Water flows from an under$-$sluice gate into a very wide rectangular channel. For a wide rectangular channel, the hydraulic radius is approximated as the depth of flow. Assume the channel with a bed slope of $1$ in $1000.$ The sluice is regulated to discharge $10$ m$3/$s$/$m$,$ the depth at Vena$-$Contracta being $0\mathrm{.}5$ m$.$ The slope of the energy line $($Sf$),$ is approximated by Manning$$s formula for gradually varied flow. Manning$$s n $=0\mathrm{.}015.$ i$.$ Find the normal depth and critical depth ii$.$ What is the type of bed slope? iii. Find the conjugate depth for the normal depth iv$.$ Find the specific energies at Vena$-$Contracta and the location of conjugate depth v$.$ Distance between the Vena$-$Contracta section and the section of conjugate depth $($