050b3b29-6039-4e1a-a181-deafdc0af49f 19 6 9 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 :

0. Water masse volumique kg/m^3/°C

t0 1 time :

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 :

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 heating 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 392323.244203 - 300 0.000572 325 930691.11682 - 350 0.000314 360 76987.173789 - 370 0.000284 - 374 35984.735997 - 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 : 21 line

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"

x kgm3 999.9 1 x r / - :

recast as function of 'x'

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 exct @ the support points

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

XY X Y . 10 black plotG :

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

322 W XY 3 1 sys

Interpolate in-situ 100 kgm3 958.35

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 xx yy . 10 black plotG :

uv v 2 1 sys

1 time t0 - 109 sec *

timing 109 sec * ≡

jmGiraud:revisited 2016/06/02