$($b$)$ A $20$m wide and $1$km long rectangular channel has a sudden fall in the channel bed approximately half$-$way downstream. The excavated step is $0\mathrm{.}3$m deep. A discharge is $10$m$3/$s and water depth upstream is $0\mathrm{.}12$m$.($i$)$ Calculate the water depth downstream $($ii$)$ What flow regime occurs in the channel for these flow conditions. $($iii$)$ Discuss the consequences of the downward step on the flow conditions.