The expression Ergun shown below is used to describe a fluid flowing through a granular fixed bed. p is the pressure drop, is the density of the fluid, G0 is the mass velocity, Dp is the diameter of the particles in the bed, is the viscosity of the fluid, L is the length of the bed and is the void ratio of the bed.

Given the above parameters, find the bed void ratio with the Newton-Raphson method with an approximation error of 0.001 (the initial condition value for the bearing void ratio can be taken as o = 0.3).

G02pLDp(1)3=150[DpG0](1)+1.75,[DpG0]=1000,G02pLDp=10