$(8$ marks$)$

c$)$ Two reservoirs are connected by a $3\mathrm{.}5$ km pipeline. One reservoir has an elevation of $120$ m $($AOD$)$ and the second an elevation of $60$ m $($AOD$).$ Determine the minimum diameter of pipe required to ensure a discharge of $200$ litres$/$s if the pipe roughness is $0\mathrm{.}2$ mm $.$ The kinematic viscosity of water may be taken as $1\mathrm{.}13{10}^{-6}\frac{m^2}{s},$ and the following expressions may be used:

$(13$ marks$)$

$1=0\mathrm{.}0055[1+(\frac{20000k_s}{D}+\frac{{10}^6}{R_e}{)}^{\frac{1}{3}}]$

$R_{}=\frac{VD}{U},h_t=\frac{1L{V}^2}{2gD}$

Answer: $D=0\mathrm{.}325m$

Hint: Assume pipe D$.$ Calculate V$,$ Re$,$ and $h_t.$ Compare $h_t$ to available head $($elevation difference$)$ and iterate if required.

c$)$ Two reservoirs are connected by a $3\mathrm{.}5$ km pipeline. One reservoir has an elevation of $120$ m $($AOD$)$ and the second an elevation of $60$ m $($AOD$).$ Determine the minimum diameter of pipe required to ensure a discharge of $200$ litres$/$s if the pipe roughness is $0\mathrm{.}2$ mm $.$ The kinematic viscosity of water may be taken as $1\mathrm{.}13{10}^{-6}\frac{m^2}{s},$ and the following expressions may be used:

$(13$ marks$)$

$=0\mathrm{.}0055[1+(\frac{20000k_s}{D}+\frac{{10}^6}{R_e}{)}^{\frac{1}{3}}]$

$R_e=\frac{VD}{U},h_r=\frac{1L{V}^2}{2gD}$

Answer: $D=0\mathrm{.}325m$

Hint: Assume pipe D$.$ Calculate V$,$ Re$,$ and $h_t.$ Compare $h_t$ to available head $($elevation difference$)$ and iterate if required.