$12-31$ Water at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ is siphoned from a reservoir as shown in Fig. P$12-31.$ For $\backslash ($ d$=10\backslash$mathrm$\{$~cm$\}\backslash )$ and $\backslash ($ D$=16\backslash$mathrm$\{$~cm$\}\backslash ),$ determine $($a$)$ the minimum flow rate that can be achieved without cavitation occurring in the piping system and $($b$)$ the maximum elevation of the highest point of the piping system to avoid cavitation.

FIGURE P$12-31$