EXPRESSIONS FOR GRAVITY DRAINAGE OF ANNULAR AND TOROIDAL CONTAINERS

The time required to drain process or storage vessels of their liquid contents can be of crucial importance in many emergency situations. Ov er the years, many formulas have been developed to compute the time re quirements for draining vessels of various geometric configurations. T hese formulas typically assume gravity drainage through an orifice typ e of opening at the bottom of the vessel. In this article, analytical expressions are developed to compute the times required for complete d rainage of annuli (both horizontal and vertical), as well as horizonta l tori, solely under the influence of gravity. Annuli often form the s hell side of double-pipe heat exchange devices, while horizontal tori are often employed as distributing rings or manifolds in various mass transfer operations. Large vertical tori are sometimes used as promoti onal devices for advertising purposes (e.g., huge tires), but are not commonly used to contain fluids (presumably because of structural and other considerations). The drainage time expression for horizontal ann uli incorporates elliptic integrals.