f1, f2, f3

6a3a75c2-abd1-458b-b8a6-423cbc2b0811 48 4 5 decimal

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

8. Rod mill for PID schematic diagram ...

'n' population
'w' aperture  
radius OD n 2000 : w 1.125 : OD 3.5 : 31 sys

size 175 :

svg 0.625 :

Mill j 1 n range rod j el OD w i 2 * π * j w / *^eval * : for rod Re rod Im augment 21 line :

size via ► Wingrab ► IrfanView

1 - 1 - . size svg * gray 1 5 mat 1 1 - . size svg * gray 1 5 mat 0 0 . size svg * gray 1 5 mat svg Mill * 6 1 sys

9. Operators pie chart ...

============ Unary ▼ radius /radials ===============

set 'N' radials

size radials s 1 :

r 1 : N 360 : 12 mat step 011 N / range : r θ f r i θ * exp * : 31 sys

step real r 2 π * step * f Re : step imag 12 π * step * f Im : X step real vectorize eval s * : Y step imag vectorize eval s * : 12 mat 31 sys

From here . . .

1. Set N radials

2. Size s radials

]]>

circle X Y augment :

circle

sweep angle ° j 360 :

i 1 j range vx i 2 * el X i el : for

i 1 j range vy i 2 * el Y i el : for

sweep vx vy augment :

pie p1 sweep 1120 range 12 range el : p2 sweep 121180 range 12 range el : p3 sweep 181270 range 12 range el : p4 sweep 271540 range 12 range el : p5 sweep 541720 range 12 range el : 51 sys :

x y axes x y / - :

pie axes 2 1 sys

10. Inspection aperture ...

Adjustable aperture . . . project

for Ω=1 aperture disappears . . . experiment

]]>

clear  previous 'i' range i Clear 1

Solve/plot for a given aperture

svg 0.625 :

imaginary unit

'n' population
'w' aperture  
radius OD svg n 2000 : w 1.56019262501239 : OD 2.5 : 31 sys *

rad svg OD w i π * w /^eval * Re * : 0.976562503

x circle rad 2^x 2^- sqrt ± :

Disk j 1 n range F j el OD w i 2 * π * j w / *^eval * : for F Re F Im augment 21 line :

solve aperture

rad 0 + 200 blue 1 5 mat x circle svg Disk * 4 1 sys

Ω 1.25 : OD 2 : 21 sys

solve aperture here ... bracket wisely.

sol OD w i π * w /^eval * Re Ω - 0 ≡ w 12 solve :

plug in 'w'

sol 1.56019262501239

aperture otherwise

svg 0.875 :

'n' population
'w' aperture  
radius OD n 2000 : w 0.375 : OD 2 : 31 sys

a svg OD w i π * w /^eval * Re * :

x circle a 2^x 2^- sqrt ± :

ring svg OD * a - : 2.3714

Disk j 1 n range F j el OD w i 2 * π * j w / *^eval * : for F Re F Im augment 21 line :

plot 00 + 100 blue 15 mat x circle svg Disk * 41 sys :

plot

a 0.62138126198173 -

thin ring
circle only
peep hole w 1.125 ≡ w 1 ≡ w 0.25 ≡ 31 sys

11. Personel safety warning ...

svg 0.5 :

∠ rot ∠ cos ∠ sin - ∠ sin ∠ cos 22 mat :

∠1 π - 2 / 22.5 ° * + : ° 67.5 -

∠2 22.5 ° * :

'n' population
'w' aperture  
radius OD n 2000 : w 0.70349 : OD 2 : 31 sys

'w' sytem companion 0.703467417226959 0.70348 0.70349 0.7035 0.703513 0.703536 61 sys

0.70349 45° ≡ 0.703513 90° ≡ 21 mat

peep hole
circle only
thin ring w 0.25 ≡ w 1 ≡ w 1.25 ≡ 31 sys

Quad_1 svg Nuc * ∠1 rot * : Quad_2 svg Nuc * ∠2 rot * : 21 sys

Nuc j 1 n range F j el OD w i 2 * π * j w / *^eval * : for F Re F Im augment 21 line :

similar MCD global

Templar Cross

Quad_2 Quad_1 2 1 sys

Some radioactive Instruments bear this warning symbol, displayed in PID diagram.

