$($a$)$ The flow correction for the pipe flow in a network loop for Hardy$-$Cross

method is given as $=-\frac{{\displaystyle \underset{?}{\overset{?}{}}}K{Q}_a^p}{{\displaystyle \underset{?}{\overset{?}{}}}|q{Q}_a^r|}.$ Using Hazen$-$Williams formula, derive

the values of $p,q,r$ and $K$ in the above relationship.

$($b$)$ Using the relationship in Part $($a$)$ find out the first correction for the following

network:

ized iron

diameter

$ng$ in the