A similarity solution has been carried out to investigate the steady Newtonian water base-Copper nanofluidss flow and heat transfer characteristics of a stationary wedge. A similarity transformation based on the boundary layer approximation is employed to transform the Navier-Stokes equations and the energy equations into a set of nonlinear ordinary differential equations. The set of coupled nonlinear ordinary differential equations with the boundary conditions are solved numerically to study the effects of the nanoparticle volume fraction, on the different physical properties of the flow, namely: the hydraulic and thermal boundary layer thickness, and the local Nusselt number. The numerical results thus obtained show that the hydraulic boundary layer thickness decreases nonlinearly as the nanoparticle volume fraction increases. In addition, Nusselt number increases, as a result of increase nanoparticle volume fraction.