Wind mill . . . Process Diagram

]]> f1, f2, f3

f1 00 0.006 - 0.004 0.012 - 0.007 0.019 - 0.011 0.025 - 0.015 0.031 - 0.019 0.038 - 0.022 0.044 - 0.026 0.05 - 0.03 0.056 - 0.034 0.062 - 0.038 0.069 - 0.042 0.075 - 0.046 0.081 - 0.05 0.088 - 0.055 0.094 - 0.059 0.1 - 0.063 0.106 - 0.067 0.112 - 0.072 0.119 - 0.076 0.125 - 0.081 0.131 - 0.085 0.138 - 0.09 0.144 - 0.094 0.15 - 0.099 0.156 - 0.104 0.162 - 0.109 0.169 - 0.113 0.175 - 0.118 0.181 - 0.123 0.188 - 0.128 0.194 - 0.133 0.2 - 0.138 0.206 - 0.144 0.212 - 0.149 0.219 - 0.154 0.225 - 0.16 0.231 - 0.165 0.238 - 0.17 0.244 - 0.176 0.25 - 0.182 0.256 - 0.187 0.262 - 0.193 0.269 - 0.199 0.275 - 0.205 0.281 - 0.211 0.288 - 0.217 0.294 - 0.223 0.3 - 0.229 0.306 - 0.236 0.312 - 0.242 0.319 - 0.249 0.325 - 0.255 0.331 - 0.262 0.338 - 0.269 0.344 - 0.276 0.35 - 0.283 0.356 - 0.29 0.362 - 0.297 0.369 - 0.304 0.375 - 0.312 0.381 - 0.319 0.388 - 0.327 0.394 - 0.335 0.4 - 0.343 0.406 - 0.351 0.412 - 0.359 0.419 - 0.368 0.425 - 0.376 0.431 - 0.385 0.438 - 0.394 0.444 - 0.404 0.45 - 0.413 0.456 - 0.423 0.462 - 0.433 0.469 - 0.443 0.475 - 0.454 0.481 - 0.465 0.488 - 0.476 0.494 - 0.488 0.5 - 0.5 0.506 - 0.513 0.512 - 0.526 0.519 - 0.54 0.525 - 0.555 0.531 - 0.572 0.538 - 0.589 0.544 - 0.609 0.55 - 0.632 0.556 - 0.661 0.556 - 0.783 0.55 - 0.803 0.544 - 0.818 0.538 - 0.829 0.531 - 0.838 0.525 - 0.846 0.519 - 0.852 0.512 - 0.857 0.506 - 0.862 0.5 - 0.866 0.494 - 0.869 0.488 - 0.872 0.481 - 0.874 0.475 - 0.876 0.469 - 0.878 0.462 - 0.879 0.456 - 0.88 0.45 - 0.88 0.444 - 0.88 0.438 - 0.88 0.431 - 0.879 0.425 - 0.879 0.419 - 0.878 0.412 - 0.876 0.406 - 0.875 0.4 - 0.873 0.394 - 0.871 0.388 - 0.869 0.381 - 0.867 0.375 - 0.864 0.369 - 0.861 0.362 - 0.858 0.356 - 0.855 0.35 - 0.852 0.344 - 0.848 0.338 - 0.844 0.331 - 0.84 0.325 - 0.836 0.319 - 0.831 0.312 - 0.827 0.306 - 0.822 0.3 - 0.817 0.294 - 0.812 0.288 - 0.806 0.281 - 0.801 0.275 - 0.795 0.269 - 0.789 0.262 - 0.783 0.256 - 0.776 0.25 - 0.769 0.244 - 0.763 0.238 - 0.755 0.231 - 0.748 0.225 - 0.74 0.219 - 0.733 0.212 - 0.725 0.206 - 0.716 0.2 - 0.708 0.194 - 0.699 0.188 - 0.69 0.181 - 0.68 0.175 - 0.671 0.169 - 0.661 0.162 - 0.65 0.156 - 0.64 0.15 - 0.629 0.144 - 0.617 0.138 - 0.605 0.131 - 0.593 0.125 - 0.581 0.119 - 0.568 0.112 - 0.554 0.106 - 0.54 0.1 - 0.525 0.094 - 0.51 0.088 - 0.494 0.081 - 0.477 0.075 - 0.46 0.069 - 0.442 0.062 - 0.422 0.056 - 0.402 0.05 - 0.38 0.044 - 0.356 0.038 - 0.33 0.031 - 0.302 0.025 - 0.271 0.019 - 0.235 0.012 - 0.193 0.006 - 0.137 001802 mat :

