$11-13.$ A rectangular raft chute $20ft$ wide, as described by Bakhmeteff $[1],$ is to be

built between levels A and $B($Fig$.11-17).$ The design conditions are:

The tailwater fluctuates by $8ft.$

The depth in the steep reach is kept to a minimum navigable depth of $2\mathrm{.}5ft.$

The average velocity should not exceed $14\mathrm{.}7fps.$

The discharge should be kept below $750$ cfs$.$

The roughness coefficient $n=0\mathrm{.}03.$

The entrance discharge is computed by a weir formula $Q=0\mathrm{.}4\sqrt[\phantom{2}]{2g}$ by $A^{1\mathrm{.}5}.$

Determine the following items by the Manning formula and by any method of flow$-$

profile computation as described in this book:

a$.$ Slope of the steep reach

b$.$ The entrance depth $y_A$

c$.$ Length of the flow profile in the transition reach

d$.$ Slope of the neutralizing reach

e$.$ Length of the neutralizing reach

$f.$ Length of the steep reach