Question $2(35$ marks$)$

A rectangular channel is $10ft$ wide and carries a flow of $400cfs$ at a normal depth of $3ft$ and Manning's roughness $(n)$ of $0\mathrm{.}017.$ If an obstruction causes the depth just upstream of the obstruction to be $8ft$ deep:

a$)$ Why will a hydraulic jump form upstream of the obstruction? Explain in terms of the definition of hydraulic jumps, $y_n,y_c$ and $y.$

b$)$ What type of water profile would be present?

c$)$ What is the slope of the channel at normal depth $S_0?$

d$)$ What is the conjugate depth of the hydraulic jump?

e$)$ How far upstream from the obstruction will the jump be$?$