# How much time for solving a system of equations?

I wrote the following code for system of 11 equations; however when I run, it shows "Running" and has not converged to any answer after 2 hours. Please let me know whether it is normal or how I should enhance the code? how much time does it require approximately? Could it be a reason that one or some of the equations are not independent?

Many thanks,

dd = 2.83*10^-3;
dp = 2*10^-3;
vdbi = .82;
vpbi = 8.1;
mp = 4.4*10^-6;
md = 1.18*10^-5;
sigma = 0.0734;
rod = 1000;
rop = 1050;
mu = .0010527;
vpai = 6.2;

NSolve[{
π/12 (rod*dd^3*vdbi^2 + rop*dp^3*vpbi^2) == π*sigma*L*(db + dp)+ π^2*2*h*db*sigma +
π*mu*L*(dp + db)/2*64/h*delt + π/12*rop*dp^3*vpai^2 + π/8*dp^2*rop*.5*H*(vpai*dd/H)^2,
π/6*dd^3 == π*L/2*(dp + db)*h + π^2*h^2*db,
vlam*delt == 4*π*h,
c4 == vpai/Cos[θ],
3*c1*h^2 + 2*c2*h + c3 == 0,
c1*h + c2 == 0 ,
c1*(h/3)^3 + c2*(h/3)^2 + c3*h/3 + c4 == 0,
c1*h^4/4 + c2*h^3/3 + c3*h^2/2 + c4*h == vlam*h,
db == dp + 2*L*Sin[θ],
delt == L*Cos[θ]/vpai,
H == L*Cos[θ]},

{L, db, h, delt, H, vlam, c1, c2, c3, c4, θ}]

• Instead of solving for θ, consider solving for the quantity Tan[θ/2] instead (i.e. use the Weierstrass substitution). – J. M.'s ennui Jun 8 '15 at 17:10
• It may help if you can add constraints to some of the parameters (based on your understanding of the actual problem, eg. I'd guess L>0 for example).. Also I would hand reduce as much as possible, eg, H,delt,db and a few other unknowns can be readily eliminated. – george2079 Jun 8 '15 at 17:26