Water is flowing in a rectangular channel at $375$ ft$3$

$/$s and a depth of $8\mathrm{.}5$ ft$.$ The bottom width of the

channel is $7\mathrm{.}0$ ft$.($a$)$ Find the depth and change in water surface elevation caused by a smooth contraction

in channel width of $2\mathrm{.}0$ ft $($from $7$ ft to $5$ ft wide$)$ and with no changes in channel bed elevation. $($b$)$ What is

the greatest allowable contraction in width so that choking is prevented?