- Connection node

In order to take into account any sudden change in the pipeline cross-section, the earlier established connection node condition was used. It involves assigning two sets of values describing the flow parameters to the connection node, which causes it to act as two separate nodes (Figure 2). The detailed derivation of the junction boundary condition is described in [12]. Here, only the final equations are given for brevity. The relation between the flow velocity on the left-hand side of the connection node and the value of the flow velocity on the right-hand side of the connection node is given by:


where *vi,L* is the velocity on the left-hand side of the connection node, *vi,R* is the velocity on the right-hand side of the connection node, *DL* is the inner diameter of the pipe on the left-hand side of the connection node and *DR* is the inner diameter of the pipe on the right-hand side of the connection node.

Equation (21) is a cubic function, so it has three roots, only one of which satisfies the physical conditions. After computing the value of the flow velocity on the left-hand side of the connection node *vi,L*, the value of the flow velocity on the right-hand side of the connection node *vi,R* was calculated with the following:

$$v\_{i,R} = \left(\frac{D\_L}{D\_R}\right)^2 v\_{i,L} \tag{22}$$
