A viscous liquid is pumped through a pipe network in a chemical plant. The annual pumping cost per unit length of pipe is given by C_pump=(48.13 q²μ)/D⁴. The annual cost of the installed piping system per unit length of pipe is given by C_piping=45.92D. Here, D is the inner diameter of the pipe in meter, q is the volumetric flowrate of the liquid in m³s^-1 and μ is the viscosity of the liquid in Pa.s.
If the viscosity of the liquid is 20×10^-3 Pa.s and the volumetric flow rate of the liquid is 10^-4 m³s^-1, the economic inner diameter of the pipe is _______ meter (round off to 3 decimal places).