Stem Style

89f432d4-4510-4286-bc73-c4978e47ce7e 28 3 5 decimal

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

Stem Style

Stem plot for QuickPlot unicolor data s i 1 data rows 1 - range vy i el data i el data i 1 + (1 el 1 el 012 mat stack : for V vy 1 el : j 2 data rows 1 - range V V vy j el stack : for V 41 line :

Prepare stem style data S stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for stem 31 line :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

Turbulent: Q1, Q2 L 1 - : H 1 : N 199 : 13 mat U L H N xd : 21 line

n 0.875 0.125 0.05 13 mat transpose : n x Profile x 1 + (x 1 - (* - (n^: 21 line

j Q i 1 U rows range vx i el U i el : vy i el n j el U i el Profile : 21 line for vx vy augment 21 line :

Q1 1 Q : laminar ≡ Q2 2 Q : mid turbulent ≡ Q3 3 Q : high turbulent ≡ 31 line

Stem style codes

Observe laminar => Q(1)
to capture N 29 stems
laminar Q1 captures N 199 L 1 - : H 1 : N 29 : 13 mat U L H N xd : laminar 1 Q : 31 line

Observe: laminar Q(1) collects N 29 stems laminar Q1 collects N 199 stems

What you see on the graph is purely suggestive.

laminar laminar 1 col 1 laminar 2 col * augment :

data laminar S : stem data s : 21 line

plot laminar Q2 Q3 stem 51 sys :

Flow profile: laminar, turbulent

plot

Description . . .

This project is typical of caracterising a throat-ejector of adjustable profile.

It is represented by three parameters, thus reproducible at will for lab testing.

The proposal is unsourced from other feasibilty study Consultant.

The profile is in fact a two paramaters mathematical formulation

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Venturi shape from "Orphan" Polygamma size 10 : shift 0.5 : X 2 : 13 mat n z Ψ 1 - (n 1 +^n! (* 1 z k + (shift + / (k 0 size sum * : x c 1 shift - x ≤ (x 2 ≤ (& cases : 31 line

