ON LOW-REYNOLDS-NUMBER ENTRY FLOW INTO A CIRCULAR CYLINDRICAL TUBE

In the circulation system the blood vessels have many generations of branching or subdivision. Similarly in the lung the airway bifurcates as many as 23 generations. The flow of blood or air into each new branch is subjected to a change in the entry region. It is important to know how the transition to Poiseuille flow takes place. In this article the axisymmetric low-Reynolds-number entry flow in the inlet region of a circular cylindrical tube is studied on the basis of the Stokes' approximation. The purpose of this study is to find a theoretical solution of the entry flow at very low Reynolds numbers, for which no previous solution is known to the authors. The present solution shows that the entry length at low Reynolds number is simply of the order of the tube radius. For microcirculation (in blood vessels with diameters smaller than 100 μ) the Reynolds number is of the order of 1 or smaller, and the low-Reynolds number approximation is valid. Similarly, for air flow in the respiratory bronchioles and alveolar ducts and sacs of the lung the Mach number is essentially zero and the Reynolds number lies in the range 1-10-2 and the present analysis is also applicable. © 1969.