In this paper we study the effect of wall-shape on laminar flow in corrugated pipes. The main objectives of this paper are to characterize how the flow rate varies with wall-shape, and to identify which shapes enhance the flow rate. We conduct our study by numerically solving the Navier-Stokes equations for a periodic section of the pipe. The numerical model is validated with experimental data on the pressure drop and friction factor. The effect of wall-shape is studied by considering a family of periodic pipes, in which the wall-shape is characterized by the amplitude, and the ratio between the lengths of expansion and contraction of a periodic section. We study the effect that varying these parameters has on the flow. We show that for small Reynolds numbers, a symmetric shape yields a higher flow rate than an asymmetric shape. For large Reynolds numbers, a configuration with a large expansion region, followed by a short contraction region, performs better. We show that when the amplitude is fixed, there exists an optimal ratio of expansion/contraction which maximizes the flow rate. The flow rate can be increased by 8%, for a geometry with small period; in the case of a geometry with large period, the flow rate increases by 35%, for large Reynolds number, and even 120% for small Reynolds numbers.

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