There are ways to get moving water in a network without demands. One way is to have two or more tanks or reservoirs at different elevations. The head difference drives flow from the higher tank(s)/reservoir(s) to the lower one(s).
Another way is to have a pump that is pumping from low tank(s)/reservoir(s) on the suction side to higher one(s) on the discharge side.
A third way is to have a pump that recirculates flow back to its suction side. This is not common, but years ago I worked with a very complex municipal water system that had this situation as a possibility, though I can't ever remember it happening operationally. The main pressure zone in the system served about 20,000 people. It was divided in two by a bi-directional pumping station. In the winter, all water came in from the east and was pumped to the west to serve the larger population there and to fill a seasonal storage reservoir. In the summer, water still came in the from east, but water was also pulled from the seasonal reservoir to meet the higher overall demand. In the summer, the pumping station would pump either east or west depending on local demands and the need to fill the three main reservoirs (8 MG, 4 MG, and 3 MG, each at a slightly different elevation…I designed the 3 MG steel tank, which was the lowest of the three). Remotely controlled valves were used to control the direction of pumping. There was one large neighborhood near the pumping station that was always on the discharge side of the pumping station, again controlled by valves. There was also a pressure relief back to suction (back to suction by a very long path) in case demands in this neighborhood dropped to very low levels. I don't remember demands ever dropping so low as to open the relief valve, but maybe it did from time to time.
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"Is it the only lesson of history that mankind is unteachable?"
--Winston S. Churchill