c823b4be-8d69-40b9-8bac-954724a0bfa8 38 4 5 decimal

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Part 1: Rings of ≡ area in unary system

t0 1 time :

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

D:=1 unary D≠1 'user' System is auto-refresh ▼ plot wrt either D/N

'N even' increase4smaller ring area. D 1 : N 12 : 12 mat

4 appVersion 0.98.6179.21440 ≡

Ø i 1 N 2 / range vu i 1 + el D 2 / D N 2 i * - 4 N * / sqrt * - : for j N 2 / 1 + (N range vy j N 2 / - el D 2 / D 2 j * N - 4 N * / sqrt * + : for vu vy stack D 2 / - 31 line :

Ø Ø eval :

i N 2 / 1 + (Ø rows range area i N 2 / - 1 - el π Ø i el 2^Ø i 1 - el 2^- (* : for

Ø 0.5 - 0.4564 - 0.4082 - 0.3536 - 0.2887 - 0.2041 - 0 0.2041 0.2887 0.3536 0.4082 0.4564 0.5 131 mat

area 0.1309 0.1309 0.1309 0.1309 0.1309 0.1309 61 mat

center circle [Ø ,area] Ø N 2 / 2 + el π Ø N 2 / 2 + el (2^* 21 mat 0.2041 0.1309 21 mat

idx 1 Ø rows range : Cheb Ø 3 round vectorize 0 idx * augment : 21 sys

Composed
manually Cheb transpose 0.5 - 0.456 - 0.408 - 0.354 - 0.289 - 0.204 - 0 0.204 0.289 0.354 0.408 0.456 0.5 0000000000000213 mat

t Y D A Y 1 el Y 2 el 21 mat * :

A 022 - 022 mat :

Centroids Cheb . 14 black plot :

'Npts' governs
the sub 'D'
blue circle Npts 200 : span 1 Npts π * / : 12 mat α π : (overlap ≡ 21 sys

t Y D 2 Y 2 el * 2 Y 1 el * - 21 mat

'Circle-in-blue' J 4 :

support Ø N 2 / 1 + (Ø rows range 11 range el :

support support 3 round vectorize :

start J 1 Npts + (* : end start Npts + : radius support J 1 + el : 31 sys

support transpose 0 0.204 0.289 0.354 0.408 0.456 0.5 17 mat

Circles U 00013 mat : p support transpose W p span 21 mat : ODE W 0 α Npts t Y D dn_GearsBDF : U U ODE stack : 31 line for B U 3 col U 2 col augment : 31 line :

out-circle D Circles start end range 12 range el :

Centroids of 'n ... rings' of ≡ Area.

D Circles Centroids 3 1 sys

Each ring has ≡ Area to central circle

1 time t0 - 9 s *

radius 0.408

Part 2: Annubar centroids disposition

'N' even ... increase for smaller centroid-ring area D 1 : N 24 : 12 mat

x_D i 1 N 2 / range su i 1 + el D 2 / D N 2 i * - 4 N * / sqrt * - : for j N 2 / 1 + (N range sv j N 2 / - el D 2 / D 2 j * N - 4 N * / sqrt * + : for su sv stack 31 line :

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 :

x_D x_D eval : j 1 x_D rows range : XY j x_D augment : sub XY 2 XY rows range 12 range el : 41 sys

sanity ASHREA source sanity sub 3 Decimate : 2 0.0213 4 0.067 6 0.1181 8 0.1773 10 0.25 12 0.3557 14 0.6443 16 0.75 18 0.8227 20 0.8819 22 0.933 24 0.9787 122 mat

sub 2 0.021 3 0.044 4 0.067 5 0.092 6 0.118 7 0.146 8 0.177 9 0.211 10 0.25 11 0.296 12 0.356 13 0.5 14 0.644 15 0.704 16 0.75 17 0.789 18 0.823 19 0.854 20 0.882 21 0.908 22 0.933 23 0.956 24 0.979 251242 mat

Annubar is a Pitot tube transversal to pipe ID.

The dynamic holes are distributed on the centroid principle.

Annubar is an insertion flow measuring device [dirty fluids].

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Part 3: parametric μ rings

. . . solve μ for user ring area . . .

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parametric  Ø μ 0.5 :

ω n rnd ω n round :

v 8765432181 mat :

μ v * 4 3.5 3 2.5 2 1.5 1 0.5 81 mat

Acircle π 4 / μ v * sqrt (2^* vectorize 9 rnd vectorize : 3.1416 2.7489 2.3562 1.9635 1.5708 1.1781 0.7854 0.3927 81 mat

each ring has  ≡ area as center circle. N v rows : Acenter Acircle 1 el Acircle 2 el - : i 2 N range Aring 1 el Acenter : Aring i el Acircle i 1 - el Acircle i el - : 21 line for 31 line

rings area Aring 0.3927 0.3927 0.3927 0.3927 0.3927 0.3927 0.3927 0.3927 81 mat

solving for user ring area U 0.5 :

μU π 4 / μ sqrt (2^* U ≡ μ 02 solve : 0.6366

solving for user ring area U 1 :

μU π 4 / μ sqrt (2^* U ≡ μ 02 solve : 1.2732

Part 3: else pseudocentroid

has application in Greville PseudoInverse

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v 10987654321101 mat :

PseudoCentroid of a real vector (V) V Psctrd i 1 V rows range W i el V i el V i el i i V rows sum * : for W W sum V rows / 12 mat 21 line :

v Psctrd 55040528819612675401861101 mat 170.5 12 mat

psdV v Psctrd 1 col 1 el eval :

uv 1 psdV rows range psdV augment :

uv uv o 5 red plot 2 1 sys