Related Experiment Video
Updated: May 18, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Flow rate of particles through apertures obtained from self-similar density and velocity profiles
Alvaro Janda1, Iker Zuriguel, Diego Maza
1Departamento de Física, Facultad de Ciencias, Universidad de Navarra, E-31080 Pamplona, Spain.
Abstract:
"Beverloo's law" is considered as the standard expression to estimate the flow rate of particles through apertures. This relation was obtained by simple dimensional analysis and includes empirical parameters whose physical meaning is poorly justified. In this Letter, we study the density and velocity profiles in the flow of particles through an aperture. We find that, for the whole range of apertures studied, both profiles are self-similar. Hence, by means of the functionality obtained for them the mass flow rate is calculated. The comparison of this expression with the Beverloo's one reveals some differences which are crucial to understanding the mechanism that governs the flow of particles through orifices.
Related Concept Videos
Steady, Laminar Flow in Circular Tubes
Uniform Depth Channel Flow
Couette Flow
Steady, Laminar Flow Between Parallel Plates
Uniform Depth Channel Flow: Problem Solving
General Characteristics of Pipe Flow II
The distance to reach a fully developed flow is called the entrance length and depends on the flow...

