  In this paper we estimate the relative strengths of various terms of the
Rayleigh-B\'enard equations. Based on these estimates and scaling analysis, we
derive a general formula for the large-scale velocity, $U$, or the P\'eclet
number that is applicable for arbitrary Rayleigh number $\mathrm{Ra}$ and
Prandtl number $\mathrm{Pr}$. Our formula fits reasonably well with the earlier
simulation and experimental results. Our analysis also shows that the
wall-bounded convection has enhanced viscous force compared to free turbulence.
We also demonstrate how correlations deviate the Nusselt number scaling from
the theoretical prediction of $\mathrm{Ra}^{1/2}$ to the experimentally
observed scaling of nearly $\mathrm{Ra}^{0.3}$.
