Numerous experimental and computational studies show that continuous hopper flows of granular materials obey the Beverloo equation that relates the volume flow rate Q and the orifice width Q ∼ (w/σavg - k)β, where σavg is the average particle diameter, kσavg is an offset where Q∼0, the power-law scaling exponent β=d-1/2, and d is the spatial dimension.
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