The problem of describing an unsteady cylindrical pipe flow with one-dimensional equations is investigated, and an exact method for obtaining a closure relationship is proposed for the transient shear stress in a laminar flow submitted to an arbitrary transient pressure gradient. Extensive comparisons are given for a step or a harmonic pressure gradient between the approximate solution derived from this method, some results of the literature and exact solutions of the Navier–Stokes equations.
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Achard et al. (1981) studied this question.
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