Water flow through a parabolic channel

The cross-section of a straight canal is modelled by the curve \(y=\dfrac{x^2-16}{8}\) for \(-4\le x\le4\), where \(x\) and \(y\) are in metres and the bank tops are at \(y=0\).

1. When the canal is full to the level \(y=0\), find the area of the water's cross-section.[3]
2. The water flows at a uniform speed of \(0.6\) m/s. Find the volume of water passing a point each second.[2]
3. In a dry spell the water level falls to \(y=-1\), so the depth halves from \(2\) m to \(1\) m. Find the new cross-sectional area exactly, and explain why it is much less than half the area in (a).[3]
4. Real water flows more slowly near the bed and banks than at the centre. State how this affects your answer to (b).[2]