Bernoulli’s Theorem

Named after the Swiss physicist who established it. This theorem states that the total sum of the energies in an incompressible fluid flow is constant provided that losses are ignored. The total energy in a fluid flow (liquid or gas) in a pipe/duct system does not change irrespective of whether the speed or the height changes – provided, for a gas, the speed of sound is not approached and there are no losses.

The energies in the system:

• Potential energy or positional energy=pgh
• Kinetic energy=1/2pV2
• Pressure energy=P

Where

• p=density (kg m-3) pronounced (‘rho’)
• g=gravity (9.81ms-2)
• h=height (m) above a specific datum
• v=velocity (ms-1)
• P=static pressure (Pa or Nm-2). The Pa is called Pascal

Potential energy is the energy stored in a mass at some height from a datum. With solids the mass is taken as m (kg) but with fluids it is usually taken as p (density in kg/m3).

Kinetic Energy is the energy that is stored in a moving object.
Formulas: for solids it is ½Mv2
               for fluids it is ½pV2
This is directly related to the density and is related to velocity as the square of the velocity.

Pressure energy is the energy stored as pressure (P)