x ≤ (x 374 ≤ (* :

EnthalWater x He v / 2 1 sys EnthalpySteam x Hs v / 2 1 sys

Entropy saturation

Entropy 10 0.03596 2.1262 50 0.1681 1.9293 100 0.3121 1.7568 150 0.4398 1.6327 200 0.5567 1.5353 250 0.6673 1.4499 300 0.7774 1.3636 370 0.9820 1.1498 83 mat :

X Entropy 1 col : Y Entropy 2 col : 12 mat EntropyWaterWater X Y augment . 12 black plot : 21 line

X Entropy 1 col : Y Entropy 3 col : 12 mat EntropySteam X Y augment . 12 black plot : 21 line

se 1.87804 104 -^* - 3.8091 103 -^* 1.76923 105 -^* - 3.3417 107 -^* 4.7508 109 -^* - 3.9818 1011 -^* 1.9778 1013 -^* - 5.7415 1016 -^* 8.998 1019 -^* - 5.8805 1022 -^* 101 mat :

kcal_kg 1 :

sv 2.18785 6.6924 103 -^* - 4.34896 105 -^* 3.62069 107 -^* - 2.4730 109 -^* 1.0247 1011 -^* - 2.2014 1014 -^* 1.8911 1017 -^* - 81 mat :

Entropy water phase x se se j el x j 1 -^* j 110 sum 11 line :

Entropy vapor phase x sv sv j el x j 1 -^* j 18 sum 11 line :

s 0.01 x ≤ (x 374 ≤ (* :

x se s / x sv s / EntropyWaterWater EntropySteam 4 1 sys

Observe => Lagrange criterium

coefficients 'se, sv' alternate ±

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CT 10 1.001 50 1.0013 100 1.0093 150 1.0303 200 1.0744 250 1.1619 300 1.3495 370 2.5756 82 mat :

kcal_kg_°C 1 :

c 1.001646 2.0188 104 -^* - 1.161 105 -^* 2.1897 107 -^* - 1.8655 109 -^* 6.6982 1012 -^* - 8.8248 1015 -^* 71 mat :

cT CT . 12 black plot :

Heat mass water phase x c c j el x j 1 -^* j 17 sum 11 line :

250 c kcal_kg_°C 1.16

cT x c s / 2 1 sys

acc 100 x c x 030 int kcal_kg 30.03

x so 1 0.01 x ≤ (x 374 ≤ (* cases :

Sonic velocity [m/s] ... given °C

sonic vapor phase sonicS 15 420.5 50 443.96 100 472.97 150 494.04 200 504.88 250 503.11 300 482.97 350 429.97 370 391.06 92 mat :

sonic water phase sonicW 101447501545100154515014662001332250114930091035057882 mat :

σe 1406.1281 4.53204 0.040837 - 0.00010935 1.4023 107 -^* - 51 mat :

σv 406.64 0.93143 0.0037462 - 0.00001323 2.7532 108 -^* - 51 mat :

soW sonicW . 12 black plot :

soS sonicS . 12 black plot :

x sonicW σe j el x j 1 -^* j 15 sum 11 line :

x sonicS σv j el x j 1 -^* j 15 sum 11 line :

x sonicW x so * x sonicS x so * soW soS 4 1 sys

°C ... Vapor phase Isentropic .... bar

isentropic_°C 10 1.3275 50 1.3276 100 1.337 150 1.368 200 1.446 250 1.627 300 2.094 325 2.684 350 4.467 360 6.882 370 21.071 373 86.89 122 mat :

χ.t 1.3275 400000 0.00012803 - 402748.412 - 0.1686548 8407.8399 0.0128743 - 7559.6214 - 0.1079548 - 863.11255 - 0.0011947 - 703.6825 121 mat :

isentropic_bar 5 1.37 10 1.4 25 1.514 50 1.713 75 1.961 100 2.297 125 2.791 150 3.624 175 5.298 200 10.817 210 20.237 215 37.82 122 mat :

χ.p 1.3280 128.08 2.3893 1.2349 3.6434 - 461.032 0.3511 235.242 0.1815 - 284.33 - 101 mat :

t χ°C χ.t 1 el t 10 - χ.t 2 el t 50 - χ.t 3 el t 100 - χ.t 4 el t 150 - χ.t 5 el t 200 - χ.t 6 el t 250 - χ.t 7 el t 300 - χ.t 8 el t 325 - χ.t 9 el t 350 - χ.t 10 el t 360 - χ.t 11 el t 370 - χ.t 12 el / + / + / + / + / + / + / + / + / + / + / + :

p χbar χ.p 1 el p 0.01 - χ.p 2 el p 10 - χ.p 3 el p 25 - χ.p 4 el p 50 - χ.p 5 el p 100 - χ.p 6 el p 150 - χ.p 7 el p 175 - χ.p 8 el p 200 - χ.p 9 el p 210 - χ.p 10 el / + / + / + / + / + / + / + / + / + :

