Critical Review of One-Dimensional Tube Flow Equations

Abstract
Flows through ducts or pipes are often analyzed theoretically and numerically using one-dimensional flow equations. Generally it is assumed that the equations describe relations between average flow properties and that they are adequate if the axial component of the flow dominates. This paper reviews the derivation of the governing equations. It is shown that equations which are traditionally used for tube flows have a very limited scope of applicability. Their theoretical validity is in essence restricted to steady incompressible flows. In cases of more complicated flows some terms in the traditional momentum and energy equations can be in error by up to 50%. It is also shown that the popular approximation of the energy dissipation function by the product of the average velocity and average shear stress is appropriate for the simplest flows only. The paper reveals shortcomings of traditional methods of derivations of tube flow equations and provides explicit formulas for correction terms which should be used in the governing equations.

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