The concept of position-dependent residence time is revisited, eventually leading to the definition of another diagnostic timescale, tentatively called flushing time. As opposed to the residence time, this timescale is not prescribed to be zero on open boundaries (Dirichlet boundary conditions). Instead, Robin and Neumann boundary conditions are prescribed, with a different treatment of the inlet and the outlet of the domain of interest. In an idealised channel flow, the behaviour of the flushing time is similar to that obtained for a well-mixed reservoir (resp. plug flow) if advection (resp. diffusion) is negligible. The residence time behaves in a markedly different manner for small values of the Peclet number, which may be deemed to be somewhat counterintuitive.