  As a promising probe for the new physics beyond the standard model of
particle physics in the early Universe, the predictions for the stochastic
gravitational wave background from a cosmological first-order phase transition
heavily rely on the bubble wall velocity determined by the bubble expansion
dynamics. The bubble expansion dynamics is governed by the competition between
the driving force from the effective potential difference and the backreaction
force from a sum of the thermal force and friction force induced by the
temperature jumping and out-of-equilibrium effects across the bubble wall,
respectively. In this paper, we propose a hydrodynamic evaluation on this total
backreaction force for a non-runaway steady-state bubble expansion, which,
after evaluated at the wall interface, exactly reproduces the pressure
difference $\Delta_\mathrm{wall}[(\bar{\gamma}^2-1)w]$ obtained previously from
the junction condition of the total energy-momentum tensor at the wall
interface, where $w$ is the enthalpy and
$\bar{\gamma}\equiv(1-\bar{v}^2)^{-1/2}$ is the Lorentz factor of the
wall-frame fluid velocity $\bar{v}$.
