Granular discharge rate for submerged hoppers

TL;DR

This study investigates the underwater discharge rate of spherical grains from submerged hoppers, revealing dependence on filling height and a higher cutoff size compared to dry grains, with the rate influenced by grain and hole diameters.

Contribution

It introduces the first measurement of submerged granular discharge rates and identifies key differences from dry grain behavior, including a larger cutoff size and height dependence.

Findings

Discharge rate depends on filling height underwater.

Discharge rate increases as hopper empties.

Small-hole cutoff is about 2.5 grain diameters, larger than dry case.

Abstract

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.