Empirical predictions of discharge rates for dry non-cohesive grains are commonly based on the Beverloo law (Chem Eng Sci 15:260–269, 1961). The present work extends this practical configuration to submerged and cohesive cases to investigate the flow behaviour of granular media with applications in the geophysical process of sinkhole formation. The analysis of the hydrostatic collapse of soil in the presence of underground conduits is performed with a 2D GPU-parallelized simulation coupling the lattice Boltzmann method and the discrete element method to describe the fluid and the solid phases, respectively. The discharge rate of a large submerged granular sample is analysed by varying orifice sizes and inter-particle cohesion strengths. For the submerged cohesionless case, we first study the revisited Beverloo relationship that includes the terminal velocity of a single falling particle in the fluid, proposed in the experimental work of Wilson et al. (Pap Phys 1307: 2812, 2014). We consistently take into account the interstitial fluid with an effective orifice size smaller than in the dry case. Then, the additional contribution of grain cohesion is examined. Our main finding is that the empirical prediction remains valid provided that the orifice cut-off increases with cohesion. Finally, the evolution of fluid pressure during the discharge, at the vicinity of the orifice, is studied and favourably compared with the recent experimental study of Guo et al. (Granul Matter 19(3): 1–8, 2017). By considering the pressure drop around the orifice as a driven-term, we succeed in predicting the solid flow rate with a similar Beverloo approach.