  It is known that the apparent film flow rate $j_0$ of superfluid $^4$He
increases significantly when the container wall is contaminated by a thin layer
of solid air. However, its microscopic mechanism has not yet been clarified
enough. We have measured $j_0$ under largely different conditions for the
container wall in terms of surface area (0.77-6.15 m$^2$) and surface
morphology using silver fine powders (particle size: $0.10$ \mu m) and porous
glass (pore size: 0.5, 1 \mu m). We could increase $j_0$ by more than two
orders of magnitude compared to non-treated smooth glass walls, where liquid
helium flows down from the bottom of container as a continuous stream rather
than discrete drips. By modeling the surface morphology, we estimated the
effective perimeter of container $L_{\mathrm{eff}}$ and calculated the flow
rate $j~(= j_0L_0/L_{\mathrm{eff}})$, where $L_0$ is the apparent perimeter
without considering the microscopic surface structures. The resultant $j$
values for the various containers are constant each other within a factor of
four, suggesting that the enhancement of $L_{\mathrm{eff}}$ plays a major role
to change $j_0$ to such a huge extent and that the superfluid critical
velocity, $v_{\mathrm{c}}$, does not change appreciably. The measured
temperature dependence of $j$ revealed that $v_{\mathrm{c}}$ values in our
experiments are determined by the vortex depinning model of Schwarz (Phys. Rev.
B $\textbf{31}$, 5782 (1986)) with several nm size pinning sites.
