Energy

Energy, an abstract quantity basic to many areas of physics, is a property of a body or physical system that enables it to move against a force. It is an expression of work, which is force applied over a distance. Energy is the amount of work required to move a mass through a distance. Or, it is the amount of work a physical system is capable of doing, in changing from its actual state to some specified reference state.

Many useful concepts of energy exist, the primary one being that, in a closed system, the total energy is constant, the concept of conservation of energy. Water energy is comprised of a number of components, often called head and expressed as a vertical distance. The potential energy of water, or pressure head, is a result of its mass and the Earth’s gravitational pull. The kinetic energy of water is related to its movement and is called the velocity head.

The Bernoulli equation (eq. 9) is an expression of the conservation of energy.

This expression shows the interrelationship of these energy terms, between two cross sections (1 and 2). Each term represents a form of energy, with depth y representing potential energy, the velocity term V representing kinetic energy, and z, a potential energy term relating all to a common datum in a plane perpendicular to the direction of gravity. The head loss or hL term is called a loss because any energy consumed between the two cross sections must be made up for by a change in height (or head). The head loss is the energy consumed by boundary friction, turbulence, eddies, or sediment transport. The velocity term represents velocity head and the depth term the pressure head.

Although energy is a scalar quantity, without direction, the concept of energy as head has an orientation in the direction of gravity. Pressure, however, represents the magnitude of a force in the direction of whatever surface it impinges. So, as a channel slope steepens, the orientation of the pressure head is technically moving further from vertical. It is represented by the depth times the cosine of the slope angle. For most natural channels, the channel slope is sufficiently gradual for this angle to be small enough to be ignored. However, in slopes that are greater than 10 percent, this may become an issue that should be addressed.

Another assumption is that flow is always perpendicular to the cross sections. Finally, alpha (α) in the equation is the energy coefficient, and it varies with the uniformity of velocity vectors in the cross section. For a fairly uniform velocity, alpha may be taken to be one. If velocity varies markedly over the cross section, alpha may go as high as 1.1 in sections of sudden expansion or contraction (Chow 1959).

Specific energy is a particular concept in hydraulics defined as the energy per unit weight of water at a given cross section with respect to the channel bottom.

As shown in figure 2, specific energy can be helpful in visualizing flow states of a stream. The points d1 and d2 are alternate depths for the same energy level. Only one depth exists at the critical state, which is the lowest possible energy level for a given discharge. In natural streams, this is an unstable state since a very 

small change in energy results in a relatively significant undulating change in depth. An understanding of flow energy is fundamental in hydraulic modeling.

The specific energy at any cross section for a channel of small slope (most natural channels) and α = 1 is: