$4.$ A pump at a distance H above the water level extracts hot water of density $\backslash (\backslash$rho $\backslash )$ from a well. The head loss in the pipe from the well to the pump is $\backslash (\backslash$mathrm$\{$h$\}\_\{\backslash$mathrm$\{$L$\}\}=1/3*\backslash$mathrm$\{$H$\}\backslash ).$ Assuming constant H $,$ determine the net positive suction head, NPSH$,$ as a function of $\backslash (\backslash$rho$,\backslash$mathrm$\{$H$\}\backslash ),$ atmospheric pressure, $\backslash (\backslash$mathrm$\{$p$\}\_\{\backslash$mathrm$\{$a$\}\}\backslash ),$ vapor pressure, $\backslash (\backslash$mathrm$\{$p$\}\_\{\backslash$mathrm$\{$v$\}\}\backslash ),$ and gravitational acceleration, g $.$ Two pumps are available with required NPSH values of $11$ ft and $6$ ft $.$ What is the maximum water temperature that can be pumped without cavitation for each pump?