Bernoulli Principle - Flow - FRCA Topic

Fluid is the term used to describe a liquid or a gas. In our day-to-day practice, we encounter fluid flow and the consequences of alteration of fluid flow, in the gases and vapours our patients receive and the liquids we administer. Types of flow are important.

The Bernoulli Principle is important if you are to further consider the venturi effect.

“For a non-compressible, non-viscous fluid undergoing laminar flow, the sum of the pressure, kinetic and potential energies per unit volume remains a constant at all points along the line of flow”

• It's about the principle of conservation of energy.
• In a steady flow, the sum of all forms of energy in a fluid in a streamline is the same at all points on that streamline.

• In a fluid that isn't compressible or viscous (or moves at a low Mach number or ratio of flow to sound)

Theoretically,  a perfect system so all the energy is conserved as either pressure energy, potential (or stored) energy, and the energy existing as flow. In concept, no loss of energy through heat caused by friction within the fluid or caused by drag on the tube’s walls is assumed.

This means that if we alter the energy of one portion of the system, it has an effect on the rest of the system. So if the kinetic energy rises, the potential energy and pressure must fall. 

P + 1/2 . p v2 + pgh = constant 

Where: P = Pressure,    g = Acceleration due to gravity (m/s2)      h = Height of tube    p = liquid Density     v = Velocity of fluid
(PV is squared)

In practice, ignore the component due to gravity.  If we confine our thoughts to a horizontal system, the potential energy is the same, so will cancel out mathematically.​

Bernoulli's principle can also be derived directly from Newton's 2nd law. If a small volume of fluid is flowing horizontally from a region of high pressure to a region of low pressure, then there is more pressure behind than in front. This gives a net force on the volume, accelerating it along the streamline.

If using an atomiser for example, if air is passed along a tube with a narrow escape nozzle - an area of low pressure will be created at the nozzle compared to the tube itself. Thus, if a connection dipped in liquid is connected to the tube, it will be drawn up into the tube by the pressure difference. (See video below).