We consider a hanging cantilevered pipe conveying water within a water-filled container; the upper portion of the pipe is surrounded by a rigid cylindrical tube of larger diameter, forming an annular fluid-filled region around the pipe. Two flow configurations are investigated : (a) water enters the pipe at its clamped end and flows downwards, discharging at its free end into the container; the fluid exits the container by flowing upwards in the annulus and out; (b) the reverse flow arrangement: water enters the system at the upper end of the annulus and exits by flowing upwards in the pipe. The dynamics of the system is studied theoretically and experimentally for both configurations. The analytical models utilized are outlined and the experiments are described. Theory and experiment find that the system loses stability at sufficiently high flow velocity by flutter or static divergence.