The anisotropic flow ($v_n$) in relaitvistic heavy ion collisions arises due to the initial spatial anisotropy ($\varepsilon_n$) of the overlapping zone between the two colliding nuclei. The linear correlation between $\varepsilon_{n}$ and $v_{n}$ for small n is a quantitative measure of the efficiency of conversion of the initial spatial anisotropy to the final momentum anisotropy. We study the collision centrality, transverse momentum ($p_{T}$) and collision energy dependence of this correlation for charged particles using a hydrodynamical model framework. The $p_{T}$ dependent correlation coefficient is found to be strongly dependent on the mass as well as $p_{T}$ of the emitted particles. We also study $p_{T}$ dependent relative fluctuation in anisotropic flow and show that it is sensitive to the value of $\eta/s$ specially in low $p_{T}$ region. In addition, we study the sensitivity of the correlation coefficient to the fluctuation size parameter.