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This study provides a theoretical and numerical modelling of shear stress due to the friction of transient laminar flow on pipe wall. This work is a simplified model of Prado et al. [1]. It is based on the expansion of the instantaneous velocity profiles of the flow in polynomial series in time and radial variable across the section of pipe. The set partial derivatives equations obtained from the conservation of mass and the theorem of momentum is then solved by the method of characteristics. The results obtained are in good agreement with those of Holmboe and Rouleau [2], in steady state Newtonian laminar flow.

A polynomial expansion of axial velocity profiles to solve transient laminar flow in elastic pipe