Superhyhobic micro-structured surfaces utilize a combination of chemical treatment and microscale surface topography to increase the hyhobicity of a surface. Superhyhobic surfaces exhibit a number of interesting properties such as dramatically decreased wettability and reduced friction in laminar flows. These characteristics make them a potential enabling technology for a variety of applications including microfluidics, lab-on-a-chip devices, self-cleaning surfaces, and reduction. In this talk, we discuss the reduction capability of the microstructured surfaces to understand the fundamental interfacial phenomena that allow these surfaces to exhibit such properties. Along with experimental efforts, numerical simulations and theoretical studies have been conducted. Among those parallel efforts, in this seminar, we focus on the analytic solution method using conformal mapping to solve pressure driven fluid flow problems under mixed boundary conditions within microchannel.