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When a granular material is freely discharged from a silo through an orifice at its base, the flow rate remains constant throughout the discharge. However, it has been recently shown that, if the discharge is forced by an overweight, the flow rate increases at the final stages of the discharge, in striking contrast to viscous fluids [Madrid et al. Europhys. Lett. (2018)]. {Although the general mechanism that drives this increase in the flow rate has been discussed, there exist yet a number of open questions regarding this phenomenon. One such questions is to what extent is the internal velocity profile affected, beyond the trivial overall increase consistent with the increasing flow rate.} We study via Discrete Element Method simulations the internal velocity profiles during forced silo discharges and compare them with those of free discharges. The changes in velocity profiles are somewhat subtle. Interestingly, during free discharges, while the velocity profiles are steady at the silo base and above a height equivalent to one silo diameter, there exists a transition region where the profile evolves in time, despite the constant flow rate. In contrast, forced discharges present steady profiles at all heights of the granular column during the initial constant flow phase, followed by an overall increase of the velocities when the acceleration phase develops.