f2 0.011 0.006 0.022 0.013 0.033 0.019 0.044 0.025 0.056 0.031 0.067 0.036 0.078 0.042 0.089 0.047 0.1 0.053 0.111 0.058 0.122 0.063 0.133 0.068 0.144 0.073 0.156 0.078 0.167 0.083 0.178 0.087 0.189 0.092 0.2 0.096 0.211 0.101 0.222 0.105 0.233 0.109 0.244 0.113 0.256 0.117 0.267 0.121 0.278 0.124 0.289 0.128 0.3 0.131 0.311 0.135 0.322 0.138 0.333 0.141 0.344 0.144 0.356 0.147 0.367 0.15 0.378 0.153 0.389 0.155 0.4 0.158 0.411 0.16 0.422 0.162 0.433 0.165 0.444 0.167 0.456 0.169 0.467 0.17 0.478 0.172 0.489 0.174 0.5 0.175 0.511 0.177 0.522 0.178 0.533 0.179 0.544 0.18 0.556 0.181 0.567 0.182 0.578 0.183 0.589 0.183 0.6 0.184 0.611 0.184 0.622 0.184 0.633 0.185 0.644 0.184 0.656 0.184 0.667 0.184 0.678 0.183 0.689 0.183 0.7 0.182 0.711 0.181 0.722 0.18 0.733 0.178 0.744 0.177 0.756 0.175 0.767 0.173 0.778 0.171 0.789 0.169 0.8 0.166 0.811 0.163 0.822 0.16 0.833 0.157 0.844 0.153 0.856 0.149 0.867 0.145 0.878 0.14 0.889 0.135 0.9 0.13 0.911 0.123 0.922 0.117 0.933 0.109 0.944 0.101 0.956 0.091 0.967 0.079 0.978 0.065 0.989 0.047 1010 0.989 0.047 - 0.978 0.065 - 0.967 0.079 - 0.956 0.091 - 0.944 0.101 - 0.933 0.109 - 0.922 0.117 - 0.911 0.123 - 0.9 0.13 - 0.889 0.135 - 0.878 0.14 - 0.867 0.145 - 0.856 0.149 - 0.844 0.153 - 0.833 0.157 - 0.822 0.16 - 0.811 0.163 - 0.8 0.166 - 0.789 0.169 - 0.778 0.171 - 0.767 0.173 - 0.756 0.175 - 0.744 0.177 - 0.733 0.178 - 0.722 0.18 - 0.711 0.181 - 0.7 0.182 - 0.689 0.183 - 0.678 0.183 - 0.667 0.184 - 0.656 0.184 - 0.644 0.184 - 0.633 0.185 - 0.622 0.184 - 0.611 0.184 - 0.6 0.184 - 0.589 0.183 - 0.578 0.183 - 0.567 0.182 - 0.556 0.181 - 0.544 0.18 - 0.533 0.179 - 0.522 0.178 - 0.511 0.177 - 0.5 0.175 - 0.489 0.174 - 0.478 0.172 - 0.467 0.17 - 0.456 0.169 - 0.444 0.167 - 0.433 0.165 - 0.422 0.162 - 0.411 0.16 - 0.4 0.158 - 0.389 0.155 - 0.378 0.153 - 0.367 0.15 - 0.356 0.147 - 0.344 0.144 - 0.333 0.141 - 0.322 0.138 - 0.311 0.135 - 0.3 0.131 - 0.289 0.128 - 0.278 0.124 - 0.267 0.121 - 0.256 0.117 - 0.244 0.113 - 0.233 0.109 - 0.222 0.105 - 0.211 0.101 - 0.2 0.096 - 0.189 0.092 - 0.178 0.087 - 0.167 0.083 - 0.156 0.078 - 0.144 0.073 - 0.133 0.068 - 0.122 0.063 - 0.111 0.058 - 0.1 0.053 - 0.089 0.047 - 0.078 0.042 - 0.067 0.036 - 0.056 0.031 - 0.044 0.025 - 0.033 0.019 - 0.022 0.013 - 0.011 0.006 - 1802 mat :

