The Physics of Waterfall

Yet another Canada-related physics blog : ) The picture below was taken during our trip to the Biodome de Montreal, which showcases replicas of the four ecosystems of the Americas. It features the Tropical Rain Forest of the South Americas, the Laurentian Forest of the North American Wilderness, the Saint Lawrence Marine Ecosystem, and of course the Polar Regions (Arctic and Antarctic). The picture below is part of the Laurentian Forest and as I saw the waterfall, I was instantly reminded of Physics!

If we consider the pool below as PE = 0, then at the top of the waterfall, there is high potential energy as given by the equation PE = mgh (because the height value is at its greatest). As the water at the top of the waterfall falls below, the water's PE is converted into KE with a high momentum due to the water's velocity and constant accelaration of 9.8 m/s^2. Thus as the water falls, it loses PE and gains KE. Once the water reaches the bottom it undergoes an inelastic collision with the water below and as a result its KE is transformed into other forms of energy. One possible type of energy is mechanical energy when at the bottom, the pool water splashes upwards and outwards and further creates ripples and waves, which carry energy from the waterfall. Furthermore, some of the energy is also converted into the generation of sound, which is a mechanical vibration of the air molecules surrounding the environment. The increased kinetic energy of the air molecules around the waterfall explains why we hear the waterfall "roar". In addition, some of the energy is also converted to thermal / heat energy because of the friction between the falling water and the pool water, which explains why the water at the bottom is warmer than the water at the top.