The Navier-Stokes equation is linearized for the steady flow in the laminar inlet of a pipe with annular space. This solution shows the family of velocity profiles defined by the modifled Bessel functions. By applications of this family to the momentum equation and the energy equation, respectively, the inlet length and the pressure drop are presented. Some examples of computation are given for the ratio of the inner and outer radii of annular space, m=1.2∼5. The results of computation prove that the relation between the dimensionless distance from pipe entrance σ=x/(R₂-R₁) R₆ and the pressure drop (p₀-p)/(ρu₀²/2) is almost unaffected by m, and the inlet length σ_L also unaffected. Practically, σ_L maybe evaluated to be 0.02.