The simultaneous flow of the superfluid and normal components of liquid He II through a capillary is studied. The manner in which the two fluids are forced to flow with independently adjustable velocities is described. The temperature and chemical-potential drop over the capillary are measured, from which the pressure drop can be derived. In subcritical as well as in supercritical flow with small vs, the pressure drop equals the Poiseuille pressure drop of the normal fluid, indicating that the normal fluid is not turbulent, but flows laminarly. No pressure drop of the superfluid has been present. The results on the pressure drop are contrary to the results of other experiments, in which an additional pressure drop has been observed.