An engineer makes careful measurements with a weir (see Sect. 10.7 later) which monitors a rectangular unfinished

Question:

An engineer makes careful measurements with a weir (see Sect. 10.7 later) which monitors a rectangular unfinished concrete channel laid on a slope of
1°. She finds, perhaps with surprise, that when the water depth doubles from
2 ft 2 inches to 4 ft 4 inches, the normal flow rate more than doubles, from 200 to 500 ft3/s.
(a) Is this plausible?
(b) If so, estimate the channel width.