“Flow is the mass of a substance (gas/fluid etc), that passes a certain point in one second.”
The units are Litres per second.
n = Viscosity in Pa.s Pi = Pi
P = Pressure in Pascals
r = Radius of the tube in meters
l = Length of the tube in question in meters
Elsevier/Mosby Image - Venturi
The Bernoulli principle gives rise to the Venturi effect because of the PRESSURE DROP.
The pressure drop induced by the increase in velocity of a fluid passing through a narrow orifice can be used to entrain air or a nebuliser solution.
The drop in pressure seen here - draws air in.
Reynold’s number attempts to describe the point at which flow changes from laminar to turbulent, and the spectrum in-between.
For numbers <2000, the flow in tube tends to be laminar.
Between 2000 - 4000, a mix of the two
Dr. David Lyness
LAMINAR - This is a flow pattern where all the particles in the fluid follow
the same line of flow (each other). Can be visualised as “sheets” known as streamlines.
i.e.) In cross-section - the fluid at the middle of the cross section is the fastest flowing
TURBULENT - In contrast to laminar flow, the particles in this case are moving in different directions to each other. Like 'smoke rising from a cigarette' - if there isn’t a breeze you can observe the straight plume of smoke rising in a laminar way until it breaks into fluffy turbulent flow some way up.
Laminar flow requires lower pressures for the same flow rate compared with turbulent flow. This means lower energy to get the same work done and if applied to respiration for example, lower work of breathing.
Which explains in part why acute asthmatics have such difficulty breathing.
Flow is directly proportional to the pressure difference & 4th power of the radius.
If pressure goes up the flow increases - pressure bag
The flow increases markedly as the radius increases - big cannulas
Flow is inversely proportional to viscosity and length - (think honey v water)
Viscosity only affects laminar flow, so the density of fluid affects turbulent flow by making it less likely to be turbulent - think of helium in bronchospasm - thus easing work of breathing.
P = Pressure
g = Acceleration due to gravity (m/s2)
h = Height of the tube
p = Density of liquid
v = Velocity of fluid
It's a 'perfect system analogy' --> all the energy is conserved as either pressure energy, potential (or stored) energy, and the energy existing as flow. 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. If you narrow a portion of a tube with an extra tube connected to the narrowing - the volume at the start and end of the tube must be the same- and so the flow in the narrower bit must be faster and can cause the VENTURI effect, because the PRESSURE drops prior to the narrowing.
When we apply the Bernoulli principle in our practice we can ignore the portion due to gravity.
If we confine our thoughts to a horizontal system, the potential energy is the same, so will cancel out mathematically.
Principle in perfume atomisers/water fountains etc
100% oxygen flows into the wider point via a narrow orifice. Because of the narrowing the oxygen speeds up and the pressure drop at that point is below atmospheric pressure and room air is drawn to this low pressure point, hence diluting the 100% oxygen to the calibrated value set by the coloured nozzle.
Any fluid coming into contact with a curved surface will cling to this surface and alter its direction of flow.
You can see this in the spoon diagram - it does so because the solid stationary surface of the spoon slows the layer in immediate contact. This has a drag effect on the other layers, in effect pulling them into the line of the curved surface.