Abstract
A quasi two-dimensional model of transient flows in pipes of circular cross-section is developed, using the one dimensional method of characteristics in concentric cylindrical annuli. Lateral velocity components are permitted between adjacent cylinders. The model can nominally incorporate any desired relationship between shear stresses and local velocities. In this paper, it is applied to laminar flows and to a five-region model of turbulent flows. The accuracy of Zielke's (1969) one-dimensional expression for transient wall-shear stresses in laminar flows is verified, and it is shown that his expression is also a reasonable approximation for smooth-wall, turbulent flows, at least at low Reynolds numbers. Quasi-steady relationships are shown to be highly inaccurate in transient laminar or turbulent flows.
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