Example $4\mathrm{.}2$: Estimation of Discharge Given Diameter and Head Loss

A pipeline $10km$ long, $300mm$ in diameter and with roughness size $0\mathrm{.}03mm,$ conveys water from a reservoir $($top water level $850m$ above datum$)$ to a water treatment plant $($inlet water level $700m$ above datum$).$ Assuming that the reservoir remains full, estimate

the discharge, using the following methods:

$($a$)$ The Colebrook$-$White formula

$($b$)$ The Moody diagram

$($c$)$ The HRS charts

Note: Assume $v=1\mathrm{.}13{10}^{-6}\frac{m^2}{s}.$