continuity equation, Bernoulli equation, Torricelli formula, solid of revolution, volume norm condition, cylinder, cone frustum, spherical segment, paraboloid, funnel, catenoid, hyperboloid, solid of revolution of the Gaussian curve, variational treatment of the outflow problem

We study the problem of draining fluid from containers represented by solids of revolution through a small aperture at their bottom under the influence of their own weight. We analyze the shape of a container for which outflow velocity remains constant - outlet. We investigate a profile of a container for which the velocity of decrease of the fluid level is constant - fluid clock. Finally we present the variational aspects of the problem.