The core velocity dispersion (CVD) is a potentially useful tool for studying the turbulent velocity field of molecular clouds. CVD is based on centroid velocities of dense gas clumps, thus is less prone to density fluctuation and reflects more directly the cloud velocity field. Prior work demonstrated that the Taurus molecular cloud CVD resembles the well-known Larsons linewidth-size relation of molecular clouds. In this work, we studied the dependence of the CVD on the line-of-sight thickness of molecular clouds, a quantity which cannot be measured by direct means. We produced a simple statistical model of cores within clouds and analyzed the CVD of a variety of hydrodynamical simulations. We show that the relation between the CVD and the 2D projected separation of cores ($L_{2D}$) is sensitive to the cloud thickness. When the cloud is thin, the index of CVD-$L_{2D}$ relation ($gamma$ in the relation CVD$sim L_{2D}^{gamma}$) reflects the underlying energy spectrum ($E(k)sim k^{-beta}$) in that $gammasim(beta-1)/2$. The CVD-$L_{2D}$ relation becomes flatter ($gammato 0$) for thicker clouds. We used this result to constrain the thicknesses of Taurus, Perseus, and Ophiuchus. We conclude that Taurus has a ratio of cloud depth to cloud length smaller than about 1/10-1/8, i.e. it is a sheet. A simple geometric model fit to the linewidth-size relation indicates that the Taurus cloud has a $sim 0.7$ pc line-of-sight dimension. In contrast, Perseus and Ophiuchus are thicker and have ratios of cloud depth to cloud length larger than about 1/10-1/8.
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