A centrifugal pump having a head$-$capacity relationship given by the equation $ha=180-6\mathrm{.}10{10}^{-4}{Q}^2,$ with ha in feet when Q is in gpm$,$ is to be used with a system as shown below. For $z_2-z_1=50ft,$ what is the expected flowrate if the total length of constant diameter pipe is $600$ ft and the fluid is water? Assume the pipe diameter to be $4$ in $.$ and the friction factor to be equal to $0\mathrm{.}02.$ Neglect all minor losses. $[25$ pts $]$