Conservation of Energy
General
This article pertains to fluid energy and uses conservation of energy laws to determine the various dynamics in airside or waterside systems. For the purposes of the PE exam and typical questions encountered on the test, the following equations assume laminar fluid flow, no change in internal energy, no friction losses, and no viscous fluid effects.
The total energy of a fluid in motion consists of “pressure” energy (e.g. fluid static pressure, dynamic pressure), kinetic energy, and potential energy.
Pressure energy is energy added to a fluid when it is compressed i.e. when the fluid passes through a pump. A mass of fluid at a higher pressure has more energy than a mass of fluid at a lower pressure.
It takes energy to accelerate a stationary body. Therefore, a moving mass of fluid has more kinetic energy than a stationary mass of fluid.
It takes work to raise the elevation of a mass of fluid. Therefore, a mass of fluid at a higher elevation has more potential energy than a mass of fluid at a lower elevation.
Description of Variables
Theory
The following equations are used to determine each type of energy, in units of energy per unit mass:
The total energy per unit mass of a fluid is the sum of all three energies listed above:
Conservation of energy states that energy cannot be created or destroyed, only converted from one form of energy to another. Therefore, the energy of a unit mass of fluid at two different instances remains the same. However, the individual components of the total energy (i.e. pressure, kinetic, or potential energy) can change in value. For example, imagine a body of water held back by a dam. Initially, the water is at rest at a certain elevation and has potential energy. If the dam is opened, allowing a pathway for the water to flow, the potential energy is converted into kinetic energy as the water starts to flow. The potential energy decreases while kinetic energy increases, while total energy remains the same.
This concept, where energy remains constant at two different instances, is summarized and is termed Bernoulli’s equation. Again, please remember that this example assumes laminar flow with no changes in energy due to the internal energy of the fluid or frictional losses. This is an idealized case but a common scenario encountered on the PE exam.
Bernoulli’s Equation in Terms of Head
In hydraulics, engineers commonly express the individual energy components in Bernoulli’s equation in terms of head whose units are in feet. This is achieved by multiplying the entire equation by (gravitational constant) / (gravitational acceleration), resulting in the following:
Density, gravitational acceleration, and gravitational constant can be combined to give:
Bernoulli’s equation in terms of head, therefore, may also be presented as:
