For the simple pipe networks shown in Figure P14–7, determine the pressures at nodes 1,...

For the simple pipe networks shown in Figure P14–7, determine the pressures at nodes 1, 2, and 3 and the volumetric flow rates through the branches. Assume the pressure at node 4 is zero. In network (a), let Q = 1 m³/s. Let the resistances be, R₁ = 1; R₂ = 2; R₃ = 3; R₄ = 4 and R₅ = 5 all in units of N-s/m⁵. In network (b), let Q = 1000 in³/s and the resistances be R₁ = 10; R₂ = 20; R₃ = 30; R₄ = 40, and R5 = 50 all in units of lb-s/in.⁵