Venturi nozzle of prescribed design

0 x Ψ x c * 1 x Ψ x c * X 5 X 5 - 2 2 mat 3 1 sys

datum 'Y' 00 Ψ 10 Ψ 21 sys 4.3617 - 4.3617 21 sys

datum 'throat' 0 X Ψ 1 X Ψ 21 sys 1.8620 - 1.8620 21 sys

R

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G

G 000000052543648410412414316418320322224525425425425425425425425425425425425425425525425425425425425425425425425425425425425425124222620919317716114312711195786145271700000001133151698910612614416418220122023925225425425425425425425425425425425425425425425425425425425425425425425425525425425425425425124323021419918316915213612210591750000000032037567291107125141161177196213231247254254254254254254254254254254254254254254254254254254254254254254254254254255254254254254254253247239226210197181168153138000000000825405873911061231391551721882052212372502542542542542542542542542542542542542542542542542552542542542542542542542542542542542542542542542542532482402292152020000000001122741587288103117133148163178193209224238250254254254254254254254254254254254254254254254254254255254254254254254254254254254254254255254254254254254253252000000000011327405568829711012413715116517919320822123524725325425425425425425425425425425425425425425425425425425425525425425425425425425425425425425425425525425400000000000111243649627488101113125138150163176189201214228239249253254254254254254254254254254254254254254254254254254254254254255254254254254254254254254254254000000000000171930415365768810011012213414415716817919120321422723624625025425425425425425425425425425425425425425425425425425425425425425425525425425425425400000000000000311223241526373839310411412413514415616517618619620621722823624524925225425425425425425425425425425425425425425425425425425425425425425425400000000000000013111928364756657383921021101201271371461561641741831932012102192292352432482502532542542542542542542542542542542542542542542542542540000000000000000002513202835445260687584919910711512313013814615516216917818619420120821722523223724324724925225425425425425425425425425425400000000000000000000024815202734404854606874818894100108114121127133140146155161167173179188195201207213219227231236241244246249251000000000000000000000000013581317222733384450556165717683889499103109115121126132136141146154160164170174179185193198000000000000000000000000000000012346913172023262934394348535760646871768287919499102106109115121000000000000000000000000000000000000000000124456689121418212325273031333638410000000000000000000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011334456677991100000000000000000000000000000000000013445791216182124272932353944495256586265687175800000000000000000000000000000134610151822263136404751566064697480869094991031071131201241281331371411461531580000000000000000000000024612162229354047535965717784909610110711312012613113614314915716216717317818619419820420921422022623100000000000000000001381521293643505765728087931011081151231301361441521601661721801891962032092162242302352412442472502522542542542542540000000000000000028162533415058677584921011091181261341431521601681771851952022102192282342402462492522542542542542542542542542542542542542542540000000000000003112130394960697888991071181261371461561651761851952042142242332402472502532542542542542542542542542542542542542542542542542542542542540000000000000192131425364748697107118129140150161173184194205216228236246250253254254254254254254254254254254254254254254254254254254254254254254254255254000000000000316283852647588101112124136148160172184196209221233244250254254254254254254254254254254254254254254254254254254254254254255254254254254254254254254000000000005193145597185991111251381511641771922052182312442502542542542542542542542542542542542542542542542542542542542552542542542542542542542542542542542542540000000000520334863779210612113615016417819320922323724925425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425425400000000031933506581971121291431601751912072222382502542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542542532502422340000000011430486582991151321491671832002172352492542542542542542542542542542542542542542542542552542542542542542542542542542542542542542542542542532482392272121991851720000000072643628099116134152171188208225244253254254254254254254254254254254254254254254255254254254254254254254254254255254254254254254249241227211198182168153137123107000000021937587697114134153174193211232249254254254254254254254254254254254254254255254254254254254254254254254255254254254254254247236219203188172156139124108937659443364 mat :

B

B 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mat :

gray R G + B + 3 / :

gray Min 86

gray Max 167

gray rows gray cols 12 mat 336412 mat

M 0.19 0.59 0.35 0.82 0.71 0.61 0.27 0.59 0.12 0.03 2.66 4.21 0.45 0.23 5.48 5.20 44 mat :

Explode mirror Matrix M mirror v M M cols col : ct 1 : j M cols ct range N 1 ct el M j col : ct ct 1 + : 21 line for N Unest N v N 1 el : j 2 N cols range v v N j el augment : for v 81 line :

M mirror 0.82 0.35 0.59 0.19 0.59 0.27 0.61 0.71 4.21 2.66 0.03 0.12 5.2 5.48 0.23 0.45 44 mat

A rotate_90 A transpose :

A rotate90 A mirror transpose :

A inverse 255 A - :

Smath does not take submatrix reversed cols order, to mirror. Alternately, use mirror(M).

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gray inverse

data Strip2 nest striped in 'R' u data 1 col : v data 2 col : k 0 : i 1 data rows range u i el v i el * 0 ≠ strip k k 1 + : el u i el v i el 12 mat : 11 line Undefined if 11 line for 21 line Un-nest R v strip 1 el : j 2 strip rows range v v strip j el stack : for v 81 line :

The contour extractor , pair wise in X direction M ε cntr CONTR count 1 : i 1 M rows range j 1 M cols range M i j el cntr - abs ε ≤ u count el i : v count el j : 21 line count count 1 + : if for for u v augment 31 line :

ε 1 :

cntr 99 :

θ rot θ cos θ sin - θ sin θ cos 22 mat :

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 :

Q gray ε cntr CONTR :

Q rows 2042

θ π 2 / :

θ 1.5708

contour Q Strip2 :

Rot contour θ rot * 16.5 + :

contour rows 62

a b c spec . 8 black 13 mat :

Pts Rot a b c spec pts :

The Venturi image as captured by a digital RGB camera is symmetric, though it may not look so after the processing. Engineer will isolate the trace most relevant of the continuous path of the fluid. The search is done manually, much less difficult than one might think.

Select/collect a path

r 18 :

search Rot r 1 el Rot r 2 el augment :

search 27.5 7.5 12 mat

collect 359121820212325272931112 mat :

Selected contour for user to extract and fit NON-linear.

