<p> Source </p>

96e25127-cbd2-4821-92e3-377995a9837d 10 4 5 decimal

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

Polygon Area/Perimeter

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 :

A method for finding the area of any polygon when the coordinates of its vertices are known

x 2064215 mat transpose :

y 0550015 mat transpose :

uv x y augment :

Area Polygon wrt vertices coordinates A 12 / x i el y i 1 + el * x i 1 + el y i el * - (i 1 x rows 1 - sum * abs :

a b c spec . 14 red 13 mat : XY uv a b c spec pts : 21 sys

Perimeter is calculated wrt each hypotenuse from the projections ... Inspect the plot.

uv XY 2 1 sys

Perimeter  Polygon wrt vertices coordinates P x i 1 + el x i el - (2^y i 1 + el y i el - (2^+ sqrt i 1 x rows 1 - sum :

Hydraulic radius r A P / :

A P 12 mat 20 18.77 12 mat

A P r 31 mat 20 18.77 1.066 31 mat

N 10000 : X 2 N 1 Random (* 1 - : Y 2 N 1 Random (* 1 - : 31 line

uv XY 2 1 sys

Fill the circle exclusive of the square Circle i 1 N range U i el X i el X i el (2^Y i el (2^+ r < 0 cases : V i el Y i el X i el (2^Y i el (2^+ r < 0 cases : 21 line for U V augment 21 line :

A P r 13 mat 20 18.77 1.066 13 mat

Monte Carlo 'Pi'

Circle 2 1 sys <p> Source </p>

from bottom pipe datum

r 1 : h 0.25 : 12 mat

θ 2 r h - r / acos * : A r 2^θ θ sin - (* 2 / : arc r θ * : Pwetted arc : Hr A Pwetted / : 51 line

Hr x f Hr 2^x 2^- sqrt ± :

θ ° 82.8192

Hr x f Hr Hr Hr Hr - 2 2 mat 2 1 sys

above datum

r 1 : d 0.25 : h 2 r * d - : 13 mat

θ 2 r h - r / acos * : A r 2^θ θ sin - (* 2 / : arc r θ * : 4.8377 = Flow π 2^r * A - : Pwetted 2 π * r * arc - : Hr Flow Pwetted / : 61 line

Hr x f Hr 2^x 2^- sqrt ± :

Hr x f Hr Hr Hr Hr - 2 2 mat 2 1 sys