Universal Free-Fall Law for Liquid Jets under Fully Developed Injection Conditions Articles uri icon

publication date

  • November 2023

start page

  • 224001-1

end page

  • 224001-5


  • 22


  • 131

International Standard Serial Number (ISSN)

  • 0031-9007

Electronic International Standard Serial Number (EISSN)

  • 1079-7114


  • We show that verticals lenderjets of liquid injected in air with a fully developed outlet velocity profile have a universal shape in the common case in which the viscous force is much smaller than the gravitational force. The theory of ideal flows with vorticity provides an analytical solution that, under negligible surface tension forces, predicts RjðZÞ¼½ð1þZ=4Þ1=2−ðZ=4Þ1=21=2, where Rj is the jet radius scaled with the injector radius and Z is the vertical distance scaled with the gravitational length, lg¼u2 o=2g, where uo is the mean velocity at the injector outlet and g is the gravitational acceleration. In contrast with Mariotte"s law, Rj¼ð1þZÞ−1=4, previously reported experiments employing long injectors collapse almost perfectly on to the new solution.


  • Industrial Engineering
  • Materials science and engineering
  • Mechanical Engineering
  • Physics