Abstract
In the analysis of flow in piping networks, dividing and combining losses at branches are usually ignored as being minor compared to the friction losses in pipes. But the losses at branches are not minor in many industrial piping systems. In this report, followed by previous ones, Part 1 and 2, the basic T-type dividing and combining flows with a dividing loss at the upstream branch and with a combining loss at the downstream branch are analysed. The results obtained are, 1) Basic T-type dividing and combining flow are classified into two types, type I and type II, according to the effect of a combining loss at the downstream branch to the flow. 2) The errors in the flow distributions and over-all loss coefficients caused by neglecting both losses at branches are calculated and illustrated in several graphs. The differences of the effects of both losses to the flows of type I and type II are clarified. 3) Arora's idea, "Flows in closed hydraulic networks will ajust so that the expenditure of system energy is minimum." is sasisfied only in the assumption that all the pressure losses in pipes are proportional to the n-th power of flow rate. When the variation principle in the flow distributions of piping networks becomes a problem, Millar's CONTENT function shoud be considered. The CONTENT function of the flow of type I are formulated and calculated.