Pts 0 Rot r 1 el Rot r 2 el + 15 red 1 5 mat 3 1 sys

data ListCollect collects index list select collect : ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 51 line :

Venturi Pts ListCollect :

Venturi transpose 22.5 23.5 24.5 25.5 27.5 28.5 30.5 33.5 36.5 42.5 52.5 77.5 14.5 12.5 10.5 9.5 7.5 6.5 5.5 4.5 3.5 2.5 1.5 0.5 212 mat

XY 22.5 23.5 24.5 25.5 27.5 28.5 30.5 33.5 36.5 42.5 52.5 77.5 14.5 12.5 10.5 9.5 7.5 6.5 5.5 4.5 3.5 2.5 1.5 0.5 212 mat transpose :

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 :

vx XY 1 col :

vy XY 2 col :

Thiele 22.5 14.5 23.5 0.5 - 24.5 2.66 25.5 0.044 - 27.5 20.717 - 28.5 0.515 - 30.5 0.259 33.5 2.992 36.5 0.909 42.5 7.565 52.5 1.203 77.5 134.369 122 mat :

K Thiele 2 col :

vx vy 0 Thiele

X Thiele 1 col :

vx vy 0 Thiele 22.5 14.5 23.5 0.5 - 24.5 2.66 25.5 0.044 - 27.5 20.717 - 28.5 0.515 - 30.5 0.259 33.5 2.992 36.5 0.909 42.5 7.565 52.5 1.203 77.5 134.369 122 mat

vx vy 1 Thiele Activate to see Thiele table ≡

vx vy 0 Thiele Activate to see Thiele K ≡

CF(x)

Optimiz => Numeric x CF K 1 el x vx 1 el - K 2 el x vx 2 el - K 3 el x vx 3 el - K 4 el x vx 4 el - K 5 el x vx 5 el - K 6 el x vx 6 el - K 7 el x vx 7 el - K 8 el x vx 8 el - K 9 el x vx 9 el - K 10 el x vx 10 el + K 11 el x vx 11 el + K 12 el / + / + / + / + / + / + / + / + / + / + / + :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 21 line 31 line :

L vx 1 el :

H vx 12 el :

N 23 :

α 0 :

U L H N xd :

a b c spec + 10 blue 13 mat :

Ω XY a b c spec pts :

data i 1 U rows range u i el U i el : v i el U i el CF eval 1 * : 21 line for u v augment 31 line :

a b c spec . 10 black 13 mat :

Fit data a b c spec pts :

1rst run Thiele on 23 discrete samples. It suggests a 2nd Thiele run, RemToDo.

Fit 0 Ω 3 1 sys

Highlight by negative pixelation

Irfan

Irfan 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mat :

