  We show the existence of a smooth solution for the flow deformed by the
square root of the scalar curvature multiplied by a positive anisotropic factor
$\psi$ given a strictly convex initial hypersurface in Euclidean space suitably
pinched. We also prove the convergence of rescaled surfaces to a smooth limit
manifold which is a round sphere. In dimension two, it is shown that, with a
volume preserving rescaling, the limit profile satisfies a soliton equation.
