The developing laminar flow and pressure drop in the entrance region of annular ducts

A new analytical method lias been applied for determining the developing laminar flow in the hydrodynamic entrance region of annular ducts. Detailed results are presented for the development of the velocity distribution and the pressure drop over a wide range of annulus radius ratios r₁/r₂ (r₁ = inner radius of anmdus, r₂ = outer radius of annulus). It is found that the pressure drop and flow development in annular ducts with radius ratios substantially less than unity is quite similar to that in a parallel-plate channel (r₁/r₂ → 1). On the other hand, the results for an annular duct with radius ratio as small as 0.001 depart significantly from those for a circular tube (r₁/r₂ = 0). The hydrodynamic entrance length, measured as a multiple of the hydraulic radius, increases as the duct radius ratio decreases at a fixed Reynolds number.