Recent work by MorrIson and Richmond on a theory of granular flow has been used to analyze a bunker system conslstmg of a vetical-aded bm and a wedge or comcally shaped hopper Also, wall fnction has been included m the basic equations and these have been used to design profiles for constant-pressure hoppers as well as to analyze the bunkers mentioned above Usmg average stresses and mass flow rates on any honzontal sectlon, closed-form solutions have been obtamed for wall pressures and maternal velocrtles These are easdy evaluated for gtven matenal and bunker conddlons to determme numerical results, and contam sufficient versattity to provide both analytical and design capablhtles For given bunker geometries and matenal propefies, transrent and steady-state wall-pressure profiles and flow rates can be computed For desued flow rates of gwen materials, bunker geometnes can be calculated The results mclude expresslons for mmunum opemngs and wall slopes to prevent arching, and are sufficiently general to treat dtierent wall-fnction values m the hopper and bm se&Ions Comparisons with avadable experlmental data and previous theoretical results show reasonable agreement, mcludmg the wall-pressure Jump at the transition point from bm to hopper, particularly when test condltlons approximate the restrIctions Imposed by the onedunenslonahty of the solution ' = 1+ sm + โขt b(l+ sm 4) (1 + S*y*Xgbw,,-Q}