$($a$)$ Using Darcy$-$Weisbach equation, Colebrook equation $($for friction factor$)$ and Manning's formula, derive a relationship between Manning's $n$ and relative roughness.

$10\%$

$($b$)$ Compute Manning's $n$ from the relationship derived in Part $($a$)$ for a concrete pipe having $30cm$ diameter $)=(3mm$ and compare it with the standard value of $n$ provided for this material in Table $1.$

$[10\%]$