  We investigated effects on flow variables of transonic advection-dominated
accretion flows (ADAFs) for different outer boundary locations (BLs) with a
changing energy constant ($E$) of the flow. We used the ADAF solutions and
investigated a general power index rule of a radial bulk velocity $(\vr\propto
r^{-p})$ with different BLs, but the power index with radius for a rotation
velocity and sound speed is unchanged. Here, $p\geq0.5$ is a power index. This
power rule gives two types of self-similar solutions; first, when $p=0.5$ gives
a self-similar solution of a first kind and exists for infinite length, which
has already been discovered for the ADAFs by Narayan \& Yi, and second, when
$p>0.5$ gives a self-similar solution of a second kind and exists for finite
length, which corresponds to our new solutions for the ADAFs. By using this
index rule in fluid equations, we found that the Mach number ($M$) and
advection factor ($\fadv$) vary with the radius when $p>0.5$. The local
energies of the ADAFs and the Keplerian disk are matched very well at the BLs.
So, this theoretical study is supporting a two-zone configuration theory of the
accretion disk, and we also discussed other possible hybrid disk geometries.
The present study can have two main implications with a variation of the $p$;
first, one that can help with the understanding of outflows and non-thermal
spectrum variations in black hole candidates, and second, one that can help
with solving partial differential equations for any sized advective disk.
