On flow through bends and branchings

Theoretical modelling of bending and branching tube flows at medium-to-high flow rates is described for current industrial and biomedical projects. This mostly uses slender-flow modelling. Much pressure loss occurs in bends, with increased swirl, large variations in velocity components and wall shear stress, skewing of the downstream motion and reduced flow rate, but the flow regime which is established shows sensitive dependence on the imposed pressure drop and entrance conditions. A small side-branch off a mother tube produces most rapid variation in pressure and velocity near the daughter entrance, this variation now being quantifiable. A multiple branching yields large flow rates and nonunique flow patterns, depending on the form of the imposed pressure differences.