f3 00 0.006 - 0.004 - 0.012 - 0.007 - 0.019 - 0.011 - 0.025 - 0.015 - 0.031 - 0.019 - 0.038 - 0.022 - 0.044 - 0.026 - 0.05 - 0.03 - 0.056 - 0.034 - 0.062 - 0.038 - 0.069 - 0.042 - 0.075 - 0.046 - 0.081 - 0.05 - 0.088 - 0.055 - 0.094 - 0.059 - 0.1 - 0.063 - 0.106 - 0.067 - 0.112 - 0.072 - 0.119 - 0.076 - 0.125 - 0.081 - 0.131 - 0.085 - 0.138 - 0.09 - 0.144 - 0.094 - 0.15 - 0.099 - 0.156 - 0.104 - 0.162 - 0.109 - 0.169 - 0.113 - 0.175 - 0.118 - 0.181 - 0.123 - 0.188 - 0.128 - 0.194 - 0.133 - 0.2 - 0.138 - 0.206 - 0.144 - 0.212 - 0.149 - 0.219 - 0.154 - 0.225 - 0.16 - 0.231 - 0.165 - 0.238 - 0.17 - 0.244 - 0.176 - 0.25 - 0.182 - 0.256 - 0.187 - 0.262 - 0.193 - 0.269 - 0.199 - 0.275 - 0.205 - 0.281 - 0.211 - 0.288 - 0.217 - 0.294 - 0.223 - 0.3 - 0.229 - 0.306 - 0.236 - 0.312 - 0.242 - 0.319 - 0.249 - 0.325 - 0.255 - 0.331 - 0.262 - 0.338 - 0.269 - 0.344 - 0.276 - 0.35 - 0.283 - 0.356 - 0.29 - 0.362 - 0.297 - 0.369 - 0.304 - 0.375 - 0.312 - 0.381 - 0.319 - 0.388 - 0.327 - 0.394 - 0.335 - 0.4 - 0.343 - 0.406 - 0.351 - 0.412 - 0.359 - 0.419 - 0.368 - 0.425 - 0.376 - 0.431 - 0.385 - 0.438 - 0.394 - 0.444 - 0.404 - 0.45 - 0.413 - 0.456 - 0.423 - 0.462 - 0.433 - 0.469 - 0.443 - 0.475 - 0.454 - 0.481 - 0.465 - 0.488 - 0.476 - 0.494 - 0.488 - 0.5 - 0.5 - 0.506 - 0.513 - 0.512 - 0.526 - 0.519 - 0.54 - 0.525 - 0.555 - 0.531 - 0.572 - 0.538 - 0.589 - 0.544 - 0.609 - 0.55 - 0.632 - 0.556 - 0.661 - 0.556 - 0.783 - 0.55 - 0.803 - 0.544 - 0.818 - 0.538 - 0.829 - 0.531 - 0.838 - 0.525 - 0.846 - 0.519 - 0.852 - 0.512 - 0.857 - 0.506 - 0.862 - 0.5 - 0.866 - 0.494 - 0.869 - 0.488 - 0.872 - 0.481 - 0.874 - 0.475 - 0.876 - 0.469 - 0.878 - 0.462 - 0.879 - 0.456 - 0.88 - 0.45 - 0.88 - 0.444 - 0.88 - 0.438 - 0.88 - 0.431 - 0.879 - 0.425 - 0.879 - 0.419 - 0.878 - 0.412 - 0.876 - 0.406 - 0.875 - 0.4 - 0.873 - 0.394 - 0.871 - 0.388 - 0.869 - 0.381 - 0.867 - 0.375 - 0.864 - 0.369 - 0.861 - 0.362 - 0.858 - 0.356 - 0.855 - 0.35 - 0.852 - 0.344 - 0.848 - 0.338 - 0.844 - 0.331 - 0.84 - 0.325 - 0.836 - 0.319 - 0.831 - 0.312 - 0.827 - 0.306 - 0.822 - 0.3 - 0.817 - 0.294 - 0.812 - 0.288 - 0.806 - 0.281 - 0.801 - 0.275 - 0.795 - 0.269 - 0.789 - 0.262 - 0.783 - 0.256 - 0.776 - 0.25 - 0.769 - 0.244 - 0.763 - 0.238 - 0.755 - 0.231 - 0.748 - 0.225 - 0.74 - 0.219 - 0.733 - 0.212 - 0.725 - 0.206 - 0.716 - 0.2 - 0.708 - 0.194 - 0.699 - 0.188 - 0.69 - 0.181 - 0.68 - 0.175 - 0.671 - 0.169 - 0.661 - 0.162 - 0.65 - 0.156 - 0.64 - 0.15 - 0.629 - 0.144 - 0.617 - 0.138 - 0.605 - 0.131 - 0.593 - 0.125 - 0.581 - 0.119 - 0.568 - 0.112 - 0.554 - 0.106 - 0.54 - 0.1 - 0.525 - 0.094 - 0.51 - 0.088 - 0.494 - 0.081 - 0.477 - 0.075 - 0.46 - 0.069 - 0.442 - 0.062 - 0.422 - 0.056 - 0.402 - 0.05 - 0.38 - 0.044 - 0.356 - 0.038 - 0.33 - 0.031 - 0.302 - 0.025 - 0.271 - 0.019 - 0.235 - 0.012 - 0.193 - 0.006 - 0.137 - 001802 mat :

