Consider a stream that can be approximated as a rectangular channel that is $6m$ wide and has a

Manning roughness of $0\mathrm{.}035.$ The flow in the stream is now $6\mathrm{.}1\frac{m^3}{s}.$ The profile along the

section in question is as follows:

Upstream of Section $1,$ the depth of flow is $0\mathrm{.}46m($the flow upstream of Section $1$ is uniform, so

this is the normal depth for the upstream section$).$

a$.$ What is the slope of the stream upstream of Section $1?$

b$.$ Between Sections $1$ and $2,$ the stream bed drops $2\mathrm{.}2m$ over a relatively short distance.

Downstream of Section $2,$ the slope of the channel is $5\%.$ There is no obstruction to the

flow downstream of Section $2.$ Assuming that there is no significant head loss between

Sections $1$ and $2,$ compute the depth of flow at Section $2.$

c$.$ Prove that there is no hydraulic jump downstream of Section $2.$ Your answer must

include a brief explanation with reference to the critical depth. Sketch the general

shape of the flow profile downstream of Section $1,$ indicating the depths that are

known.

d$.$ Estimate the distance from Section $2$ to the point downstream where the flow is normal

again. Do this using the direct step method for gradually varied flow profiles. Use two

steps with equal depth increments.