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The figure below shows the cross-section of an axisymmetric vessel with a radius R(z)

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The figure below shows the cross-section of an axisymmetric vessel with a radius R(z). z is measured from the bottom of the vessel. A small hole of diameter d allows water to drain out of the container. The water level in the vessel is to fall at a fixed, given rate Vl: if you mark the vessel, you could mea- sure the passage of time, potentially.

(i) Determine the shape of the container: that is, what is R(z)?

(ii) If the drain is 5mm in diameter and this is to operate for 12 hours without refilling, how tall would this be?

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