People of Interest: Daniel Bernoulli

Daniel Bernoulli

Whenever there is a discussion about fluid dynamics, Bernoulli’s equation generally comes up. This equation is unique as it relates flow energy with kinetic energy and potential energy. The formula was mainly linked to non-compressible fluids, but under certain conditions, it can be significant for gas flows as well. My colleague, Tyler Daniel, wrote a blog about the life of Daniel Bernoulli (you can read it HERE). I would like to discuss how he developed the Bernoulli’s equation and how EXAIR uses it to maximize efficiency within your compressed air system.

In 1723, at the age of 23, Daniel moved to Venice, Italy to learn medicine. But, in his heart, he was devoted to mathematics. He started to do some experiments with fluid mechanics where he would measure water flow out of a tank. In his trials, he noticed that when the height of the water in the tank was higher, the water would flow out faster. This relationship between pressure as compared to flow and velocity came to be known as Bernoulli’s principle. “In fluid dynamics, Bernoulli’s principle states that an increase in the speed of fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluids potential energy”1. Thus, the beginning of Bernoulli’s equation.

Bernoulli realized that the sum of kinetic energy, potential energy, and flow energy is a constant during steady flow. He wrote the equation like this:

Equation 1:

Bernoulli’s Equation

Not to get too technical, but you can see the relationship between the velocity squared and the pressure from the equation above. Being that this relationship is a constant along the streamline; when the velocity increases; the pressure has to come down. An example of this is an airplane wing. When the air velocity increases over the top of the wing, the pressure becomes less. Thus, lift is created and the airplane flies.

With equations, there may be limitations. For Bernoulli’s equation, we have to keep in mind that it was initially developed for liquids. And in fluid dynamics, gas like air is also considered to be a fluid. So, if compressed air is within these guidelines, we can relate to the Bernoulli’s principle.

  1. Steady Flow: Since the values are measured along a streamline, we have to make sure that the flow is steady. Reynold’s number is a value to decide laminar and turbulent flow. Laminar flows give smooth velocity lines to make measurements.
  2. Negligible viscous effects: As fluid moves through tubes and pipes, the walls will have friction or a resistance to flow. The surface finish has to be smooth enough; so that, the viscous effects is very small.
  3. No Shafts or blades: Things like fan blades, pumps, and turbines will add energy to the fluid. This will cause turbulent flows and disruptions along the velocity streamline. In order to measure energy points for Bernoulli’s equation, it has to be distant from the machine.
  4. Compressible Flows: With non-compressible fluids, the density is constant. With compressed air, the density changes with pressure and temperature. But, as long as the velocity is below Mach 0.3, the density difference is relatively low and can be used.
  5. Heat Transfer: The ideal gas law shows that temperature will affect the gas density. Since the temperature is measured in absolute conditions, a significant temperature change in heat or cold will be needed to affect the density.
  6. Flow along a streamline: Things like rotational flows or vortices as seen inside Vortex Tubes create an issue in finding an area of measurement within a particle stream of fluid.
Super Air Knife has 40:1 Amplification Ratio

Since we know the criteria to apply Bernoulli’s equation with compressed air, let’s look at an EXAIR Super Air Knife. Blowing compressed air to cool, clean, and dry, EXAIR can do it very efficiently as we use the Bernoulli’s principle to entrain the surrounding air. Following the guidelines above, the Super Air Knife has laminar flow, no viscous effects, no blades or shafts, velocities below Mach 0.3, and linear flow streams. Remember from the equation above, as the velocity increases, the pressure has to decrease. Since high-velocity air exits the opening of a Super Air Knife, a low-pressure area will be created at the exit. We engineer the Super Air Knife to maximize this phenomenon to give an amplification ratio of 40:1. So, for every 1 part of compressed air, the Super Air Knife will bring into the air streamline 40 parts of ambient “free” air. This makes the Super Air Knife one of the most efficient blowing devices on the market. What does that mean for you? It will save you much money by using less compressed air in your pneumatic application.

We use this same principle for other products like the Air Amplifiers, Air Nozzles, and Gen4 Static Eliminators. Daniel Bernoulli was able to find a relationship between velocities and pressures, and EXAIR was able to utilize this to create efficient, safe, and effective compressed air products. To find out how you can use this advantage to save compressed air in your processes, you can contact an Application Engineer at EXAIR. We will be happy to help you.

John Ball
Application Engineer
Email: johnball@exair.com
Twitter: @EXAIR_jb

  1. Wikipedia https://en.wikipedia.org/wiki/Bernoulli%27s_principle

Laminar Flow and Digital Flowmeters: An Explanation On How To Achieve Laminar Flow

When I see turbulent flow vs. laminar flow I vaguely remember my fluid dynamics class at the University of Cincinnati.  A lot of times when one thinks about the flow of a liquid or compressed gas within a pipe they want to believe that it is always going to be laminar flow. This, however, is not true and there is quite a bit of science that goes into this.  Rather than me start with Reynolds number and go through flow within pipes I have found this amazing video from a Mechanical Engineering Professor in California. Luckily for us, they bookmarked some of the major sections. Watch from around the 12:00 mark until around the 20:00 mark. This is the good stuff.

The difference between entrance flow, turbulent flow and laminar flow is shown ideally at around the 20:00 mark.  This length of piping that is required in order to achieve laminar flow is one of the main reasons our Digital Flowmeters are required to be installed within a rigid straight section of pipe that has no fittings or bends for 30 diameters in length of the pipe upstream with 5 diameters of pipe in length downstream.

This is so the meter is able to measure the flow of compressed air at the most accurate location due to the fully developed laminar flow. As long as the pipe is straight and does not change diameter, temperature, or have fittings within it then the mass, velocity, Q value all stay the same.  The only variable that will change is the pressure over the length of the pipe when it is given a considerable length.

Another great visualization of laminar vs. turbulent flow, check out this great video.

 

If you would like to discuss the laminar and turbulent flow please contact an Application Engineer.

Brian Farno
Application Engineer
BrianFarno@EXAIR.com
@EXAIR_BF

1 -Fluid Mechanics: Viscous Flow in Pipes, Laminar Pipe Flow Characteristics (16 of 34) – CPPMechEngTutorials – https://www.youtube.com/watch?v=rQcZIcEa960

2 – Why Laminar Flow is AWESOME – Smarter Every Day 208 – SmarterEveryDay – https://www.youtube.com/watch?v=y7Hyc3MRKno

 

 

Laminar Flow vs. Turbulent Flow – Calculations and Examples

Super Air Knife

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:

Hydraulic Diameter Calculations

 

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:

Reynolds Number Calculation

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).

Turbulent Water from Pipe
Turbulent Water from Pipe

 

From Channel to River
From Channel to River

With the engineered design of the Super Air Knife, the thin slot helps to create that laminar flow.  All the air is moving in the same direction, working together to give a higher force to remove debris.  If you have turbulent flow like that of a blower air knife, the noise level is much higher, and the disoriented forces are less effective in blowing.  Turbulence is useful for mixing, but horrible for trying to clean or wipe a conveyor belt.  If you have any open pipes, drilled pipes or blower-type air knives in your application, you should try an EXAIR product to see the difference.  An Application Engineers can help you take advantage of laminar airflow.

John Ball
Application Engineer
Email: johnball@exair.com
Twitter: @EXAIR_jb