Granular discharge rate for submerged hoppers


  • T. J. Wilson
  • C. R. Pfeifer
  • N. Mesyngier
  • D. J. Durian University of Pennsylvania



Granular physics, Bottlenecks, Clogging


The discharge of spherical grains from a hole in the bottom of a right circular cylinder is measured with the entire system underwater.  We find that the discharge rate depends on filling height, in contrast to the well-known case of dry non-cohesive grains.  It is further surprising that the rate increases up to about twenty five percent, as the hopper empties and the granular pressure head decreases.  For deep filling, where the discharge rate is constant, we measure the behavior as a function of both grain and hole diameters.  The discharge rate scale is set by the product of hole area and the terminal falling speed of isolated grains.  But there is a small-hole cutoff of about two and half grain diameters, which is larger than the analogous cutoff in the Beverloo equation for dry grains.


Received: 11 September 2014,  Accepted: 10 October 2014; Reviewed by: L. Staron, CNRS, Universite Pierre et Marie Curie, Institut Le Rond d'Alembert, Paris, France; Edited by: L. A. Pugnaloni; DOI:

Cite as: T J Wilson, C R Pfeifer, N Meysingier, D J Durian, Papers in Physics 6, 060009 (2014)


Author Biography

D. J. Durian, University of Pennsylvania

Physics & Astronomy, professor
Open Review



How to Cite

Wilson, T. J., Pfeifer, C. R., Mesyngier, N., & Durian, D. J. (2014). Granular discharge rate for submerged hoppers. Papers in Physics, 6, 060009.