A rectangular concrete channel 10 m wide has a bed slope of 1 m/km and surface roughness equivalent to a Manning n of 0.02. It is proposed to use a hump on the channel bed for the purpose of flow measurement. If the maximum discharge is 150 m3/s:
(a) determine the minimum height of the hump (?x) to produce critical flow over the hump, and
(b) if the actual height of the hump is 0.5 m calculate the depth of flow immediately upstream of the hump.