<p> plotG(vx,vy,char,size,color) ... UnestH(data) </p>

ebb37a17-0239-4da0-8ad6-6d5af15c8960 15 4 5 decimal

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

Partially filled tank . . . process physics

]]>

x Clear 1

U 0 :

Filling the segment project

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

1. Prepare the project

2. Construct the project

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

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 :

h 0.5 :

level 0 h ≤ (h 2 ≤ (& (≡

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' in: 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

<p> plotG(vx,vy,char,size,color) ... UnestH(data) </p>

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 :

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 - 106 -^+ / (* Low + :

The infinite vector circulation

Range 'n' ∞ - n ≤ (n ∞ ≤ (&

User scale xs 1 : ys 1 : 12 mat

v 012345678910111 mat transpose :

n v rotate N v length : p n N mod : p p p 0 ≥ p N + p 0 < ignored cases : Ω v : p 0 ≡ i 1 p range Ω i N + p - el v i el : for i p 1 + (N range Ω i p - el v i el : for 21 line cases Ω 51 line :

n 17 - :

<= Pilot the rotation

v transpose n v rotate transpose 21 mat 012345678910111 mat 567891001234111 mat 21 mat

Vrot n v rotate :

XY xs v * ys Vrot * augment :

rot xs v * ys Vrot * . 10 black plotG :

C 55 + 200 black 15 mat :

Reversible rotation of vector. You can shrink/expand either direction via [xs, ys]. Illustrative plot wrt 'n'.

x n v rotate x 1 + el rot C 4 1 sys

Typical Matrix Scheduler M v transpose 19 - v rotate transpose 0 v rotate transpose 1 v rotate transpose 7 v rotate transpose 51 mat transpose : 012345678910111 mat 345678910012111 mat 012345678910111 mat 123456789100111 mat 789100123456111 mat 15 mat

The "rotated" XY 051627384951060718293104112 mat

U M UnestH : Schedule day Pet Jos Art Leslie 15 mat : Assign Schedule U stack : 31 line

A possible application:

Assume you are looking at aspecific star, you need several

parameters [Azimut, Horizon, Focus ...]. If the vector 'v' is

wrt parameters, easy to address and automate the system.

]]>

Assign day Pet Jos Art Leslie 030171412825239363410474505856169672710783808949191051021006125 mat

'R' is subscripted to explode  100*Random(1) v transpose R 1001 Random 1 el * Floor : R v rotate transpose 31 mat 012345678910111 mat 27567891001234111 mat 31 mat

U U 0255 Scale :

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 :

image U 1010 zoom :

U 0 76.5 0 25.5 178.5 25.5 102 25.5 5120451 127.5 51 76.5 229.5 76.5 153 76.5 102255102 178.5 102 127.5 0 127.5 204 127.5 153 25.5 153 229.5 153 178.5 51 178.5 255 178.5 204 76.5 2040204 229.5 102 229.5 25.5 229.5 255 127.5 255512550153115 mat

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 image