This work examines the beneficial role of an unsteady stenosis, operating without the use of any external energy source, as a means for augmenting the flow rate of a valveless pump in a hydraulic loop, including an open tank. In contrast to our previous work that the loop was horizontal, here gravity was taken into account. The stenosis neck cross-sectional area was controlled by the fluid pressure and an opposing force applied externally by a spring of adjustable tension. The pincher compressed and decompressed periodically a part of a flexible tube with frequencies from 5 Hz to 11 Hz and compression ratios Ab from 24% to 65%. The presence of the stenosis increased the net flow rate 19 times for Ab = 24%, and 6.3 times for Ab = 38%, whereas for Ab = 65%, the flow rates were comparable. The volumetric efficiency varied from 30% to 40% under the presence of the stenosis, and from 2% to 20% without the stenosis. The role of the stenosis role was to cause a unidirectional flow, opening during tube compression and closing during decompression. The pressure amplitudes along the flexible tube increased towards the rigid-flexible tube junction (as a result of the wave reflections) which were found to be significantly attenuated by the presence of the stenosis.