A 12 h water clock is to be designed with the dimensions shown in Fig. 1.4.10, shaped like the surface obtained by revolving the curve y =  f (x) around the y-axis. What should this curve be, and what should the radius of the circular bottom hole be, in order that the water level will fall at the constant rate of 4 inches per hour (in./h)?

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4 ft I I I 1 I y-f(x) or x-g(y) Water flow FIGURE 1.4.10. The clepsydra. X