An incompressible fluid flows through a pipe network of circular pipes as shown in Figure 2.12. If \(0.1 \mathrm{~m}^{3} / \mathrm{s}\) of fluid enters and leaves the piping network, using a 4-node 5-element model, calculate the nodal pressure and the volume flow in each pipe. If the nodes 1 and 3 are directly connected, in addition to the existing arrangement, what change takes place in the nodal pressure and volume fluid in each pipe? The viscosity of the fluid is \(1 \times 10^{-2}\) \(N \mathrm{~s} / \mathrm{m}^{2}\). For laminar flow, the resistance for the flow is given by \(128 \mu \mathrm{L} / \pi D^{4}\). The details of the elements are given in Table 2.3.

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2 2 1 5 3 3 4 4