Fluid mechanics at a very small scale, particularly micro-flows and nano-flows, have many technical applications, and the elastic properties of small-scale flows are strongly expressed even for dilute aqueous solutions of non-Newtonian fluids. We have investigated the flow properties of water and several types of surfactant solutions with spherical or rod-like micelles. Before the flow property investigations, Newtonian and non-Newtonian viscosities for the test fluids were observed by using a capillary viscosity meter. Pressure drops were experimentally measured, and the frictional coefficient of the pipe was estimated in flows through capillaries ranging from 133 m to 2.87 mm in diameter. For water flow, good agreement was obtained between the experimental results and the predictions for Hagen-Poiseuille flow and the Blasius expression. The flow properties of the spherical micelle surfactant solutions agreed with those of water. However, the rod-like micelle surfactant solutions maintained laminar flows in the transition regions. Thus, a pseudo-laminarization effect for surfactant solutions with rod-like micelles is indicated. A relationship between these experimental results and estimated first normal stress differences is also strongly suggested.