svg 1 :

Eol system in there

x c svg 2^x 2^- sqrt ± : θ π 5 / - : 12 mat Eol f1 f2 f3 stack : θ rot θ cos θ sin - θ sin θ cos 22 mat : 31 sys

Smath 2D vector rotation system t Eol Eol θ π 30 / t * + rot * eval :

Hub 00.15 red 15 mat : step1 060 range : 21 line

svg Eol * x c 2 1 sys

Eol svg t Eol * x c Hub 31 sys :

Smath "Wind Mill" project

Eol

Trunion valve . . . symbol

]]>

svg 0.75 :

valve svg 1 - 0.5 1 0.5 - 1 0.5 1 - 0.5 - 1 - 0.5 000 0.5 0.5 0.5 82 mat * :

valve 0 0 . 20 red 1 5 mat 2 1 sys

Control valve . . . symbol

]]>

Globe valve 15 range 12 range el : globe Globe 1 col Globe 2 col 1 - augment : 21 sys

DeCasteljau

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 :

data n Decimate collect every 'n' pairs range 1 data rows n range : k 1 : i range u k el data i 1 el : v k el data i 2 el : k k 1 + : 31 line for u v augment 31 line 31 line :

svg svg : NDP 40 : 12 mat

actuator 0001 - 22 mat svg 0 0.25 - 0.5 0.25 - 0.5 0.75 - 0 0.75 - 0 0.25 - 52 mat * 21 sys :

p svg 1 - 0100023 mat 1 - 0101023 mat 12 mat transpose * :

diaphragm NDP p 1 el DeCasteljauNDP :

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

local 1.25 :

diaphragm actuator globe 3 1 sys local diaphragm actuator globe 3 1 sys *

plot argument local diaphragm actuator globe 31 sys *

'local' size factor to accomodate graphic 36" valve vs 4"

The red actuator is savant.It is delivereed by the valve manufacturer. In itself, it is a "servomechanism" ... It receives the 4-20 mA signal from the controller. Converts in diaphragm pneumatic 3-15 psi Via a mechanical Laplace servo, it auto-stabilizes on the input governing signal [4-20 mA]. This advanced technology dates back years 1940 and earlier.

Pump . . . process control symbol

]]>

svg 0.75 :

Circle definition t u D u 2 el u 1 el - 21 mat :

out svg 01 1.25 1 1.25 0.51 0.861 0.51 42 mat * :

t0 0 : t1 2 π * : N 200 : 31 line

unary radius
clockwise IC 0121 mat :

Either 'rkfixed' or 'Rkadapt' s IC t0 t1 N t u D rkfixed :

base 0.861 svg * - 0.51 svg * - svg - svg - svg svg - 0.861 svg * 0.51 svg * - 42 mat :

x s 1 col : X s 2 col : Y s 3 col : 13 mat C svg X Y augment (* : 21 mat

C out base 3 1 sys

pump C out base stack :

The line can be removed ... through reverse circulation

pump C out stack base 2 1 sys

Partially filled tank . . . process physics

]]>

x Clear 1

U 0 :