experiment around A = -1.75 xo = 127

iVBORw0KGgoAAAANSUhEUgAAAIAAAABBCAIAAACW6DuNAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABVuSURBVHhe7Zz1j13HEoQtRVEUWdELMyugKMzMnNhhZmZmZmZmZmZmZmamv+R9e2tSbvfMOWtFeY5ftP1DFK/v3jNTX1d1X8fZUZttttnWW2+9ww477LLLLnvuued+++138MEHH3744UcfffQJJ5xw6qmnnnnmmeedd97FF198+eWXX3PNNTfccMOtt95611133XfffQ899NDjjz/+zDPPvPjii6+++upbb731/vvvf/zxx1988cW33377448//vbbb7/++usPP/zw9ddff/755x999NG777775ptvvvLKK88///xTTz312GOPPfjgg/fcc8/tt99+8803X3fddVdfffWVV17Jsy677LJLLrmE51544YUXXHABZzj33HPPPvtsznPGGWecdtppnO3kk08+6aSTOOdxxx13zDHHHHXUUUcccQSHP+SQQ7jFgQceuP/++3OjffbZZ6+99tpjjz122223XXfddfvtt99qq6022WSTjTbaaL311ltjjTVWWWWV5Zdffskll1x00UUXXHDBeeedd84555x55pmnm266/wxqmmmmmXbaafnl9NNPP8MMM8w000z87iyzzDLrrLPONttss88+O6+fa6655p577nnmmYd/8ku+yO/yshlnnJHv4tt5n6mmmmr06NFTTjnlFFNMMfnkk0822WQFAGcSgH333ZdzH3bYYVzm+OOPP+WUU7jtOeecgwqXXnrpVVddhUY33XQTet19990PPPDAI4888uSTTz777LMvvfTSa6+99vbbb8Pgk08+qRl88803MADPe++9BwOAvfDCC8AD4cMPPwzOO++8E7QABjMPuuKKK2DAQ8Fw0UUXcYDzzz8fBl0YOG3CcOihh0KC6xxwwAFg4Gpg4I677747GHbaaadtt912yy23HDt27IYbbrjOOuusvvrqK6200rLLLrvEEkssssgiCyywAGr2k0BcfpcyiTnmmEMw+F6Kf+Er/Ba0wMa38L28iWEMAaAdALDzzjtzMpqF43L0I488kvtwMS7Jhbl8NMEtt9yCXvfeey/9++ijj9LLzz33HAxef/11GHzwwQcw+PLLL82A4l/4JWD4LSDxMoDxLcADISDBWVvBGHg6GLCCMNATPW449thjcTBXgATNBIaDDjpIhgBDMgTu32abbbbYYosxY8ZssMEGa6+99mqrrRZJRE+g+9RTT418/FMwTKLfFl0wMoC9994bAJyYo9NNTiHuLBMgyrXXXnvjjTfedtttMYiefvppUuXll19+44033nnnHTGwDzABDH766afvvvsOMJ9++umHH37Iy3gxcYQV+HZbgbflzXkED8IKTqQaA2UMp59+OkfFspA48cQTMQQY+g0BCQwRSRAGm2++uUjIEyuvvPJyyy2ndFpooYXmm28+dEREFFeqmES0hWHwSsq2qGEUANtttx2W5By0RhwDXIP7cLdoAnrz+uuvp08VRPfffz/CmQGCJgaEDxH0yy+//P777z///PP333/vkUAcMTlkBTyEk/ATrsJbTqQuDAolz4azzjpLGDBExJAMIRKaECZB2yUS8oTSad1119WcWGGFFZZeeunFF1984YUXjgGF6MkWTRjRGZRgFACk4Y477igAGgNKIY7ONZomUBDdcccd5IaGwRNPPBEZaB4Q+miN4uiO+jDQSHAcwQlamsyaCryPE4n35yn9GDyiySUwJEOQSyYhQ8Ro6iehOaGJvfHGG6+//vprrbWWAkq2WGyxxbDF/PPPj5R0dDOj+mEMAWAQCQCP1Bx2CtUm4M7cHy0URDSphkFiQBZpHsCATv/ss8+++uor8scjQXHEFzWZNRX4Fr5xQjDEEd3MJRmC8oSwJxxN9kRNQnNCEzvaQkNb69Oaa6656qqralo4owSDBpczNG8NgxIM8eA1ozbddFMB0CYKfLqAYaUU4pQ0jk1Ai3FPBxGjUsOgyUB7EQnD6knik/ukf4wjrKDJzNch5EQSBt6B9zEGhxJPjCO63xD9JOSJlE7A8MS2LQRDJFBJ00IZJRh2BuvsUksthTMUU0xvzQx6HysAI5mjAIAtb6o5rDGgFOJYHFEm4AJchrspiLg8GxHDgK00MdA80F7Eukm8aCQojmwFAGgqaEn1cI4Y7AbNBo9oJhCP1sLaNMSwJOp0oqItmjB6nOGY0vTWzFhmmWVYpZI5yB/P8HEAtAh5DCiFkgk4vYOI23LzJgPNZCYqKyaf0TwSUJY2R2VNZk0FJZKGM1/kt4xBoaTZwFvpgxtvzthXLkVDQCIaokmCEol6cYq20NDm4pCgNC16YMSZwTqjVSqao4fHEACsJAB8v8aAUojnRRPQLw4ibURctWaANAjEbkrPsuDTv44jWUGTmcxxIkUMdoNCiRdrROMk3iTmkgzBGsYyxoTQ2josCS9Omti1LSCRnCEYHt3RGZoZFDA0wCmbg7GaeOAPPmeIx4orrsjwKAB4ES/lGwi4mEI8SSagKfhMwPk4aBwGkYFmMo2JKEiDQDGOZAU6WlNBiSQMjIEaA1/UiNamxLcol3gT3kqG4M2bJOyJNCdqGLKFYMgWCYac4c934uGYSuZIPFJY0d90ufOKTxvsuAWANlGNgZhCjGKZgKcqiDgWzuW4nDsx0ExGAoQgqRVHsoIms6eCEilhUCixHTEb/vjjD41opgUrrHIpGgI/aUI0SSidMCVtIVskEhQn74KRYirODAoYXWOj9kfMKyEhryKSNgC48Wq+0ybgGTzMQZQYcB+uxz25LcsiE1JxlKyAUk4kYUhuQGjk1ohmU4qG6CJhT0BX6QRv5oQWJ/rAtkhDWzDEoyumqAgj8UhhZX8kJAOHtJHAYwgACQUAjwGnEC/SJBAD3rdmoHnA0bkGV+J6MFAc2QqaCk0MCiXPBpQlcIgdG0IkWJaaJMCmdMJP4NSciLYABhbk6RFGdEZXTPXzMJImj2GRRJcUAF6EGAPJBDGINAwiA80DjshZOTR34D62AlclCpxIEQPz2bOBMCFSYi5pWdLOyjBIJPgXpZPGteYEi5NsoVGRYCRnKKa0znJOwjOaY8J5pLxqIhEVBRfqiYqRjGIa6MMwAJjDSiHiSSbAJgqiOAzMgGfwMJ7NITgTh7MVuImmghLJGHCDQgktPBvQyIbQslSTiJ7QuNaciLZIMHgHYMDVAwPemA/2mhk2R+ShGc7ha390IRGVhGRYKkIyDgCLEGNAJiCFZAIHkYYB9pEPlEWA5R15X57B86IVnEjGgBsUSpoNXFsjOhoikbAnnE6aE8kWwNDnasMAlTYoxxSfKjwzMEfk4bCSP+gPuoRDclT6JlqkC4mpgMRUolGoLq8UAJrDSqFoAgWRNiIxcBbBgJgDIzBhYCvwsIRBbvBs0Iim42yISCJ6Qumkca05YVs0YQBAn64VUyxUyRzioU95Civ5A97OK54uiwiJNivOyWmjS+IUiVQEJlIRmOiVCCYD0C7kSaAgigyURdqLHEdYAWd5KnRh4KAcOhqii4TSid7UnLAtDMPOQE00dUyhdZNH9Ic+YQBPeQVOWwQkvHlEYpdwHj6HK7hsFFPRbJdX4ngfFswoPqFpE40pBAOtQzBgbzUDZREMtBdFKzQx4DvPBp7HCURCU1ok7ImYThEG1zYMOwN1gKGYQjWZo+aB0MQRoiN9zCsj4YvQAoldgrGaVJxdPJ0zyCs1GA+VGGLcsc4xsSkAtAjZBF6Hagbai7SbygpdGAglki4awiSiJ5xO0RY1DM9txVTNw2ND/kA45FNeCYkjCyTRJV1UPEvkFceXwfAUgYmOabJRlIlN9A14CgClkE2gdSgy0DzwXhStEDE4lDQbNKIjCXvC6WRbJBhyBkd0TCUe9odnOFmhvDISehaBkktqKs4ue6UJRkPFjolsbBptX9E3xmPrKNM0aTKAaIIuBtEKYEhu0GywIUTCnlA6aWXCFhEGyShnYEx4YNWaR/RHF5LkkkRFU91eSWCUYJrwKCvHmI1MAwbYgAQwrMI1HllHmZYI8f48KBpoHABSqIsB80B7URMDbvB8TiTsCadTgpGcoZiCh5Mq+kOTIyIhsuySmgqWb4Kh9ZxgTTYyjaMs4onWQVmNmUioNpAh8RUg8bu8hhfzLXAaAsAilExAEIkBWZSskDD0k+BzQ4IRnSEeiikhEQ/80YVELklUZBRGXAJju5BgkU0yDQHdxIN1akKKNRkoQaKvY77R8uaklPP4iajGAxBNYB/YCsYgEmBokhAMSBhGPw/7w0iwiIeHXWIqCq4eMGZDiU0XHlsnEmJI1gayh8yJEiehglNERQlVTSsBGwJAASAxSFYQBrtBoSQS9gTLUoTBuBaMyIOBIR4JCQWSRKULTGJDwSbhSYQoCBmSxkzyUOTURFXTipYysGQsMUv2EjYcNmrMmDE2QWRQYxAJhZJIdMEQD5mjRlJTqcFQgDEbO0Z4KOOJhGpIiZNtZFQ2U6IlSxlYk1nCZoeZXBc88RPCAiAxaGKIJCjZouaRkNRUZBSDoWBT49FESYQSJBlIFVElWtFPBpaYGRsVySV4TX4JoSlSEWST5TgAlBlQwkCZBCUYlHhQNRLKVCiBoczGeCgTMiTKnLpQUaZFCRhlZpSwUSZHCR4lflSNkDJFSiApszROykQTVAquXWgp0x0CEBlQYIgkVIXGoEASqVAFy6AKmUGBJxJSFUqDAlWkRRVcgxIzVSKnEj9VokgJpCriVBWkf1YBOyjoRsBUITwoMEfSVEH9Z4E8UqcK9kEV8oMCfwHgKhCqEhVVYdKqgqgqMVMVaFUVgK0qPKsSYFXB26pCuyrhVxX+VZVeaFVpjarUK6rSKa1S34wAKFX0rqqI3aqid1VF+0EVsVs1HoAi86CaKhchB1XrWHQaVNFmUE1pyu0HVV++XG5Q5UKDat5Hd1D9H0dQEX5kCP9ZE3sIJ/WT7lHxWm5rnVRO+iZlm7Ja06Rm0jEq+O9ZQ6P6tfTWval4lDtpHYWuJa71jeLWskZNa0GjmrWOUcRawShfLVyt2t/5QUztn9RP0qvZrXtTdLd2kjtpnYRWC0tld27qWeubxI3Kujf///4owu0f1R/kzcgfxk2sP4wzAKvvxlfgWPrY70l3RFdqS/QexZPcsamT1v1Cp/5tSlzr64adhP44um5/qZ8CJ0nfo3sS3T3uBk/d3SV3rbXaOQntRo4qpxZuSjyp/AeZ1P5JfQdOLb10J9aT7qnTk+jqcYeJFHd3I7cC2q1tuWNTJ62bQruRmypL4knoP0kKAOGj5OlSn9Gqrq9b3v1u3R3lqdMteurxWnF1NxnSJfe/5D/Kkz+p/aP6rDep8VPXI71bnpxxv1t3ml3x4mxpik6kxB5PihPWqbu5TJTbfa3ooNFqrR3Eauem0HzdjRxV5n1oYd4ztnCU+K//tZTY/gofcr9WPzZ+j/TKmdjv0t3NrjRnbLrTm6K7x5uKO0lidytDEMsBjYju6y6t1dG8nu+Ck9tZQruXeSIJ5kZOKnNaziyVuQV34UZIzO24IzflvnQbd6ftEIEibEf+amJD69jRPF2JkYTmtLGXuQs3ksrcManM9Sn6Dykoph2yUPTlyF/OnTT+cm7MH9pf4aOp6+RBffZ6q6/G15gl67XYJOk5GdLHlo85E3XXFJXuanbFizu9S3SnSuxxZbcVd4PHJIndbbnd2jFA6vSQ1gidtEZoa52ERhy6E5VoU+SiSAu6dhwA2l/Lj9vfO4+TB/UdO1py3PjOekmvrpf03IGbcB+3vCdq7Hfr7oRRsztekNWdjuj/kv9BwyuQ8sfpr/DRzmP16X2r78SPjc8ROTFHx57qekvPPbkt0seWRxHlTOz3qHtqdscLv1SnJ9EVLGpzp4oS3D2eFHeDW24r