$100-$m$-$long concrete$-$lined triangular channel $($side slope $2\mathrm{.}5)$ carries $50$ m$3$ s$-1$ water $20\backslash$deg C$.$ If the average water depth in the channel is $2$ m$,$ determine the friction

loss using:

$(1)$ Darcy$-$Weisbach equation $($Answer: $0\mathrm{.}3774$ m$)$

$(2)$ Manning formula $($Answer: $0\mathrm{.}3974$ m$)$