A $450mm$ diameter culvert has been designed to convey a discharge of $Q=0\mathrm{.}55\frac{m^3}{s}$ of

storm$-$water under a residential road. The culvert is $37\mathrm{.}5m$ long and has a slope of $1\mathrm{.}3\%.$ The

downstream flow depth was obtained as $0\mathrm{.}35m$ from a hydraulic analysis. You are required

to determine:

$1\mathrm{.}1$ the head required to convey the discharge through the culvert at full flow conditions;

$($a$)$ If concrete pipe is used with a Manning's roughness coefficient of $n=0\mathrm{.}0155$ with an

inlet headwall of socket type.

$($b$)$ If corrugated steel pipe is used with a Manning's roughness coefficient $n=0\mathrm{.}024$ with

an inlet headwall of square edge design.

$1\mathrm{.}2$ What is the corresponding headwater depth in $1\mathrm{.}1(a)$ and $($b$)$ above?