<p> DeCasteljau </p>

e940aeb4-9cc3-4504-909e-fa1ed42d43ba 21 6 9 decimal

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Understanding SVG

Model from jmG Mathcad 8 Pro. made work in Smath by Dave Carpi

t = interpolation point in [0,1]
p = control points t p DeCasteljau De Casteljau SMath M 1 t - (p 1 row * t p 2 row * + : p rows 2 > i 2 p rows 1 - range M M 1 t - (p i row * t p i 1 + row * + stack : for t M DeCasteljau 21 line M if 31 line :

t = range of interpolation points in [0,1]
p = control points t p DeCasteljauRange M t 1 el p DeCasteljau : i 2 t length range M M t i el p DeCasteljau stack : for M 31 line :

ndp =  number of discretization points (> 1)
p = control points ndp p DeCasteljauNDP t 011 ndp 1 - / range : M t 1 el p DeCasteljau : i 2 t length range M M t i el p DeCasteljau stack : for M 41 line :

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

XY 100020201015 - 05050015 - 26 mat transpose :

a b c spec . 14 black 13 mat :

xy XY a b c spec pts :

p svg 1010015 - 15 - 023 mat 0102050605023 mat 202020500023 mat 201010015 - 15 - 23 mat 14 mat transpose * :

svg 1 :

NDP 100 :

C 0200020000505025 mat transpose :

bin NDP p 1 el DeCasteljauNDP :

level 510151022 mat :

i 2 p length range bin bin NDP p i el DeCasteljauNDP stack : for

C bin level 3 1 sys

A 1 : a 0.025 : g 9.8067 : 13 mat

h time A a / 2 g / sqrt * 1 h - sqrt * :

0 time 18.06

x time 0 x ≤ x time Not physcic if :

x time 18.064 x time - 0 18 . 14 red 1 5 mat 3 1 sys

Theoretical Unary Discharge

The ratio A/a is typical to enable a demo graph. User will addapt more parameters to suit installation. "h" is unit [1m], time is [sec]. Consider: 1. Viscosity 2. Length of piping, elbow ... 3. If used for metering => test wrt to fluid properties ... level metering is the rule, time metering is backup safety.

@ 20% remaining level 40% of the time has to elapse i.e: 7.1 unit time of the 18.064

1 0.80 time - abs 0 time / 0.4

1 0.80 time - abs 7.1