Abstract
A theory of one-dimensional flow is derived to include outflow due to branching and/or vessel permeability. A result of the derivation is that an outflow term appears in the momentum balance as well as the equation of mass conservation. Even in a simplified version of the momentum balance the outflow term remains, a fact evidently unnoticed thus far, and it is proposed that this equation replace that previously used. The derivation proceeds without resource to assumptions of axisymmetry, broadening the field of potential applications of the theory to the venous circulation, and it is shown that only a minor change is engendered by this generalization.
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