Hydropower (Water Power) Physics

Hydropower Physics

A hydropower resource can be measured according to the amount of available power, or energy per unit time. In large reservoirs, the available power is generally only a function of the hydraulic head and rate of fluid flow. In a reservoir, the head is the height of water in the reservoir relative to its height after discharge. Each unit of water can do an amount of work equal to its weight times the head.

The amount of energy $\, E$ released by lowering an object of mass $\, m$ by a height $\, h$ in a gravitational field is

$\, E = mgh$ where $\, g$ is the acceleration due to gravity.

The energy available to hydroelectric dams is the energy that can be liberated by lowering water in a controlled way. In these situations, the power is related to the mass flow rate.

$\frac{E}{t} = \frac{m}{t}gh$

Substituting $\, P$ for $\frac{E}{t}$ and expressing $\frac{m}{t}$ in terms of the volume of liquid moved per unit time (the rate of fluid flow $\, \phi$ ) and the density of water, we arrive at the usual form of this expression:

$P = \rho\, \phi\, g \, h.$

For $\, P$ in watts, $\, \rho$ is measured in kg/m³, $\,\phi$ is measured in m³/s, $\, g$ (gee) is measured in m/s², and $\, h$ is measured in metres.

Some hydropower systems such as water wheels can draw power from the flow of a body of water without necessarily changing its height. In this case, the available power is the kinetic energy of the flowing water.

$P = \frac{1}{2}\,\rho\,\phi\, v^2$ where $\, v$ is the velocity of the water,

or with $\phi = A\, v$ where A is the area through which the water passes, also

$P = \frac{1}{2}\,\rho\, A\, v^3.$

Over-shot water wheels can efficiently capture both types of energy.

This article is licensed under the GNU Free Documentation License. It uses material from Wikipedia Encyclopedia article "Hydropower"

My Dog Kelly

Site Map ♣ About Us ♣ Patent-Invent ♣ Free Theses, Dissertations & Patents
Comments and inquiries could be addressed to:
webmaster@julianTrubin.com