## Laminar Flow vs. Turbulent Flow – Calculations and Examples

What is laminar flow and turbulent flow?  Osborne Reynolds popularized this phenomenon with a dimensionless number, Re. This number is the ratio of the inertial forces to the viscous forces.  If the inertial forces are dominant over the viscous forces, the fluid will act in a violent and chaotic manner.  The formula to determine the Reynolds number is as follows:

Equation 1:  Re = V * Dh/u

Re – Reynolds Number (no dimensions)

V – Velocity (Feet/sec or Meters/sec)

Dh – hydraulic diameter (Feet or Meters)

u – Kinematic Viscosity (Feet^2/sec or Meter^2/sec)

The value of Re will determine the state in which the fluid (liquid or gas) will move.  If the Reynolds number, Re, is below 2300, then it is considered laminar (streamline and predictable).  If Re is greater than 4000, then it is considered turbulent (chaotic and disarrayed).  The area between these two numbers is the transitional area where you start to get small eddy currents and velocities in a non-linear direction.  When it comes to effective blowing, cleaning and lower noise levels, laminar flow is optimal.

Let’s do a comparison of Reynolds numbers between the EXAIR Super Air Knife and a blower-type air knife.  Both products are designed to clean and blow off wide areas like conveyor belts.  The EXAIR Super Air Knife is powered by compressed air, and the blower-type air knife is powered by an air blower.  The main difference between the two products is the dimension of the slot opening.  The Super Air Knife has a gap opening of 0.002″ (0.05mm).  It uses the force of the compressed air to “push” it through the small opening to create a strong velocity.  A blower does not generate a high force, so the opening of the blower-type air knife has to be larger to overcome any back pressure the opening creates.  The gap opening is typically 0.5″ (13mm).  From Equation 1 above, the gap opening helps determine the hydraulic diameter, Dh.  The hydraulic diameter is an equivalent tube diameter from a non-circular flow area.  Since both the Super Air Knives and blower-type air knives have rectangular cross sections, the Dh can be calculated as follows:

Equation 2: Dh = 2 * a * b/ (a + b)

Dh – Hydraulic Diameter (feet or meter)

a – Gap Opening (feet or meter)

b – Gap Width (feet or meter)

If we compare for example a standard 12″ wide air knife, we can calculate the hydraulic diameter, Dh, by using Equation 2:

The exit velocity of the Super Air Knives can be changed by regulating the air pressure.  The higher the air pressure, the higher the velocity.  The blower type air knives can use a blower with a variable frequency drive (VFD) to change the exit velocity .  A reasonable air pressure for the Super Air Knife is 80 PSIG, and the exit velocity is near 540 ft/sec (164 m/s).  To equate this to a blower system, the size of the blower will determine the maximum velocity.  To do this comparison, I will use the same velocity as the Super Air Knife.  With the kinematic viscosity of air, it has a value of 0.000164 ft^2/sec (0.000015 m^2/sec) at 70 deg. F (21 deg C).  Now we have all the information for the comparison, and we can now find the Reynolds number from Equation 1:

As you can see from the above calculations, the Super Air Knife has a Reynolds number, Re, below 2300.  The flow characteristic is in the region of laminar (predictable and streamline).  The blower air knife has a Reynolds number, Re, above 4000.  The flow dynamic coming out of the blower-type air knife is turbulent (chaotic and disoriented).  To better show the difference in laminar flow and turbulent flow, I have a picture below that shows both states with water as a fluid (being that air is an invisible fluid).   Here is an example of water  coming out of a drain pipe at Cave Run Lake (first picture below).  With the inertial forces much higher than the viscosity of the water, it is in a turbulent state;  loud and disorderly.  Reynolds number is greater than 4000.  The water is traveling in different directions, even upstream.  As the water flows into the mouth of the river after the channel (second picture below), the waves transform from a violent mess into a quiet, calm stream flowing in the same direction.  This is laminar flow (Re is less than 2300).