%0 Journal Article %1 Sommerfeld:1993 %A Sommerfeld, Jude T. %A Stallybrass, Michael P. %D 1993 %J Journal of Loss Prevention in the Process Industries %K cylindrical discharge; elliptic horizontal integrals liquid vessels; %N 1 %P 11--13 %R http://dx.doi.org/10.1016/0950-4230(93)80014-D %T Elliptic integral solutions for fluid discharge rates from punctured horizontal cylindrical vessels %V 6 %X The problem of determining fluid discharge rates from the side (as opposed to the bottom) of punctured cylindrical and spherical vessels was recently addressed by Crowl1. Both vertical and horizontal cylindrical configurations were examined. Analytical solutions to the spherical and vertical cylindrical problems were obtained in rather straightforward fashion. However, the geometry is considerably more complex in the case of the horizontal cylindrical configuration. Crowl does not present an analytical solution to this more complicated problem, but employs numerical methods in order to integrate the governing differential material balance equation. The purpose of this communication is to present a direct analytical solution to the problem of side drainage from a punctured horizontal cylindrical vessel with the use of elliptic integrals, values of which are tabulated in numerous mathematical handbooks. Because of their inherently greater accuracy, analytical solutions can serve as standards or benchmarks against which to check the reliability of numerical solutions and, in addition, are generally readily programmable on computers and/or spreadsheets.

@article{Sommerfeld:1993, abstract = {The problem of determining fluid discharge rates from the side (as opposed to the bottom) of punctured cylindrical and spherical vessels was recently addressed by Crowl1. Both vertical and horizontal cylindrical configurations were examined. Analytical solutions to the spherical and vertical cylindrical problems were obtained in rather straightforward fashion. However, the geometry is considerably more complex in the case of the horizontal cylindrical configuration. Crowl does not present an analytical solution to this more complicated problem, but employs numerical methods in order to integrate the governing differential material balance equation. The purpose of this communication is to present a direct analytical solution to the problem of side drainage from a punctured horizontal cylindrical vessel with the use of elliptic integrals, values of which are tabulated in numerous mathematical handbooks. Because of their inherently greater accuracy, analytical solutions can serve as standards or benchmarks against which to check the reliability of numerical solutions and, in addition, are generally readily programmable on computers and/or spreadsheets.}, added-at = {2010-01-05T23:12:10.000+0100}, author = {Sommerfeld, Jude T. and Stallybrass, Michael P.}, biburl = {https://www.bibsonomy.org/bibtex/21ec69e5f23d616e3a673ba67171ec685/sjp}, doi = {http://dx.doi.org/10.1016/0950-4230(93)80014-D}, interhash = {fba00b061e6d38e21b49840bb479ac2a}, intrahash = {1ec69e5f23d616e3a673ba67171ec685}, journal = {Journal of Loss Prevention in the Process Industries}, keywords = {cylindrical discharge; elliptic horizontal integrals liquid vessels;}, number = 1, pages = {11--13}, review = {missing issue}, timestamp = {2010-01-19T17:39:44.000+0100}, title = {Elliptic integral solutions for fluid discharge rates from punctured horizontal cylindrical vessels}, volume = 6, year = 1993 }