A lined rectangular concrete drainage channel is 10m wide and carries a flow of 8 m3/s. In order to pass the flow under a roadway, the channel is contracted to a width of 6m. Under design conditions, the depth of flow just upstream of the contraction is 1m, and the contraction takes place over a distance of 7m.

(a) If the energy loss in the contraction is equal to \(V_1^{2}/2g\) where V1 is the average velocity upstream of the contraction, what is the depth of flow in the constriction?

(b) Does consideration of energy losses have a significant effect on the depth of flow in the constriction?

(c) If the width of the constriction is reduced to 4.5m and a flow of 8 m3/s is maintained, determine the depth of flow within the constriction (include energy losses).

(d) If reducing the width of the constriction to 4.5m influences the upstream depth, determine the new upstream depth.