A rectangular open channel consists of two long reaches with steep slopes as shown in the figure below. The second reach is steeper than the first. The discharge is $Q=300cfs,$ the channel is rectangular with a width of $10$ ft $.$ The upstream section has a slope of $0\mathrm{.}025$ and a normal depth of $2$ ft $.$ The downstream section has a slope of $0\mathrm{.}205$ and a normal depth of $1$ ft $.$ Use the directstep method to calculate and plot the water surface profile in the $S-2$ profile region. Assume that flow at the junction between the two sections with different slopes is equal to the upstream normal flow depth. Additionally, stop your calculations once the water surface profile is within $5\%$ of the downstream normal flow depth.

$v_{-}$