8bbc1551-9080-4407-abe0-c7cdc58fbc18 10 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 :

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 :

Robert [Mathsoft Collab] did convert my old Excel work sheet in Mathcad 11 program style, re-coded here Smath.

The support points Vis 5 1.518 10 1.306 25 0.890 50 0.547 100 0.282 150 0.182 200 0.134 250 0.106 300 0.086 350 0.066 102 mat :

X Vis 1 col : Y Vis 2 col : V X Y 0 Thiele : Table X Y 1 Thiele : 41 line

iVBORw0KGgoAAAANSUhEUgAAAAoAAAAKCAIAAAACUFjqAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAgY0hSTQAAeiYAAICEAAD6AAAAgOgAAHUwAADqYAAAOpgAABdwnLpRPAAAAIdJREFUKFN9z6ENxCAYhuGiGIAQtkAwSlkFi2YBBBpPMJ2ABUjYAAlhB+5zl2t6RXzif17DQQg5Xh54jPFW9N733n+L1ho45/xcXNcFPs/zmb334Dkn2Dl3j4wxYGstoNZ6Z601WAgB4JxjKaXfSCkFLqXgFGPE/nyVMQYOIQBSSti1FlZK+QF/LECWpUOt5gAAAABJRU5ErkJggg== Table

V 5 1.518 10 23.584906 - 25 1.815491 - 50 431.407721 100 0.30672 150 4743.569213 200 0.059524 250 1529.710177 - 300 0.09232 - 350 1490.913976 - 102 mat

Thiele continued fraction is constructed from 'V'. Unfortunately, I was "infinitely unable" to construct the continued fraction automatically in Smath like it does in Mathcad 11. No problem: construct a dummy continued fraction, long enough to accommodate a long vector and truncate to suit particular length of 'V'.

Thiele vector of the "interpolanting coefficients"  is the diagonal elements of 'T'.
I know no other use of the Thiele table except to make an image of it [T image above]. Table 1.518 000000000 1.306 23.585 - 00000000 0.89 31.847 - 1.815 - 0000000 0.547 46.344 - 1.758 - 431.408 000000 0.282 76.861 - 1.689 - 594.423 0.307 00000 0.182 108.533 - 1.648 - 746.606 0.317 4743.569 0000 0.134 140.896 - 1.62 - 893.472 0.325 5583.57 0.06 000 0.106 173.513 - 1.601 - 1047.872 0.324 8469.65 0.027 1529.71 - 00 0.086 206.006 - 1.59 - 1218.114 0.318 18082.766 0.011 2071.306 - 0.092 - 0 0.066 237.603 - 1.589 - 1432.712 0.3 35155.167 - 0.005 - 2324.267 - 0.126 - 1490.914 - 1010 mat

T V 1 col : μ V 2 col : 21 line

Thiele continued fraction ... Optimiz numeric t μT μ 1 el t T 1 el - μ 2 el t T 2 el - μ 3 el t T 3 el - μ 4 el t T 4 el - μ 5 el t T 5 el - μ 6 el t T 6 el - μ 7 el t T 7 el - μ 8 el t T 8 el - μ 9 el / + / + / + / + / + / + / + / + :

Optimiz => numeric μ350 t 03501 range : i 1 t rows range v i el t i el μT eval : 11 line for t v augment 31 line :

data X Y . 14 black plotG : t 75 : cp @ User [t] ≡ t cp t t μT + 20 blue 15 mat : 31 line

Water viscoity ... μ[cp] / °C ... critical range

data μ350 t cp 3 1 sys

t μT 0.38

<--- t[°C]--->

Truncate in block =>

It takes about 10 seconds to fabricate the viscosity μT(t) 1. truncate in block 2. click on 'K', press F8, rename K for μ 3. click on 'X', press F8, rename X for T 4. add/defined the LHS function μT(t):=

K 1 el x X 1 el - K 2 el x X 2 el - K 3 el x X 3 el - K 4 el x X 4 el - K 5 el x X 5 el - K 6 el x X 6 el - K 7 el x X 7 el - K 8 el x X 8 el - K 9 el x X 9 el - K 10 el x X 10 el + K 11 el x X 11 el + K 12 el x X 12 el + K 13 el x X 13 el + K 14 el x X 14 el + K 15 el x X 15 el + K 16 el x X 16 el + K 17 el / + / + / + / + / + / + / + / + / + / + / + / + / + / + / + / +