  We develop a analytical and quantitative theory of the tube model concept for
entangled networks of semiflexible polymers. The absolute value of the tube
diameter L_perp is derived as a function of the polymers' persistence length
l_p and mesh size xi of the network. To leading order we find L_\perp = 0.32
xi^{6/5} l_p^{-1/5}, which is consistent with known asymptotic scaling laws.
Additionally, our theory provides corrections to scaling that account for
finite polymer length effects and are dominated by the mesh size to polymer
length ratio. We support our analytical studies by extensive computer
simulations. These allow to verify assumptions essential to our theoretical
description and provide an excellent agreement with the analytically calculated
tube diameter. Furthermore, we present simulation data for the distribution
function of tube widths in the network.
