The major flow development in the region within a distanceO((aR)1/2) from the entrance of a curved pipe occurs near the pipe wall, whereais the radius of the pipe cross section, assumed circular, andRis the radius of curvature of the central axis of the pipe. A three‐dimensional boundary‐layer solution is obtained for elucidating the physics of this developing flow; in particular, the effect of nonzero curvature ratio &agr;=a/Ron the geometric similarity of the flow. The numerical results show that the series solution in terms of &agr; is valid only when &agr;≤0.1 ands≤0.1 (aR)1/2, wheresis the distance from the inlet along the pipe axis. The crossover of the axial wall shear is purely a geometric property and its location is a strong function of &agr;. It is also demonstrated that (aR)1/2is the proper length scale by showing that the solution of the first region,s∼O(a), is included in that of the second,s∼O(aR)1/2.