  We systematically study the hyperon global polarization's sensitivity to the
collision systems' initial longitudinal flow velocity in hydrodynamic
simulations. By explicitly imposing local energy-momentum conservation when
mapping the initial collision geometry to macroscopic hydrodynamic fields, we
study the evolution of systems' orbital angular momentum (OAM) and fluid
vorticity. We find that a simultaneous description of the $\Lambda$ hyperons'
global polarization and the slope of pion's directed flow can strongly
constrain the size of longitudinal flow at the beginning of hydrodynamic
evolution. We extract the size of the initial longitudinal flow and the
fraction of orbital angular momentum in the produced QGP fluid as a function of
collision energy with the STAR measurements in the RHIC Beam Energy Scan
program. We find that there is about 100-200 $\hbar$ OAM that remains in the
mid-rapidity fluid at the beginning of hydrodynamic evolution. We further exam
the effects of different hydrodynamic gradients on the spin polarization of
$\Lambda$ and $\bar{\Lambda}$. The gradients of $\mu_B/T$ can change the
ordering between $\Lambda$'s and $\bar{\Lambda}$'s polarization.
