The axisymmetric “best” hopper, its relevance to the plane “best” hopper and “best” hoppers integrated with bins

Abstract The profile shape of the plane “best” hopper has previously been derived [2]. Here the profile shape of the “best” axisymmetric hopper is derived and it indicates limitations to practical hoppers which approximate to the plane configuration. It is shown how a “best” hopper can be smoothly joined with a bin (i.e. vertical-walled) section to achieve a bin-hopper design that will always discharge under gravity.