A comprehensive experimental study of the pressure drop vs flow rate relationship was carried out using a variety of Newtonian as well as non‐Newtonian liquids in circular cross‐section tubes having a radius that varied sinusoidally with axial distance. The goal of this work was to verify or refute the existence of viscoelastic effects in this Lagrangian unsteady flow field under conditions of low Reynolds numbers and large Weissenberg numbers. Highly elastic and rheologically well‐characterized polyacrylamide solutions having zero‐shear viscosities as large as 140 Pa s were utilized for this purpose; some of the fluids were shear thinning while others were not. Clear elastic effects were observed at high enough Weissenberg numbers.

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