$4\mathrm{.}2\mathrm{.}9.$ A pump is installed in a $100-m$ pipeline to lift water at $20C$ from reservoir $A$ to reservoir $B($see Figure P$4\mathrm{.}2\mathrm{.}9).$ The pipe is rough concrete with a diameter of $80cm.$ The design discharge is $4\mathrm{.}5\frac{m^3}{s}.$ Determine the maximum distance from reservoir A that the pump could be installed without encountering cavitation problems.

Figure P$4\mathrm{.}2\mathrm{.}9$