What is the driving force behind the water cycle?
The sun/solar energy is the driving force behind the water cycle.
The driving force for the hydrologic cycle is the sun, which provides the energy needed for evaporation like the flame for a gas stove gives the energy for water to boil water and make steam. Water changes from a liquid state to a gaseous state as it evaporates from the oceans, lakes, streams, and soil. The oceans are where the most water is so that's where most of the evaporation happens.
When the ocean rises and falls in that rhythmic way, we call that the tide. Gravity is the driving force behind the movement of massive amounts of water around the globe on an hour-to-hour basis. The moon, and, to a lesser extent, the sun, are the culprits behind this extraordinary phenomenon. There are some links below for more information.
Solar energy is the driving force of weather on Earth. In the "water cycle", the sun is responsible for evaporation of ocean surface water. As this happens, the water vapor rises. The combination of the Earth's rotation and the changes in atmospheric pressure is the primary determinant for when and where the rain comes down.
Generally when water is used as a source of energy it is either the kinetic energy of the flowing water or the potential energy of the water as it changed height that was used as the energy source. In both cases it is gravity that is the ultimate driving force that makes the water move (for kinetic energy) or is the source of the potential energy - which is recovered as the water moves from…
The clothes have a centripetal force (the walls of the machine provide this) which pushes them towards the center of the tub, not out of it. But the water lacks a centripetal force (it fits through the holes in the walls of the wash tub) to keep it from leaving the path of circular motion, so therefore it follows its path of velocity out!