b37c2fbd-9427-4717-a8ee-5c835556a085 8 4 5 decimal

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

Constants

Gravitational acceleration g 9.81 :

4 appVersion 0.98.6179.21440 ≡

Conditions

ρ.o 1.1839 :

P.o 101325 :

T.o 25 :

T.ok T.o :

Outside

T.d 0.03 :

T.i T.o T.d + :

T.ik T.i :

Inside

T.ok 25

T.ik 25.03

Geometry

H 100 :

Height of the chimney

H.h 50 :

Height of the hydrogen section

Δ.x 0.1 :

Width of section

R 0.25 :

Radius of chimney

Fabric

ρ.m 0.034 :

SL50 30 x 20, 34 g/m2 , breaking load 45 kg/5cm

STL 510, warp x fill 250 x 250, 195 g/m2 , breaking load 250 kg/5cm

F.b 45 Δ.x 0.05 / * :

Breaking force

F.b 90

Hydrogen

ρ.h 0.0818 :

Density at 25 C and 101325 Pa

Neutral pressure level

H.NPL H 2 / :

Edges

x y E.1 x 2^y 2^+ sqrt :

Length of lower part of section

x y E.2 x 2^H.NPL y - (2^+ sqrt :

Length of upper part of section

Areas

x y A.1 x y E.1 Δ.x * :

x y A.2 x y E.2 Δ.x * :

Moments of inertia

x y I.1 x y E.1 3^Δ.x * 12 / :

x y I.2 x y E.2 3^Δ.x * 12 / :

Angles

x y α x x y E.1 / asin :

x y β x x y E.2 / asin :

Pressure

h P ρ.o T.ik T.ok - T.ok / (* g * H.NPL h - (* :

Pressure difference

H.NPL 2 / P 0.3484

Forces

F.L H.h π * R 2^* ρ.o ρ.h - (* g * :

F.L 106.1426

Lifting force

F.W H.h H + (2 * π * R * π R 2^* 2 * + (ρ.m * g * :

F.W 78.7195

Weight

F.u F.L Δ.x 2 π * R * / * ρ.m Δ.x * H.NPL * g * - :

F.u 5.0896

Lifting force on section

F.e F.u :

F.e 5.0896

Elastic force on section

y F.w1 y Δ.x * ρ.m * g * :

H.NPL 2 / F.w1 0.8339

Weight of lower part of section

y F.w2 H.NPL y - (Δ.x * ρ.m * g * :

Weight of upper part of section

H.NPL 2 / F.w2 0.8339

x y F.p1 x y A.1 y 2 / P * :

Pressure at the lower part of section

0.1 1 F.p1 0.0693

x y F.p2 x y A.2 H.NPL y - (2 / y + P * :

Pressure at the lower part of section

0.1 1 F.p2 1.6731

Levers

x y L.Δp1 x y I.1 x y A.1 H.NPL x y α cos / x y E.1 2 / - (* / :

0.1 1 L.Δp1 0.0017

x y L.Δp2 x y I.2 x y A.2 x y E.2 2 / * / :

0.1 1 L.Δp2 8.1667

x y L.p1 x y E.1 2 / x y L.Δp1 - :

Pressure lever, lower section

x y L.p2 x y E.2 2 / x y L.Δp2 + :

Pressure lever, upper section

Torques

x y T.w1 y F.w1 x y α sin * x y E.1 2 / * :

Torque of the weight, the lower section

x y T.w2 y F.w2 x y β sin * x y E.2 2 / * :

Torque of the weight, the upper section

0.1 m * 20 m * T.w1 0.0334 m 2^*

0.1 20 T.w2 0.05

x y T.p1 x y F.p1 x y L.p1 * :

Torque of the pressure, lower section

x y T.p2 x y F.p2 x y L.p2 * :

Torque of the pressure, upper section

0.1 20 T.p1 10.2206

0.1 20 T.p2 12.5433

x y T.u F.u x y α x y β + sin * x y E.1 * :

Torque of the pulling force

x y T.e F.e x y α x y β + sin * x y E.2 * :

