from pylab import *import pylab as plfrom math import *from scipy.integrate import odeintimport numpy as npimport timeepsilon=0.675 #porosidaderhog=5000 #densidade do fluido (ar) [kg/m3]rhop=930. #densidade da particula (PET) [kg/m3]mu=17.4*10**-6 #viscosidade do fluido (ar) [Pa.s]dp=0.0017 #dimetro das partculas (PET) [m]#vg=80. #velocidade do fluido () [m/s]#vp=0. #velocidade das particulas () [m/s]g=9.8 #acelerao da gravidade [m/s2]Ff=0.001 #fator de atrito volumtrico def Ergun (vg,vp):#Equao de Ergun, para dP/dz em [Pa/m], assumindo esfericidade igual a unidade#dPdz=-150.0*mu*abs(vg-vp)*((1.-epsilon)**2)/(dp**2*epsilon**3) - 1.75*rhog*(epsilon-1.)*abs(vg-vp)**2/(dp*epsilon**3)dPdz=(-150.0*mu*abs(vg-vp)*((1.-epsilon)**2))/((dp**2)*(epsilon**3)) - (1.75*rhog*(1.-epsilon)*(abs((vg-vp)**2)))/(dp*(epsilon**3))return dPdzprint ("%.2f psi/m" % (Ergun(80.,0.)*1.45*10**-4))def balanco (v,z):vg=v[0]vp=v[1]dVgdz=+Ergun(vg,vp)/(2*rhog*vg)-g/(2*vg)-(Fd(vp,vg)+Ff)/(rhog*epsilon*vg)dVpdz=-g*(rhog-rhop)/(2*vp*rhop)+Fd(vp,vg))/(rhop*(1.-epsilon)*vp)return (dVgdz,dVpdz)def mesh (L,dz):return linspace(0,dz,L)def Re(vg,vp):Re= rhog*abs(vg-vp)/mureturn Redef Fd (vg,vp):if Re(vg,vp)>=1000.0:Fd = ((3./4)*0.44*(1.-epsilon)*(epsilon**(-2.67))*((vg-vp)**2)*rhog)/dpelse:Fd = ((3./4)*(24./Re(vg,vp)(1.+0.15*(Re(vg,vp)**0.687))*(1.-epsilon)*(epsilon**(-2.67))*((vg-vp)**2)*rhog)/dp) return Fddef main():x=odeint(balanco,(80,0.0001),mesh(100,0.0001))pl.plot(x[:,0], 'blue')pl.plot(x[:,1], 'red')pl.xlabel('Comprimento [m]')pl.ylabel('Velocidade [m/s]')pl.show()return 0if __name__ == '__main__':main()