Question $3.$ A pump is installed in a $100-m$ pipeline to lift water at $20C$ from reservoir $A$ to reservoir $B.$ The pipe is rough concrete $)=(0\mathrm{.}60mm$ 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 the pump encountering cavitation problems $($with $70\%$ safety factor$).$

Viscosity $=1{10}^{-6}\frac{m^2}{sec}$

Water Vapor Pressure $=2900Pa($abs$)$

Water unit weight $=9810\frac{N}{m^3}$

Atmospheric Pressure $=101,000Pa$

Safety factor $=\frac{\text{A}\text{c}\text{t}\text{u}\text{a}\text{l}\text{p}\text{r}\text{e}\text{s}\text{s}\text{u}\text{r}\text{e}\text{u}\text{s}\text{e}\text{d}to\text{a}\text{v}\text{o}\text{i}\text{d}\text{b}\text{o}\text{i}\text{l}\text{i}\text{n}\text{g}of\text{w}\text{a}\text{t}\text{e}\text{r}\text{v}\text{a}\text{p}\text{o}\text{r}\text{a}\text{n}\text{d}\text{o}\text{t}\text{h}\text{e}\text{r}\text{d}\text{i}\text{s}\text{s}\text{o}\text{l}\text{v}\text{e}\text{d}\text{g}\text{a}\text{s}\text{s}\text{e}\text{s}}{\text{w}\text{a}\text{t}\text{e}\text{r}\text{v}\text{a}\text{p}\text{o}\text{r}\text{p}\text{r}\text{e}\text{s}\text{s}\text{u}\text{r}\text{e}}$