χ°C isentropic_°C . 12 black plot :

χbar isentropic_bar . 12 black plot :

χt 0.01 x ≤ (x 370 ≤ (* :

χp 5 x ≤ (x 215 ≤ (* :

χ°C x χ°C χt / 2 1 sys χbar x χbar χp / 2 1 sys

Latent heat of vaporisation "Latent heat of vaporization is a physical property of a substance. ... When a material in liquid state is given energy, it changes its phase from liquid to vapor; the energy absorbed in this process is called heat of vaporization. The heat of vaporization of water is about 2,260 kJ/kg, which is equal to 40.8 kJ/mol"

Latent Heat of Vaporation Data

Latent 0.0075 597.34 5 594.51 10 591.68 25 583.20 50 568.93 100 538.96 150 504.85 200 463.29 250 409.71 300 335.54 325 284.50 350 213.23 360 171.85 370 105.30 373.946 1.07 152 mat :

r 0.353357 28.3 - 0.3532526 - 84963.446 - 0.002913 - 28223.818 - 0.0104773 - 20059.1873 0.00408109 19897.0525 - 0.0043650 312195.22 - 0.000043493 622979.5218 141 mat :

X Latent 1 col : Y Latent 2 col : 12 mat Latent Latent . 12 black plot : 21 line

Latent

t Latent r 1 el t 5 - r 2 el t 10 - r 3 el t 25 - r 4 el t 50 - r 5 el t 100 - r 6 el t 150 - r 7 el t 200 - r 8 el t 250 - r 9 el t 300 - r 10 el t 325 - r 11 el t 350 - r 12 el t 360 - r 13 el t 370 - r 14 el / + / + / + / + / + / + / + / + / + / + / + / + / + :

t LatentHeat 597.34 1 t Latent / - :

λ 0.01 x ≤ (x 374 ≤ (* :

325 LatentHeat kcal_kg 284.51

Latent x LatentHeat λ / 2 1 sys

kcal_kg 1 :

kW_hr 1 :

Latent x LatentHeat x 0.01 100 int : kcal_kg 56861

Latent 0.001163 * kW_hr 66

Water saturation bar(°C )... IAPWS-97 ± 0.000 mutual conformity

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

c 7.45405359891067 103 -^* 1.325012145171 104 -^* 2.55178597883334 105 -^* 1.3180616369901 107 -^* - 5.04814989587821 109 -^* 1.20800120409375 1011 -^* - 6.56045886848592 103 -^* - 2.14781927781255 105 -^* 4.15864048208323 108 -^* - 3.73870830454988 1011 -^* 1.01734440690023 1014 -^* - 111 mat :

data 6.97 0.01 32.875 0.05 45.808 0.1 64.963 0.25 81.317 0.5 91.758 0.75 99.606 1 127.414 2.5 151.836 5 179.886 10.0001 223.956 24.9998 263.943 50.0001 310.999 99.9993 342.158 150.0002 365.746 200.0002 373.707 220.0012 162 mat :

jmGiraud: 2021/02/06

x Genfit c 1 el c 2 el x * + c 3 el x 2^* + c 4 el x 3^* + c 5 el x 4^* + c 6 el x 5^* + 1 c 7 el x * + c 8 el x 2^* + c 9 el x 3^* + c 10 el x 4^* + c 11 el x 5^* + / :

x G 1 0.01 x ≤ (x 374 ≤ (& cases :

°C 200 :

X data 1 col : Y data 2 col : 12 mat ΔGenfit X Y X Genfit - vectorize (augment : support data o 5 black plot : 31 sys

track 32 - 192256192 °C °C Genfit 32 mat :

bar 1 :

ΔGenfit 6.970 0.000 32.875 0.000 45.808 0.000 64.963 0.000 81.317 0.000 91.758 0.000 99.606 0.000 127.414 0.000 151.836 0.000 179.886 0.000 223.956 0.000 263.943 0.000 310.999 0.000 342.158 0.000 365.746 0.000 373.707 0.000 162 mat

Water saturat'n temperature bar(°C) mutual conformity ± 0.0001

track x Genfit x G * support 3 1 sys

°C °C Genfit 12 mat bar 200 15.55 12 mat

275 Genfit 11 mat bar 59.46 11 mat

4 appVersion 0.98.6179.21440 ≡

1 time t0 - 46 s *