A $5-m$ wide rectangular channel has a channel slope $(S_o)$ of $0\mathrm{.}022$ and a Manning's roughness $(n)$ of $0\mathrm{.}013.$ For a flow rate $(Q)$ of $50m\frac{3}{s},$ the normal depth $(y_n)$ is $1\mathrm{.}17m$ and the critical depth $(y_c)$ is $2\mathrm{.}17m.$

At Section $A,$ the water depth is $1\mathrm{.}6m.$ Use the direct$-$step method to compute the distance $(L)$ to Section $B,$ where the water surface elevation is $0\mathrm{.}1m$ higher or lower $($depending on the water surface slope for the flow conditions$).$ Some geometric information is given in the table for these depths $($to save you from some calculations$).$

Include a sketch in your solution and label the two sections or $B$ depending on the required direction for calculations$)$ and water depths, and then show your work to find $L.$