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This work is concerned with the flow of a Newtonian fluid through a pipe of constant circular cross section which is uniformly porous. The governing unsteady equations are solved analytically after converting them to a third order ordinary differential equation using similarity transformation method. Expressions for axial and radial velocity components and pressure distribution are obtained. The characteristics of complex axial velocity and complex radial velocity for different values of parameters are analysed. The effects of small suction and small injection are delineated through graphs. Results reveal that suction or injection has significant influence on the flow.