Ik kom op exact dezelfde oplossing als ukster. Hier de code en de tussenresultaten. Alpha is telkens de hoek in radialen.
Het is wel het meest uitgebreide raadsel dat ik hier al heb opgelost.
Bij 4 graden:
Code: Selecteer alles
from sympy import *
lwater, Fonderwater, Fbovenwater, hoogtewater, buitenopp, binnenopp, rhoAl, rhoWater, alpha, g = symbols('lwater, Fonderwater, Fbovenwater, hoogtewater, buitenopp, binnenopp, rhoAl, rhoWater, alpha, g')
eq1 = Eq(g, 9.81)
eq2 = Eq(buitenopp, 1.2*10**-4)
eq3 = Eq(binnenopp, 1*10**-4)
eq4 = Eq(rhoAl, 2700)
eq5 = Eq(rhoWater, 1000)
eq6 = Eq(hoogtewater, 0.6)
eq7 = Eq(lwater, hoogtewater/sin(alpha))
eq8 = Eq(Fonderwater, (buitenopp - binnenopp)*lwater*rhoAl*g - buitenopp*lwater*rhoWater*g )
eq9 = Eq(Fbovenwater, (buitenopp - binnenopp)*(1-lwater)*rhoAl*g )
eq10 = Eq(Fonderwater*lwater/2 + Fbovenwater*(lwater+(1-lwater)/2), 0)
solve([eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10], dict=True)
{Fbovenwater: 0.174379604879778,
Fonderwater: -0.434329371813604,
alpha: 1.10714871779409,
binnenopp: 0.000100000000000000,
buitenopp: 0.000120000000000000,
g: 9.81000000000000,
hoogtewater: 0.600000000000000,
lwater: 0.670820393249937,
rhoAl: 2700.00000000000,
rhoWater: 1000.00000000000},
{Fbovenwater: 0.174379604879778,
Fonderwater: -0.434329371813604,
alpha: 2.03444393579570,
binnenopp: 0.000100000000000000,
buitenopp: 0.000120000000000000,
g: 9.81000000000000,
hoogtewater: 0.600000000000000,
lwater: 0.670820393249937,
rhoAl: 2700.00000000000,
rhoWater: 1000.00000000000}
Bij 94 graden:
Code: Selecteer alles
g, linuitzettingAl, linuitzettingGlas, voluitzettingWater, rhoAl94, rhoWater94, buitenopp, binnenopp, buitenopp94, binnenopp94, hoogtewater, hoogtewater94, lwater94, lbuis, lbuis94,Fonderwater, Fbovenwater=symbols('g, linuitzettingAl, linuitzettingGlas, voluitzettingWater, rhoAl94, rhoWater94, buitenopp, binnenopp, buitenopp94, binnenopp94, hoogtewater, hoogtewater94, lwater94, lbuis, lbuis94,Fonderwater, Fbovenwater')
eq1 = Eq(g, 9.81)
eq2 = Eq(linuitzettingAl, 2.4*10**-5)
eq3 = Eq(linuitzettingGlas, 8*10**-6)
eq4 = Eq(voluitzettingWater, 4.4*10**-4)
eq5 = Eq(rhoAl94, 2700 /(1+3*linuitzettingAl*(94-4)))
eq6 = Eq(rhoWater94, 1000 /(1+voluitzettingWater*(94-4)))
eq7 = Eq(buitenopp, 1.2*10**-4)
eq8 = Eq(binnenopp, 1*10**-4)
eq9 = Eq(buitenopp94, buitenopp*(1+2*2.4*10**-5*(94-4)))
eq10 = Eq(binnenopp94, binnenopp*(1+2*2.4*10**-5*(94-4)))
eq11 = Eq(hoogtewater, 0.6)
eq12 = Eq(hoogtewater94, (1*0.6) * (1+voluitzettingWater*(94-4))/(1+2*linuitzettingGlas*(94-4)))
eq13 = Eq(lwater94, hoogtewater94/sin(alpha))
eq14 = Eq(lbuis, 1)
eq15 = Eq(lbuis94, lbuis*(1+linuitzettingAl*(94-4)))
eq16 = Eq(Fonderwater, (buitenopp94 - binnenopp94)*lwater94*rhoAl94*g - buitenopp94*lwater94*rhoWater94*g )
eq17 = Eq(Fbovenwater, (buitenopp94 - binnenopp94)*(lbuis94-lwater94)*rhoAl94*g )
eq18 = Eq(Fonderwater*lwater94/2 + Fbovenwater*(lwater94+(lbuis94-lwater94)/2), 0)
solve([eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10,eq11,eq12,eq13,eq14,eq15,eq16,eq17,eq18,eq19], dict=True)
{Fbovenwater: 0.168581612421343,
Fonderwater: -0.415852726616583,
alpha: 1.14723309638980,
binnenopp: 0.000100000000000000,
binnenopp94: 0.000100432000000000,
buitenopp: 0.000120000000000000,
buitenopp94: 0.000120518400000000,
g: 9.81000000000000,
hoogtewater: 0.600000000000000,
hoogtewater94: 0.622863077168877,
lbuis: 1.00000000000000,
lbuis94: 1.00216000000000,
linuitzettingAl: 2.40000000000000e-5,
linuitzettingGlas: 8.00000000000000e-6,
lwater: 0.683240940835397,
lwater94: 0.683240940835397,
rhoAl94: 2682.61664414593,
rhoWater94: 961.908426317815,
voluitzettingWater: 0.000440000000000000},