A drainpipe is to be installed to provide a maximum design discharge of $150$ l$/$s$.$ The minimum

discharge is $25$ l$/$s$.$ The pipe runs on a slope of $1$ in $300$ and has an internal surface roughness

of $1$ mm$.$ The self$-$cleansing velocity is $0\mathrm{.}7$ m$/$s$.$

a$)$ Select the pipe size for the required maximum discharge. Available pipe diameters include

$100$ mm$,150$ mm$,200$ mm$,300$ mm$,400$ mm$,500$ mm$,750$ mm$,1$ m$,1\mathrm{.}5$ m and $2$ m$.$

$(7$ marks$)$

b$)$ Determine the discharge when the pipe is half$-$full.