(Solved): 2 The operating point of a centrifugal pump is to be determined. The pump performance curve and the ...

2 The operating point of a centrifugal pump is to be determined. The pump performance curve and the system load characteristics are given as follows. \[ \begin{aligned} \text { Pump: } \Delta P & =240 \times 10^{3}-43.8 \times 10^{2} Q^{2} \\ \text { Load: } \Delta P & =40 \times 10^{3}+156.2 \times 10^{3} Q^{1.8} \end{aligned} \] where \( \Delta P \) is the static pressure rise in \( \mathrm{Pa} \), and \( \mathrm{Q} \) is the discharge in \( m^{3} / s \) 76 System Simulation - Using the successive substitution method for 2 unknowns, determine the operating point of the pump. - Decide on your own stopping critierion and start with an initial guess value of \( Q=0.5 \mathrm{~m}^{3} / \mathrm{s} \). - At the operating point, if the pump efficiency is known to be \( 85 \% \), what is the electrical power input required for the pump? - For the same electrical power input, if over time, the pump efficiency drops to \( 82 \% \), what will be the operating point for the pump? - Can you quantify the sensitivity of the discharge with respect to the pump efficiency?