at $r_{E}=1 \rm{AU}$ is 2.05 $\times 10^8$  $\mathrm{cm}^{-2}\,\mathrm{s}^{-1}$ [@McComas:etal:2000]. We take the cross sectional area of the coronal hole from @Munro:Jackson:1977 that matches the observed values extremely well, $$A(r)=A_0(\frac{r}{r_0})^2f(r),$$ where the subscript 0 refers to quantities evaluated near the solar surface and $f(r)$ is the area expansion factor which reaches an almost constant value of 7.26 beyond 3 $R_{\odot}$. Therefore, the mean proton flux density mapped to the solar surface in the coronal hole is: $$\frac{2.05\times10^8\times A(\mathrm{r_E})}{A_0}=2.05\times10^8
\times(\frac{\mathrm{r_E}}{r_0})^2\times7.26 \,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}\approx 6.88\times10^{13}
\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}.$$ On the other hand, the electron flux density contributed by plumes are estimated by taking the maximal density in Figure 13 and maximal velocity of 10 $\mathrm{km\,s}^{-1}$, that is, $10^{7.8}\,\mathrm{cm}^{-3} \times 10^6\,\mathrm{cm\,s}^{-1} \approx
6.31 \times 10^{13}\,\mathrm{cm}^{-2}\,\mathrm{s}^{-1}$. Comparing the mean flux density and the flux density from plumes, we find that the former is a little bit higher than the latter, and taking into account the filling factor of plumes in coronal holes of 10 % [@Ahmad:Withbroe:1977], it is unlikely that the plumes investigated in this work are a dominant contributor to the fast solar wind.

We assume that the plume plasma is in hydrostatic balance considering their long lifetime of one or more days and the absence of any 