Here there is an approximate solution from Rotter's guide for the economic design of circular metal silos

M(t/s) = 0.6x gamma(kN/m3) x Gf x (B-ks.dp)^2.5/sqrt(g)

with gamma lower characteristic unit weight

Gf is 1.0 or 0.75(1-0.08.cos(beta))/sqrt(sin(beta))

depending on the value beta = hopper half angle. If beta < beta0 then Gf = 1, if beta>beta0 then the former expresion. beta0 is the internal flow channel slope beta0=90-phii, with phii the internal friction angle.

This can be a starting point ■