Hydroelectric power

Hydroelectric power is power derived from moving water sources, and is a renewable energy source. We examine dams in this note.

The principle is fairly simple. Some mass $m$ of water falls down a vertical height $h$, and gravitational potential energy is converted into kinetic energy. We define the volume flow rate $Q$ to find a formula for power.

$$Q=\frac{\Delta V}{\Delta t}$$ $$P=\rho Qgh$$

$\rho$ is the density of water. The implications of this are that hydropower requires large volume flow rates and heights.

Hydropower is free, inexhaustible, and clean. It is, however, dependent on location, requires drastic changes to the environment, and has high initial costs.