  We derive a formula for the P\'eclet number ($\mathrm{Pe}$) by estimating the
relative strengths of various terms of the momentum equation. Using direct
numerical simulations in three dimensions we show that in the turbulent regime,
the fluid acceleration is dominated by the pressure gradient, with relatively
small contributions arising from the buoyancy and the viscous term, in the
viscous regime, acceleration is very small due to a balance between the
buoyancy and the viscous term. Our formula for $\mathrm{Pe}$ describes the past
experiments and numerical data quite well. We also show that the ratio of the
nonlinear term and the viscous term is $\mathrm{Re} \mathrm{Ra}^{-0.14}$, where
$\mathrm{Re}$ and $\mathrm{Ra}$ are Reynolds and Rayleigh numbers respectively,
and that the viscous dissipation rate $\epsilon_u = (U^3/d)
\mathrm{Ra}^{-0.21}$, where $U$ is the root mean square velocity and $d$ is the
distance between the two horizontal plates. The aforementioned decrease in
nonlinearity compared to free turbulence arises due to the wall effects.
