Due to the increasing popularity of additive manufacturing with continuous fibers thermoplastic composites (TPC), this paper investigates the process of in situ impregnation of dry fiber tow with molten thermoplastic resin as a means to reduce material cost. To better understand impregnation with high-viscosity polymer melts, a 1D version of Darcy’s Law is derived along with Gebart’s equations for estimating fiber tow impregnation and permeability. Rheology of the two polymer melts tested, nylon 6/12 and polycarbonate, were measured using a capillary viscometer. The experimental setup consisted of a heated and weighted plunger system to maintain polymer melt pressure in a temperature-controlled pultrusion chamber, through which a dry 3 K carbon fiber tow passes through at a constant velocity for in situ impregnation. The resulting TPC tape was collected on a reel and not used directly for AM. The setup allowed three process variables in Darcy’s equation, i.e. chamber pressure, polymer viscosity (via temperature), and exposure time, to be varied. The degree of impregnation of the thick tape specimens – quantified using digital microscopy and image analysis on polished cross-sections – matched theoretical predictions quite well (average errors of ∼10% for nylon and ∼15% for polycarbonate). However, despite pressures up to 1.2 MPa and exposure times (5.5−15 sec) consistent with current AM system feed rates, the extremely high melt viscosities (290–980 Pa⋅sec) make full impregnation of thick tapes nearly impossible in a practical setting. Improvements to the in situ impregnation process based on experimental results and impregnation models are suggested.