$(3$ pts$)$ The width of a rectangular channel is reduced from $b_1=5ft$ to $b_2=4ft.$

There is also a rise in the channel bed elevation. The flow depth upstream

and downstream of the contraction are $y_t=3ft$ and $y_2=2\mathrm{.}5ft,$ respectively,

for a flow rate $Q=55f\frac{t^3}{s}.$ Unfortunately, the field crew forgot to measure

the rise in the channel bed elevation and now it is not possible to measure it

because the field site is iced over.

$($a$)$ Using the information collected in the field, calculate the height of the

step assuming that the losses through the contraction are negligible.

$($b$)$ If a bridge were to be put in place and required the section to be further

narrowed, what is the minimum width the channel can be contracted to

prevent choking? Assume that the channel bottom would be regraded to

eliminate the step up through the transition.