An ancient device for measuring the passage of time uses an axisymmetric vessel shaped so that the water level falls at a constant rate (see Figure P11.14). The top of the vessel is open to the atmosphere and water exists through a small hole (radius \(d_{o}\) ) at the bottom. Determine the shape of the vessel, i.e., radius, \(r\), as a function of axial position, \(z\), and its volume that allows us to measure time.

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V. P, P Z r(z) FIGURE P11.14 do V2, P, P2