Dynamic wetting speeds are limited by the gross entrainment of air between the liquid and the moving substrate. We present experimental data for the curtain-coating method, in which liquid impinges at high speed on the substrate. We also show that air entrainment is strongly affected by macroscopic hydrodynamics and is subject to hysteresis. Using boundary-layer theory, a simple hydrodynamic model is developed for the flow field in the impingement zone away from the dynamic wetting line. The model approximately accounts for the shear thinning of polymer solutions and for the influence of surface tension. We apply the molecular kinetic theory of dynamic wetting, modified to account for hydrodynamic stress, to the immediate vicinity of the wetting line. The main result is a correlation for air-entrainment data. The experimentally calibrated model predicts that the hydrodynamic assist of wetting is greatest when the dynamic wetting line is located beneath the impinging curtain. Flow visualization supports this physical picture.