Abstract: In the reverse osmosis pumping system disclosed herein, a pair of work exchange vessels are located at two different heights. By means of a dense working fluid coupling one side of each of the vessels, an increased static head is maintained on one side of the apparatus relative to the static head corresponding to the fluid to be filtered which occupies the other side. The pumping system is operated alternately in low and high pressure phases. During the low pressure phase, the mean height of the dense work fluid is raised and the resultant stored energy is utilized to induce flow through a reverse osmosis membrane unit during the high pressure phase of operation. As it is important that a constant pressure and flow be maintained at the membrane chamber, multiple pumping systems are preferably provided, operating in phase alternation, so that the filter itself may be operated under relatively constant pressure.