Duct With Flow Control-Aircraft maintenance:

BERNOULLI'S THEOREM

This theorem can be related to the relationship between pressure and velocity existing in the air flowing through a duct, such as a jet engine. The theorem states that the total energy per unit mass is constant for a fluid moving inside a duct and that total energy consists mainly of pressure energy and kinetic energy:
• Pressure energy.
In gas or fluid flow the pressure energy is more often called ‘static pressure' and it can be defined as the pressure that would be felt by a body which was submerged in the medium (gas or fluid) and moving at the same velocity as the medium.

• Kinetic energy.
This kind of energy is more often called ‘dynamic pressure' and this term is used to define the extra pressure created by the movement of the medium. Dynamic pressure is proportional to ½ mass x velocity 2 (ie. ½mv2).
When the medium (gas or fluid) is moving, the total energy = static pressure + dynamic pressure.
Consider a duct which is filled with an incompressible fluid and pressurised from one end by an external force. The other end of the duct is sealed by a valve, which can be opened or closed, and a pressure gauge is fitted into the wall of the duct to indicate the static pressure (PS). With the valve closed, static pressure and total energy are the same. However, when the valve is opened to allow a fluid flow, the circumstances changes and, although the total energy must remain the same, it now consists of static pressure + dynamic pressure. As the velocity V increases, so dynamic pressure increases and the static pressure is reduced.