Inviscid and low-viscosity flows in multi-branching and reconnecting networks

We study unsteady flow problems of inviscid and low-viscosity fluids in multi-branching networks, reconnecting networks and large networks. The outer end pressures are assumed. Systematic solutions for fast flow are based on overall features of vessel shapes, lengths and end-pressure distribution. This is for rigid or elastic vessels. Favourable end-pressure gradients combined with constricting vessels lead to steady states or forced oscillations. Other conditions, however, can produce high internal transient pressures and flow surges even when the end conditions remain mild. For a small or large network a single non-linear evolution equation is derived under the additional assumption of nearly equal vessel flows; this admits the influence of all the end pressures as well as the overall features of the vessels and determines the flow through the whole network.