1. Prepare the project

1 Random earliest Smath 6179 ≡ 1 random latest Smath 6179 ≡ 21 line

Density of random
Unnary circle N 500 : r 1 : 21 sys

2. Construct the project

h 0.5 :

level 0 h ≤ (h 2 ≤ (& (≡

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

xmax 1 : xmin 1 - : 21 line

ymax 1 - h + (: ymin 1 - : 21 line

space_x xmax xmin - (: space_y ymax ymin - (: 21 line

x y1 x 1 + (2 r * x 1 + (- (* sqrt : x y2 x y1 - : 21 line

A function that tests an arbitrary point 
for its membership in the critical region. x y Test y x y1 + 0 ≥ (y x y1 - 0 ≤ (* :

t0 1 time :

A routine that finds an array of N random 
pairs in the critical region. Pts the routine is a compressor it maintains density 'N' within the variable region i 1 N range x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 1 x y Test - x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 21 line while P i 1 el x : P i 2 el y : 51 line for P 51 line :

a b c spec . 6 #A0A0A0 13 mat :

pts Pts a b c spec pts :

u f 0 u * 1 - h + (+ (:

1 time t0 - 7 s *

Mesh the datum level U x 11 - h + (2^- sqrt : u x - x 0.95 x * - range : i 1 u rows range datum i el u i el f : idx i el u i el : 21 line for idx datum augment 41 line :

3. View the project

plot x y1 x y2 pts λ 41 sys :

a b c spec . 8 black 13 mat :

4. Technical end use

λ U a b c spec pts :

The project runs on the UnitCircle ...

Partially filled

plot

level 0 h ≤ (h 2 ≤ (& (≡

... it must be converted wrt XTR [level transmitter 0..100%] and the C(x) function [0 .. 1]

Technical 'h'

h 0.5 h * :

x C 1 π / 12 x * - acos 12 x * - (4 x * 2 x * (2^- sqrt * - (* :

x cπ 2 0.5 x * 0.5 + C * 1 - :

h C 0.196

cπ x 1 - 1 0.995 - range : i 1 x rows range c i el x i el cπ : for x c augment 31 line :

References: the C(x) formula is the one used to tabuulate 'C' ... 1. Chemical Engineer's Handbook ...[Perry, Chilton, Kirkpatrik] 2. TEMA [Tubular Exchanger Manufacturers Association]

Explain ...

Figure:: Partially filled

x y1 x y2 pts λ cπ 5 1 sys

To compute the area of the segment, "solving" is not an option. The C(x) is pretty old, accurate to 5 decimals. It is a factor to 'π' in formulas involving the measure of 'h', for instance: the sole possible measurement in partially filled pipe, horizontal tank, spherical tank as well as partially filled elliptical bassin ... In the "Figure", we have superposed this curve over the partially filled circle. For experimental 'h', the area of the segment will be: C(h)*π*(D^2)/4. Observe that in the figure, the graph of C(x) has been shifted left/down to ease the pictorial understanding of the project.

Recast the C(x) function x Cπ 1 - x ≤ (x 1 ≤ (& x C invalid if :

C(x) graph and Cπ coefficient

x Cπ 0 h h Cπ + 20 red 1 5 mat 3 1 sys

h h Cπ 21 mat 0.25 0.196 21 mat

Plot arguments Figure x y1 x y2 pts λ cπ 51 sys ≡

jmGiraud: 2015_12_29

Visual relative content of 5 tanks

UnestH(data)... zoom(M,a,b)

data UnestH v data 1 el : j 2 data cols range v v data j el augment : for v 31 line :

M Low High Scale High Low - (M M Min - M Max M Min - / (* Low + :

Implicit 'zoom fractional' Up/Down M a b zoom a b ≡ (a b | (1 ≠ (& (=> ≡ => implicit conditions ≡ i 1 M rows a * (range j 1 M cols b * (range N i j el M i a / Ceil j b / Ceil el : a 1 ≥ N i j el M i a / Floor j b / Floor el : cases for for N 41 line :

v1 012345678910111 mat transpose : v2 00012345678111 mat transpose : v3 00000123456111 mat transpose : v4 00000001234111 mat transpose : v5 00123456789111 mat transpose : 51 sys

Address the  Matrix Level M v1 transpose v2 transpose v3 transpose v4 transpose v5 transpose 51 mat transpose :

U M UnestH :

U U 0100 Scale :

image U 2020 zoom :

level 2.55 image * :

