T. J. Wilson, C. R. Pfeifer, N. Mesyngier, D. J. Durian
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, by 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 basic scale is set by the product of hole area and the terminal falling speed of isolated grains. But there is a small-hole cut off of about two and half grain diameters, which is larger than an analogous cutoff in the Beverloo equation for dry grains.
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http://arxiv.org/abs/1307.2812
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