Torque of the elastic force

0.1 20 T.u 0.8483

0.1 20 T.e 1.2724

Equations

x y T.1 x y T.w1 x y T.p1 + x y T.u - :

x y T.1 479003906251700000 y * x * 100 x 2^y 2^+ sqrt x - x 2^y 2^+ sqrt + (x x 2^y 2^+ sqrt + (* x 2^y 2^+ sqrt 2^/ sqrt * - (* 11839100 y - (* 3 x 2^y 2^+ (* 100 x 2^y 2^+ sqrt x - x 2^y 2^+ sqrt + (x x 2^y 2^+ sqrt + (* x 2^y 2^+ sqrt 2^/ sqrt * - (* x 2^y 2^+ sqrt 3^x - x 2^y 2^+ sqrt + (x x 2^y 2^+ sqrt + (* x 2^y 2^+ sqrt 2^/ sqrt * - (* + (* 24851321411132800000 x x 2^y 2^+ sqrt / asin x x 2^50 y - (2^+ sqrt / asin + sin * x 2^y 2^+ sqrt * 100 x 2^y 2^+ sqrt x - x 2^y 2^+ sqrt + (x x 2^y 2^+ sqrt + (* x 2^y 2^+ sqrt 2^/ sqrt * - (* - 4882812500000000000100 x 2^y 2^+ sqrt x 2^y 2^+ sqrt x - (x 2^y 2^+ sqrt x + (* x 2^y 2^+ sqrt 2^/ sqrt * - (* /

x y T.2 x y T.p2 x y T.w2 - x y T.e - :

0.1 19 T.1 8.6026

0.057 25 T.2 6.6549

y.s γ 19 T.1 0.0017 - ≡ γ solve : 1.1959

y.s1 γ 25 T.2 0.049 ≡ γ solve : 0.6812

γ Clear 1

ε 106 -^:

x y f 479003906251700000 y * x * 100 x 2^y 2^+ sqrt x - x 2^y 2^+ sqrt + (x x 2^y 2^+ sqrt + (* x 2^y 2^+ sqrt (2^ε + / sqrt * - (* 11839100 y - (* 3 x 2^y 2^+ (* 100 x 2^y 2^+ sqrt x - x 2^y 2^+ sqrt + (x x 2^y 2^+ sqrt + (* x 2^y 2^+ sqrt (2^ε + / sqrt * - (* x 2^y 2^+ sqrt (3^x - x 2^y 2^+ sqrt + (x x 2^y 2^+ sqrt + (* x 2^y 2^+ sqrt (2^ε + / sqrt * - (* + (* 24851321411132800000 x x 2^y 2^+ sqrt / asin x x 2^50 y - (2^+ sqrt / asin + sin * x 2^y 2^+ sqrt * 100 x 2^y 2^+ sqrt x - x 2^y 2^+ sqrt + (x x 2^y 2^+ sqrt + (* x 2^y 2^+ sqrt (2^ε + / sqrt * - (* - 4882812500000000000100 x 2^y 2^+ sqrt x 2^y 2^+ sqrt x - (x 2^y 2^+ sqrt x + (* x 2^y 2^+ sqrt (2^ε + / sqrt * - (* / :

x y axes x y / - :

f axes 2 1 sys

u 7.5 :

x green user x y f y 75 - 0 solve : x user 12 mat 21 line :

pair wise u green 7.5 69.553335 - 38.776305 - 21 mat 12 mat

u 1 :

x red user x y f y 75 - 50 solve : x user 12 mat 21 line :

pair wise u red 1 74.467461 - 12.995641 - 16.306306 40.650111 41 mat 12 mat

u 0.5 :

x all user x y f y 75 - 75 solve : x user 12 mat 21 line :

pair wise u all 0.5 74.738582 - 9.037807 - 10.143447 45.608239 55.431047 70.314035 61 mat 12 mat

u 0.875 :

x specific user x y f y 2550 solve : x user 12 mat 21 line :

pair wise u specific 0.875 41.999743 12 mat