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Tank1 is full ...
Tank4 is NOT full U 000001000002000010301000204020003050301004060402005070503010608060402070907050308010080604090115 mat

Horizontal tank . . . process control symbol

]]> B-Companion adapted/compacted from Davide original

ndp p SVG t-> interpolation points [0,1] ... p-> control points t p DeCasteljau 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 21 line : t-> range of interpolation points [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 discretised points [>1] ... p-> control points 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 91 line :

pilot the thank svg 1 :

NDP 10 :

cap svg 020 - 00255023 mat 1001201005025023 mat 12 mat transpose * :

cyl svg 0000505023 mat 1001001005050023 mat 10000022 mat 13 mat transpose * :

b1 NDP cap 1 el SVG : i 2 cap length range b1 b1 NDP cap i el SVG stack : for 21 line

L cyl 2 el 1 el : ID cyl 2 el 2 el : V π 4 / ID 2^* L * : 31 sys 10050 1.9635 105^* 31 sys

b2 NDP cyl 1 el SVG : i 2 cyl length range b2 b2 NDP cyl i el SVG stack : for 21 line

cyl 1 el 0005005032 mat

2 cyl length range 2321 mat

truncate left of decimal Number part Trunc part Number part / 0 round * :

V V 10 Trunc :

m³ 1 :

Volume of the caps are subject to Pressurized Vessel Standards ... Typical: TEMA [Tubular Exchanger Manufacturers Association

svg 1

b1 b2 2 1 sys

V m³ 2105^*

ID 50

L 100

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

Pie chart helper

Radial Stem

--------
radius circle
-------- Y0 01031 mat :

t0 0 : t1 2 π * : N 360 : 31 line

Rename: Y => .. else variable name t u D u 2 el u 3 el 1 u 1 el (2^- (* u 2 el * (u 1 el - 031 mat :

Either 'rkfixed' or 'Rkadapt' s Y0 t0 t1 N t u D dn_GearsBDF :

X s 2 col : Y s 3 col : 12 mat circ X Y augment : 21 mat

Core component of the stem style P v replicate k 1 : i 1 v length range P i el 1 ≡ continue j 1 P i el range T k j + el v i el : for k k P i el + : 21 line if for T 31 line :

Stem construction vy stem N vy length : i 1 N range q i el 3 : q N el 2 : 21 line for 11 line i 1 N range v i el i : for i 1 N range S 3 i * el vy i el : for u q v replicate : V u S augment : V V 3 V rows 12 submatrix : 71 line :

i j pie circ i j range 12 range el :

i j p i j pie 1 col stem 2 col i j pie 2 col stem 2 col augment :

V 2014301512961 mat perc : 0.2 0.14 0.3 0.15 0.12 0.09 61 mat

0. Within the 6 quadrants ... update quadrants respecting 'Unary Σ' 1. Add/delete in 'V' within unary. ...Update conformal mapping ▼ .

sanity'Unary' V sum (100 * 100

x y axes x y / - :

Conformal mapping

cumulative unary v V : i 2 V length range v i el v i 1 - el v i el + : for 21 line

v 0.2 0.34 0.64 0.79 0.91 161 mat

angular convert U v 360 * Floor : 7212223028432736061 mat

pie chart suite ... u Ω°1 1 U 1 el 12 mat : i 1 U rows 1 - (range Ω° i 1 + el U i el U i 1 + el 12 mat : for Ω° 1 el Ω°1 : data Ω° : v data 1 el : j 2 data rows range v v data j el stack : for v 31 line 51 line :

conformal mapping pie u 11 el u 12 el p u 21 el u 22 el p u 31 el u 32 el p u 41 el u 42 el p u 51 el u 52 el p u 61 el u 62 el p 61 sys :

u 1727212212223023028428432732736062 mat

pie axes 2 1 sys

% 0.01 :

° 1 :

V % 2014301512961 mat

cumulative ° U v 360 * Floor : ° 7212223028432736061 mat

These two Graphic Packages are oriented for Control Room Operators. Construct a PID [Process Instrumentation Diagram] c/w live data. Otherwise meaning: PID mode = Proportional Integral Derivative. Graphic Packages for Control Room Operators dates back early 1980. 1982, I experimented Fisher Control near Des Moines [Iowa].

jmG: 20230122