Failure of local controllability at time $21/10$ for a shallow-water tank

We consider a one-dimensional tank governed by the normalized Saint--Venant equations, with the tank acceleration as its only control. We show that local exact controllability around the flat equilibrium, with uniformly small classical trajectories in $C^1$, fails at time $T=21/10$. The terminal states form an explicit family tending to equilibrium, and the tank starts and ends with zero velocity and displacement. Thus the sufficiency of every time $T>2$ is false. The proof computes the full quadratic endpoint in a spatial primitive, separates it uniformly from a prescribed terminal profile, and controls the nonlinear error in the same supremum norm. The least time for local controllability is not determined here.