An experimental rectangular open channel is $585$ mm wide, has walls of $300$ mm height, and has a sharp horizontal weir crest $185$ mm above the channel bed Assuming a loss coefficient of $0\mathrm{.}62$ for this weir, calculate $($a$)$ the maximum flow rate the weir can measure, $($b$)$ the upstream velocity head as a percentage of the head over the weir under these conditions.