Question $4$

A rectangular channel delivering Q$=200$m$^(3)//$sec has the flow velocity $10$m$//$sec and the

water depth $20$ m $.$ Answer the following questions: $($g$=9\mathrm{.}8($m$)//$sec$^(2)).$

$($a$)$ Calculate the specific energy E$.$ Is the flow critical, super$-$critical, or sub$-$critical?

why?

$(4$ marks$)$

$($b$)$ With this E$,$ what is the maximum allowable bed height at downstream? and what

is the water depth corresponding to this specific situation $?$

$(4$ marks$)$

$($c$)$ If the channel bed is lowered by $1$m$,$ what will be the water depth downstream?

$(4$ marks$)$

$($d$)$ Without reducing the total flow rate, what is the minimum width to which this

channel can be narrowed down?

$(4$ marks$)$

$($e$)$ If the channel is widened by $1$m$,$ what will be the water depth downstream?

$(4$ marks$)$

$($f$)$ Re$-$calculate the problem in $($e$),$ but assuming there is an energy loss from

upstream to downstream equal to $10\%$ of upstream velocity head. What is the

water depth downstream?

$($Note: $($b$),($c$),($d$),($e$),($f$)$ are independent questions with each considers a specific

condition as described above. Also, neglect any frictional head losses in this question$).$