3pQ7tnZXXyetiQrJjXoU+YGSDFEkHfmf9Mbr8WEVT91dy43WFCoxIKU1mWG5kZEYp5uRFGGJlpH/TXWc6D2K9zT4sHIjoOUmTuhphKW5iXe6vA1A7R/Dh/flGTyMByf1uQNXUuLHxuf+GrPOejSy9E4bSe+WZ3Uh2ZXvypmm7o51NzuMtbEoXoi+2OmpzamhJh9fdCmeUiUqjtyUwgQ1kJvq6e4kNz2NsHyuImAQmUFL3hQArEBMYO0/yp/Y/jwDvDyYQ3Aa5X5SX7HDtbl8anxnvQIndT3Sk/L0uEarW17buvJdOaNwV783dXez0wo98dIUPbZ57HGKtuPuscd7GhzdKMtNlkS5CXminonL7jMm/qgCDwBep/xR+qv9earDR+pz9KQ+7abYUeKr8Zm0zhytN8r62PW19BqtvCC2vPKdt1LONHV3rPeLrniR6FQtOjd1sEhxt3nd41FxpIuK09C0Nc3NlB3b88M6vAKl/OExan+FD+fjoNiTO3Af7larr9ghgpX49KkaX5nDMq71hkhR4ETp+SVfVNrosxLfopZ31PBZlDcHMJiVM7Hfe3RvZjrxkjrdaS7RUVyiD7q8iJ5CHMVJFfd4UnyCflyNAGgAxPyJ7c/56BGOzk24Ejfktk31Y+wo8dX4yhxtlhqz+tQau97SK22U8nhIo1Utz3TR+sijOYBzpkd3x/qg1yfJH9ikCcwAAKbyh/Gb2j9GP41G02nqJvU1bx07SnxkRVxnjjZLjVmy3oETpY9po5WGp8SWT/k+gbqnZkf0mOlN0Z3mUhyV0Io2J7pjm//FH1mmj8EAILA0AJw/nInDqf1xq8OHC9N3BC5aoEhTfRRERzJE2z36uvGVOWw7/FJjFmfwMgVO7HpJr7Qh5VlweWhXyyvfBzFTcqZLd83S2OxcloZzpvd3ukX/e35oHwC0gwLAA0D5w/k4q9ufiyl8uL/2fURBGgRK6jv0NW+RmFVSia/G15JD3GvD0ZhV1g8rfX/L1/mecsa6K9mT7hqkMdNRBn0cL/+TH1vJAxgdPEwAOIryp25/hw/5SwqzfrCEMBI1daP6Cn301bx17GjYwgMqzhySirxiZjBmlfUOnH7pvdK45bW2a65adw3VmDP9uqvZlTAT6Qe3agXCbhzF+UO/sP8221/RzzxkKrJxWn0CJKlPp2veOnY8bHkZL1bj8+28CSA9ZnlEl/QpbeqVJkWNdedeKWeS7lpg2NAn9o8uNgDOxPmUP/QO/qWhYvuzeCh8FP10Kz1L52rnUe5LfYSW+gp9zVvFjhJfjc9+yccFZw6uwltxzDal14CV9E55TutPTG55RY3nqvO97nfp/g/88G6wA4DhrgnMQTk0jUMT0VDckNuq/elHpGHvVPgo+pEPEbXzKPdj7yO9Qp8g0rwldvTBSonvxnfmaLmMY9aBk7o+Sh9TvqvlPVed7xqq/9iPrx89+r9j0IlKr0+9KAAAAABJRU5ErkJggg== Irfan

Plug in your system READ_IMAGE

xo 127 :

A 1.75 - :

x f A x xo - (1^abs * :

fmap Irfan f vectorize Re :

fmap fmap :

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 fmap

Vena contracta

A yo xo α β x f 1 - yo + A 1 x xo - α / - exp - (* x xo - β / - exp * + (- :

A 1 : yo 0 : xo 0 : α 0.5 : β 1 : 15 mat

X A yo xo α β x f x diff x 01 solve : 0.549

x φ 0 x ≤ A yo xo α β x f Not computed if :

Vena contracta, imitate pressure recovery

x φ - 0.5 + x φ 0.5 - X 0.25 X 0.25 - 2 2 mat 3 1 sys