(Solved): Determine the power that the pump gives to the cooling system shown in Figure 1 , when the system ...

Determine the power that the pump gives to the cooling system shown in Figure 1 , when the system is: a) open, and b) closed, according to the figure. In both cases the flow rate is \( Q=0.003 \mathrm{~m}^{3} / \mathrm{s} \) and the change of density and viscosity with temperature can be neglected. You are given: \[ \begin{array}{l} \rho=998.2 \mathrm{~kg} / \mathrm{m}^{3} \\ v=1.2 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s} \\ \mathrm{L}_{\mathrm{a}}=10.4 \mathrm{~m} \\ \mathrm{D}=60 \mathrm{~mm} \\ \varepsilon=0.05 \mathrm{~mm} \\ \mathrm{H}=2.4 \mathrm{~m} \\ \mathrm{~h}=0.5 \mathrm{~m} \end{array} \] All local losses in the open system are \( \sum \mathrm{K}_{\mathrm{a}}=4.5 \), and in the closed system \( \sum \mathrm{K}_{\mathrm{b}}=4.9 \) \( \mathrm{Lb}_{b}=\mathrm{L}_{\mathrm{a}}+\mathrm{H} \) (a) (b) Figure 1: Problem 1 (a) Open Cooling System; (b) Closed Cooling System